Positions


Using Player Won-Lost Records to Compare Players



The basics of how Player won-lost records are constructed and interpreted were discussed in some detail in a separate article. This article looks at how Player won-lost records can be used to compare players. The calculation of wins over positional average (WOPA) and wins over replacement level (WORL) are described in some detail. Following that, I make some comparisons across positions.

I then show a couple of examples of player comparisons. Finally, I discuss the Player Comparison tool available on the front page of this website.

Wins over Positional Average (WOPA)

Player Won-Lost Records are an excellent overall measure of player value. When context and the effects of teammates are controlled for, Player Won-Lost records can also, in my opinion, serve as an excellent starting point for measuring player talent. As a means of comparing players who play different positions, however, raw Player Won-Lost records are not really an ideal comparative tool.

In constructing Player Won-Lost records, all events are measured against expected, or average, results across the event. Because of this, fielding Player Won-Lost records are constructed such that aggregate winning percentages are 0.500 for all fielding positions. Hence, one can say that a shortstop with a defensive winning percentage of 0.475 was a below-average defensive shortstop and a first baseman with a defensive winning percentage of 0.510 was an above-average defensive first baseman, but there is no basis for determining which of these two players was a better fielder – the below-average fielder at the more difficult position or the above-average fielder at the easier position.

From an offensive perspective, batting Player Won-Lost records are constructed by comparing across all batters, not simply batters who share the same fielding position. In the National League, this means that offensive comparisons include pitcher hitting, so that, on average, non-pitcher hitters will be slightly above average in the National League, while, of course, because of the DH rule, the average non-pitcher hitter will define the average in the American League.

These are, in fact, two sides of the same coin. There is a nearly perfect negative correlation between the average offensive production at a defensive position and the importance and/or difficulty associated with playing that position. That is, players at the toughest defensive positions tend to be weaker hitters than players at easier defensive positions.

Bill James used this observation to define what he called the Defensive Spectrum:

1B    –   LF   –   RF   –   3B   –   CF   –   2B   –   SS   –   C


Positions get more difficult/valuable defensively moving left to right (e.g., shortstop is a more defensive position than second base) while offensive production increases moving right to left (e.g., first basemen out-hit left fielders).

When comparing, for example, a left fielder to a shortstop, one has to somehow balance the fact that left fielders are expected to hit better than shortstops against the fact that shortstops are, on average, better defensive players than left fielders.

There are three ways to do this:

(1) One can adjust offensive Player Won-Lost records based on the defensive position of the player,

(2) One can adjust defensive Player Won-Lost records based on the defensive position of the player, or

(3) One can adjust the baseline against which players are measured.
I believe that the best choice is (3), measuring players against different baselines based on the position(s) which they played.

Positional Averages
The table below shows (context-neutral) Player Won-Lost records based on the defensive position of the player for every season for which I have estimated Player won-lost records. Offensive Player Won-Lost records are shown first, followed by overall records. Results here distinguish between DH leagues (the American League since 1973) and non-DH Leagues.

Context-Neutral Player Won-Lost Records by Defensive Position
(Offensive Player Decisions)

DH Leagues Non-DH Leagues
Position Wins Losses Win Pct. Wins Losses Win Pct.
Pinch Hitter 1,296.41,413.90.4784,794.55,279.20.476
Pitcher 2.45.30.3105,398.510,348.00.343
Catcher 6,490.47,028.40.48014,067.014,618.30.490
First Base 8,004.27,301.60.52317,272.315,158.80.533
Second Base 7,159.17,654.70.48315,339.315,904.60.491
Third Base 7,348.47,381.10.49916,123.115,392.30.512
Shortstop 6,699.17,422.50.47414,368.415,578.60.480
Left Field 7,879.57,564.10.51017,372.015,440.90.529
Center Field 7,849.77,779.30.50216,997.415,830.80.518
Right Field 7,872.07,408.00.51517,238.915,416.70.528
Designated Hitter 7,535.67,175.70.5124.43.60.550
Pinch Runner 153.8155.90.497261.6265.60.496
All Non-P Fielders 59,302.359,539.80.499128,778.4123,341.10.511


Context-Neutral Player Won-Lost Records by Defensive Position
(Total Player Decisions)

DH Leagues Non-DH Leagues
Position Wins Losses Win Pct. Wins Losses Win Pct.
Pinch Hitter 1,296.41,413.90.4784,794.55,279.20.476
Pitcher 45,717.945,774.20.50097,786.8102,816.60.487
Catcher 7,596.78,135.90.48316,465.717,020.20.492
First Base 9,455.28,753.40.51920,221.318,106.70.528
Second Base 10,115.510,591.90.48821,430.421,964.10.494
Third Base 9,918.29,951.20.49921,471.720,746.70.509
Shortstop 10,139.610,842.80.48321,618.822,799.80.487
Left Field 11,699.311,380.00.50725,139.523,199.20.520
Center Field 11,364.511,288.10.50224,448.723,273.40.512
Right Field 11,588.311,118.00.51024,831.622,999.80.519
Designated Hitter 7,535.67,175.70.5124.43.60.550
Pinch Runner 153.8155.90.497261.6265.60.496
All Non-P Fielders 81,877.382,061.30.499175,627.7170,110.00.508


A few comments:

(1)    Non-pitchers have an offensive winning percentage about 1.2% higher in the National League than in the American League,

(2)    Designated hitters are above-average hitters, but are comparable hitters to corner outfielders and are slightly worse hitters, on average, than first basemen,

(3)    Pinch hitters are, on average, worse hitters than any other position (other than pitcher, of course). I look a bit more closely at designated hitters and pinch hitters later in this article.

Positional Averages for Non-Pitchers
Comparisons of this nature are based on an implicit expectation that an average player at every position is equally valuable. Over a long enough time period, such as the 60+ years of the "Retrosheet Era", offensive winning percentages tend to follow the defensive spectrum fairly closely, suggesting that such an assumption is probably at least generally reasonable. For specific leagues in specific seasons, however, there may be exceptions. In the 1999 American League, for example, 3 of the 14 teams’ shortstops were Derek Jeter (who batted .349/.438/.552 in 739 plate appearances), Nomar Garciaparra (.357/.418/.603 in 595 PAs), and Alex Rodriguez (.285/.357/.586 in 572 PAs). That same season, the AL Silver Slugger for third basemen went to Dean Palmer, who batted .263/.339/.518 for Detroit. For that particular league-season, AL shortstops actually out-performed AL third basemen in offensive win percentage, 0.4861 - 0.4870. It is perfectly reasonable to think that AL shortstops as a group were “above-average” in the 1999 American League. Another example of this is in the 1950s when centerfielders - led by Willie Mays, Mickey Mantle, Duke Snider, Larry Doby, et al., outhit corner outfielders in several seasons.

One way to ameliorate this problem is to combine the two leagues – American and National – so that individual performances are less important (e.g., 3 shortstops represent only 10% of all starting shortstops in the major leagues as a whole). Before doing this, however, one has to adjust National League non-pitchers’ offensive winning percentages to account for the lack of a DH in these leagues. This produces the following offensive winning percentages:

Context-Neutral Player Won-Lost Records by Defensive Position

Major-League wide: DH-Adjusted
Position Wins Losses Win Pct.
Catcher 20,273.521,930.70.480
First Base 24,927.922,809.10.522
Second Base 22,188.923,868.80.482
Third Base 23,145.823,099.10.501
Shortstop 20,777.623,291.00.471
Left Field 24,900.523,356.00.516
Center Field 24,504.023,953.30.506
Right Field 24,762.723,172.90.517


Ranking them from highest winning percentage to lowest produces the following “defensive spectrum”:

1B    –    RF    –    LF    –    CF    –    3B    –    2B    –    C    –    SS



This is extremely close to Bill James’s defensive spectrum. Third basemen and center fielders are reversed, although the basic conclusion one can draw here is that third basemen and center fielders are both basically average hitters. Shortstops and catchers are also slightly reversed, although, again, the broad conclusion is simply that both positions are populated by relatively poor hitters through major-league history.

Another way to think about these results is to figure out what defensive winning percentage would be needed for each position to have a cumulative 0.500 winning percentage. This is done below.

Implied Defensive Won-Lost Records

Major-League wide: DH-Adjusted
Position Wins Losses Win Pct.
Catcher 4,335.82,678.60.618
First Base 3,340.45,459.20.380
Second Base 9,862.08,182.10.547
Third Base 7,898.17,944.80.499
Shortstop 11,923.09,409.50.559
Left Field 10,808.612,353.10.467
Center Field 10,683.411,234.10.487
Right Field 10,506.212,096.00.465


Is there a way to compare players' defensive value across fielding positions without resorting to comparisons of offensive performance?
One possible way to do so is to compare the performance of a single player at multiple positions. For example, across all seasons for which I have estimated Player won-lost records, players who played both left field and center field within the same season had an average winning percentage of 0.488 in center field and 0.512 in left field. From this, one could reasonably conclude that center field is a more difficult position to play and one could also use this difference as a basis for adjusting these winning percentages to reflect a common base.

Comparisons of this type were done for all of the infield and outfield positions. Pitchers and catchers are not considered here. In the case of pitchers, this is because pitchers virtually never play a different position. This is also true, although to a lesser extent, of catchers. More problematic, however, in the case of catchers, is the fact that the skill set needed to be a good major-league catcher isn’t really the same skill set needed to be a good fielder at any other position (the same is true to a lesser extent, of course, when comparing infielders to outfielders, and, really, is true to at least some extent in every case here).

Average Winning Percentage at Position X
1B 2B 3B SS LF CF RF
1B 0.5280.5170.5430.5030.5040.504
2B 0.4920.4940.4990.4910.4890.488
3B 0.4800.4960.4990.4830.4810.479
SS 0.4870.4910.4910.4890.4840.489
LF 0.4860.5010.4940.5070.5100.501
CF 0.4880.4920.4910.5010.4880.490
RF 0.4800.4960.4890.4960.4930.506


This table is read as follows. For a player who played both first base and second base, the average winning percentage at first base is shown in the top row, 0.528 – this is the average winning percentage of second basemen when they are playing first base. The average winning percentage of first basemen when they are playing second base is shown in the first column, 0.492. In all cases here, average winning percentages are calculated as weighted averages where the weights used are the harmonic mean between the player decisions at the two fielding positions being compared.

The average “normalized” winning percentage for a player at position Y when playing other positions can then be calculated as the weighted average of the numbers down the relevant column. The weights used to calculate these averages were the number of games upon which the comparison was based, which, as noted above, was the harmonic mean of the number of Player decisions accumulated at the two positions being compared.

Doing so produces the following average winning percentages by fielding position:

1B0.484
2B0.496
3B0.495
SS0.500
LF0.491
CF0.506
RF0.496


This says that, on average, a first baseman amasses an average winning percentage of 0.484 at other positions. These numbers are only comparable, however, if we assume that the players being considered here are 0.500 fielders. Averaging across the rows, we can calculate the average winning percentage at first base of players who also played other positions: in this case, 0.510. Doing this for every position produces the following baseline winning percentages by position to which the above percentages should be compared:

1B0.510
2B0.495
3B0.491
SS0.490
LF0.502
CF0.490
RF0.496


The first set of winning percentages are adjusted via the Matchup Formula based on this latter set to ensure a combined winning percentage of 0.500 across all positions. These results are as follows:

1B0.474
2B0.501
3B0.505
SS0.510
LF0.489
CF0.516
RF0.500


In words, if a set of first basemen with an average winning percentage of 0.510 amass an average winning percentage of 0.484 at other positions, then we would expect a set of first basemen with an average winning percentage of 0.500 to amass an average winning percentage of 0.474 at other positions.

Based on these winning percentages, the defensive spectrum looks something like this:

1B    <    LF    <    RF    <    2B    <    3B    <    SS    <    CF

Several aspects of these results are noteworthy. First, the range of winning percentages is quite narrow. Another interesting comparison, I think, is that third base appears to be a tougher position to play than second base. Bill James discusses this in his Win Shares book, where he discusses the historical shift of the defensive spectrum with second base becoming more important than third base over time. As Bill James puts it:

Third basemen need quicker reactions, since they are nearer the batter, and they need a stronger arm, since they are further from first base. Without the double play, third base is obviously the more demanding position.” (Win Shares, p. 183)
The results here confirm this. Second base is, in one sense, the more valuable position, with approximately 14 percent more player decisions accumulated at second base than at third base, a difference which comes entirely from Component 7 (double plays). Yet, comparing how well fielders do when they play both second base and third base in the same season, third base is the more difficult position. Perhaps most interesting is the finding that CF is the most difficult fielding position (not including catchers).

The final table here compares these results with relative Fielding winning percentages implied by average offensive performances by position, which I derived above.

Adjusting Fielding Winning Percentage by Fielding Position
Position Implied by
Relative Fielding
Implied by
Offensive Performance
1B0.4740.380
2B0.5010.547
3B0.5050.499
SS0.5100.559
LF0.4890.467
CF0.5160.487
RF0.5000.465


The most striking difference between relative Fielding winning percentages implied by offensive performances and those based on comparing players who played more than one position is the former results in a much wider spread of implied fielding talent across positions. There are also several differences in the relative difficulty implied by position. Perhaps most strikingly, offensive performances by position imply that middle infielders are much better fielders than center fielders.

So, which methodology produces better results?
For my work, I have chosen to calculate my positional averages based on relative offensive performances by position. I do this for several reasons which, I believe, make this a better choice for my purposes.

First, the mathematics here, attempting to normalize winning percentages across fielding positions, is fairly murky. In contrast, simply setting the positional average equal to the average winning percentage compiled at that position seems to me to be much cleaner and more elegant mathematically.

Second, I believe that limiting the analysis only to players who have played more than one position in the same season, as is done here, may lead to issues of selection bias. That is, we are not looking at the full population of all major-league players here – since most major-league players never played a game at shortstop, for example – or a random sample of major-league players. Instead, we are looking at a selected sample of major-league players, who were selected, in part, on the basis of exactly what we’re attempting to study: with very few exceptions, the only major-league players who are selected to play shortstop are those whose manager thought they were capable of playing a major-league caliber shortstop (and the few exceptions likely only played an inning or two in an emergency situation, so they will be weighted very lightly in the above calculations).

I think that this is probably the primary reason why the winning percentages found here are generally closer to 0.500 than those implied by differences across offensive performances. The players considered here are self-selected for their ability to play multiple positions similarly well. Truly bad players at “offense-first” positions – think Frank Thomas at 1B, Manny Ramirez in LF – are so bad that nobody would ever consider trying to play Frank Thomas at 3B or Manny Ramirez in CF. But, at the other end of the spectrum, great defensive players at “defense-first” positions are so great defensively that, for example, Ozzie Smith never played a single inning of major-league baseball at any defensive position besides SS; Willie Mays never played a corner outfield position until he was 34 years old.

Finally, I believe that setting positional averages based on actual empirical winning percentages is more consistent with what I am attempting to measure with my Player won-lost records. Player won-lost records are a measure of player value. At the bottom-line theoretical level, every team must field a player at all nine positions. If one team has a second baseman that is one win above average and another team has a left fielder who is one win above average, then these two teams will win the same number of games (all other things being equal). Hence, in some sense, not only is it a reasonable assumption to view an average second baseman as equal in value to an average left fielder, it is, in fact, a necessary assumption.

Pitchers
As a general rule, pitchers tend to perform better – lower ERA, more strikeouts, better context-neutral winning percentage – as relief pitchers than as starters. This can be measured in two ways.

First, one can compare the average winning percentage for starting pitchers and relief pitchers. Over the time period for which I have estimated Player won-lost records, starting pitchers compiled an average winning percentage of 0.499, while relief pitchers amassed a 0.501 winning percentage. From this, one could conclude that the positional average for starting pitchers is about 0.001 lower than for relief pitchers.

Such a conclusion would assume, however, that an average starting pitcher is equal in value to an average relief pitcher (on a per-inning basis). This may not be a reasonable assumption. In general, starting pitchers tend to be better pitchers than relief pitchers, particularly than non-closers.

Alternately, one can look at individual pitchers who both started and relieved in the same season. Over the seasons for which I constructed Player won-lost records, a total of 13,474 player-seasons included both starting pitching and relief pitching. Weighting each of these players’ performances by the harmonic mean of their starting and relief pitching Player Decisions, these pitchers compiled a weighted average winning percentage of 0.476 as starting pitchers and 0.496 as relief pitchers. Using the Matchup Formula to re-center these winning percentages around 0.500, the average winning percentage for these pitchers as starters was 0.493 and for these pitchers as relievers was 0.517. Looked at in this way, the positional average for starting pitchers appears to be about 0.024 lower than for relief pitchers.

For my work, I use this latter difference. That is, the positional average for starting pitchers is set about 0.024 lower than the positional average for relief pitchers. Because this gap is wider than the observed gap in the cumulative winning percentage for all starting pitchers vis-à-vis all relief pitchers, the result of this is that starting pitchers are, on average, slightly above-average pitchers, while relief pitchers are, on average, slightly below-average pitchers. I believe that this fairly represents the reality of how pitchers are used in Major-League Baseball.

Positional Averages for Individual Players
Unique positional averages by position are calculated by season. A positional average winning percentage is then constructed for each individual player based on the positions at which the player accumulated his wins and losses. This is done as follows.

1.    Offensive Player Decisions
For offensive player games (wins plus losses), the positional average is the average (DH-adjusted) offensive winning percentage for that position for that season. For games played under NL rules, then, a “pitcher hitting penalty” is added to the positional average. This is equal to the difference in the average winning percentage of non-pitcher position players (i.e., excluding pinch hitters, pinch runners, and designated hitters) in NL games versus the average winning percentage of these players in AL games. As the table above shows, the “pitcher hitting penalty” has been just over 1% on average. The specific penalty used in this calculation is uniquely calculated each year.

For players who accumulated offensive player decisions while playing multiple defensive positions (where, for lack of a better term, I include “pinch hitter”, “pinch runner”, and “designated hitter” as unique “defensive positions”) or who played some games under AL rules and some games under NL rules (so that the “pitcher hitting penalty” is only applied to some of his player decisions), the overall offensive positional average is simply equal to the weighted average of the unique positional averages across positions and across leagues, weighted by the number of player decisions accumulated by position and league.

2.    Pitching Player Decisions
For pitchers, unique positional averages are calculated for starting pitchers and relief pitchers. These averages are calculated by year (with both leagues combined, with no DH-adjustments since an average pitcher is a 0.500 pitcher in both leagues by definition) by looking at pitchers who started and relieved in the same season (for the same team) and comparing average winning percentages of these pitchers as starters and as relievers. These average winning percentages are adjusted to an average 0.500 winning percentage using the Matchup Formula. As noted above, on average, the Positional Average for starting pitchers is around 0.493, while the Positional Average for relief pitchers is around 0.517. These averages vary, however, by year.

3.    Fielding Player Decisions
By construction, cumulative fielding winning percentage will be 0.500 for every defensive position in every league every year. Hence, the Positional Average for fielding player decisions is 0.500 for all players.

Overall Positional Average
The overall Positional Average for a player is then simply a weighted average of his offensive, pitching, and fielding averages where the weights used are the relative offensive, pitching, and fielding decisions compiled by the player.

These Positional Averages form the basis for comparing players across positions, either by comparing players to “average” or to “replacement level”. Positional averages by position by season are shown here.

Wins over Replacement Level (WORL)

Even having calculated Positional Averages to make comparisons possible across positions, a problem still exists in attempting to compare Won-Lost records of different players. This problem is best illustrated by example.

Which player is more valuable: a player who earns a Player Won-Lost record of 5-2 (0.714 winning percentage) or a player who puts up a Won-Lost record of 9-5 (0.667)*? The first player (call him A) has a better winning percentage, but the second player (call him B) has more wins. In this case, the answer is fairly simple: Player B is almost certainly more valuable. His value is basically the same as Player A (5-2) plus the value of another player who went 4-3.
*For simplicity, assume that all of these players played the same position(s) / had the same Positional Average.

Let’s try another one. Which player is more valuable, a player who puts up a Won-Lost record of 9-5 (player B) or a player who puts up a won-lost record of 9-8 (player C)? Again, this one is fairly simple. Clearly, the player who won 9 games with fewer losses is more valuable. Breaking value down, Player C is basically the same as Player B (9-5) plus the value of a player who went 0-3. Notice the logical inference from those last two sentences. If Player C has more value than Player B, then the value of a player who goes 0-3 isn’t zero (otherwise Player C would have the same value as Player B), it’s negative.

Finally, let’s make the problem a little harder. Who’s more valuable, Player A (5-2) or Player C (9-8)? Now the problem gets trickier. Player C has the same value as Player A plus a second player with a Won-Lost record of 4-6 (0.400). Well, how valuable is a 0.400 winning percentage from a player?

The question really is, “how valuable compared to what?” And the answer to that question is, “Compared to what the team’s other alternatives would have been,” which leads nicely to the theory of Replacement Level.

Replacement Level is the level of performance which a team should be able to get from a player who they can find easily on short notice – such as a minor-league call-up or a veteran waiver-wire pickup. The theory here is that major league baseball players only have value to a team above and beyond what the team could get from basically pulling players off the street. That is, there’s no real marginal value to having a third baseman make routine plays that anybody who’s capable of playing third base at the high school or college level could make, since if a major-league team were to lose its starting third baseman, they would fill the position with somebody and that somebody would, in fact, make at least those routine plays at third base. This is similar to the economic concept of Opportunity Cost.

Replacement Level
For my work, I define Replacement Level as equal to a winning percentage one weighted standard deviation below Positional Average, with separate standard deviations calculated for pitchers and non-pitchers. Unique standard deviations are calculated in this way for each year. These standard deviations are then applied to the unique Positional Averages of each individual player. Overall, this works out to an average Replacement Level of about 0.454 (0.463 for non-pitchers, and 0.439 for pitchers). A team of 0.454 players would have an expected winning percentage of 0.362 (59 - 103 over a 162-game season). The derivation of my choice of Replacement Level is described next.

Derivation of Replacement Level

Hitting versus Fielding

Some analysts distinguish between replacement-level hitting – the level of hitting that could be found from freely-available talent – and replacement-level fielding – the level of fielding that could be found amongst freely-available talent. The problem with this is that, except for designated hitters, a team can’t actually replace a player’s hitting and a player’s fielding independent of one another. In fact, in many cases, it’s quite reasonable to think of situations where a player’s replacement is actually better than the player he is replacing at either hitting or fielding, but is nevertheless a worse overall player. Instead, a team must make a tradeoff and settle for the replacement player who provides the best combination of hitting and fielding. Hence, in my opinion, it only makes sense to talk about replacement level at an overall level, taking into account all aspects of a player’s game: batting, baserunning, fielding, and, if appropriate, pitching.

Replacement Level by Position

Some analysts also argue that replacement level differs by position – that is, one should calculate the replacement level for first basemen differently from the replacement level for second basemen. This seems to me to be a more reasonable position and is certainly worth investigating. On the other hand, the pool of replacement third basemen is likely to overlap considerably with the pool of replacement shortstops, for example, and any possible replacement starting pitcher is likely to also be a replacement relief pitcher. Certainly, however, at a minimum, the pool of replacement non-pitchers will be distinct from the pool of replacement pitchers.

I will begin by investigating all players to get a sense of where a general Replacement Level might be. From there, I will investigate Replacement Level by position.

Replacement Player Winning Percentages
So, how does one go about determining Replacement Level? The first step, it seems to me, would be to define precisely what is meant by Replacement Level. The most obvious definition of Replacement Level to me, or, perhaps more precisely, the definition of Replacement Level which leads most obviously to a means of measuring it, would be the average winning percentage of marginal major-league baseball players.

Over the entire Retrosheet Era, there have been a total of 1,850 team seasons and 73,422 player-seasons* for which the player accumulated a non-zero number of player decisions.
*A player-season is defined as a unique player-season-team combination, so, for example, Aramis Ramirez’s 2003 performance with the Pittsburgh Pirates and Ramirez’s 2003 performance with the Chicago Cubs are treated as two distinct player-seasons.

I sorted these 73,422 player-seasons by total basic player games (wins plus losses). The total number of games ranged from a high of 48.0 for Mickey Lolich for the 1971 Detroit Tigers to a low of 0.00008 for Walt McKeel for the 1996 Boston Red Sox.*
*Actually, 15 players have appeared in a game but amassed exactly zero Player decisions during a player-season during the Retrosheet Era. This was done most recently by Charlton Jimerson in 2005, who played one inning in CF for the Houston Astros. Of course, his performance, such as it was, becomes wholly irrelevant to the results presented here.

As noted above, there have been 1,850 team-seasons over the Retrosheet Era. That works out to a total of 46,250 major-league roster spots available over this time period (1,850 teams times 25 roster spots per team). So, one could view the top 46,250 player-seasons over this time period as being “roster-level” player-seasons and the remaining 27,172 player-seasons (15 per team) as being “replacement-level” player-seasons.

Sorting by total Player games (wins plus losses), the aggregate adjusted winning percentage* for “roster-level” players was 0.504, and the aggregate winning percentage for “replacement-level” player seasons was 0.452, with “roster-level” players accounting for 94.6% of all Player decisions when measured in this way. This would imply a Replacement Level approximately 5.1% below Positional Average.
*As I explained above, a .500 winning percentage by a first baseman isn’t strictly comparable to a .500 winning percentage by a shortstop. To account for that, I adjusted player winning percentages here; adjusted winning percentage is equal to the player’s winning percentage plus (0.500 – the player’s positional average).

Is this really the best way to measure Replacement Level? Conceptually, I think that it is. The question, however, is where to draw the line between “roster-level” and “replacement-level”. Drawing the line at 25 players per team makes some obvious sense, of course, as (before September 1st) there are 25 roster spots per team. Of course, no team uses only 25 players in a single season. On average, for the seasons for which I have calculated Player won-lost records, the average major-league team played 39.7 players per season (which is quite a bit higher than I would have guessed). Given that, how much difference is there between, say, the 23rd player on a typical team and the 28th player on a typical team?

The table below sets out to answer that very question. The winning percentages shown here are the aggregate winning percentage for all players who ranked at a given roster level as well as the aggregate winning percentage for all players who ranked below the given roster level. For example, the top 16,650 players in terms of Player Games would constitute roster spots 1 – 9 (1,850 teams times 9 roster spots = 16,650). These players posted an aggregate winning percentage of 0.513, while players who occupied roster spots 10 – 40 posted an aggregate winning percentage of 0.484. The cumulative percentage of team games is also shown for those who occupied roster spots 1 through the particular roster spot(s) shown.

Winning Percentage Cumulative % of
Roster Spot at Roster Spot below Roster Spot Total Games
1-9 0.5130.48458.0%
100.4980.48262.3%
110.4940.48166.2%
120.4920.47969.7%
130.4920.47873.0%
140.4890.47775.9%
150.4870.47578.5%
160.4860.47480.8%
170.4860.47383.0%
180.4860.47184.9%
190.4830.46986.7%
200.4840.46788.4%
210.4830.46589.9%
220.4840.46291.2%
230.4800.45992.5%
240.4790.45593.6%
250.4720.45294.6%
260.4690.44995.5%
270.4640.44696.3%
280.4640.44297.0%
290.4580.43897.6%
300.4520.43498.1%
310.4500.42998.5%
320.4420.42598.9%
330.4390.42099.2%
340.4310.41599.4%
350.4300.40799.6%
360.4200.39899.8%
370.4080.39099.9%
380.3960.380100.0%
390.3860.352100.0%
400.352-0.5440.0%


So what exactly do all of these numbers really mean and how do they help us calculate Replacement Level? Well, the first thing to notice, which shouldn’t be too surprising is that, in general, average winning percentages decline as one works one’s way deeper into the roster. In fact, looking at the column showing the aggregate winning percentage for players below a given roster level, this value declines uniformly through the entire table. In terms of winning percentage by roster spot, the trend is slightly less perfect, but is still fairly clear nevertheless, particularly for the second half of the table.

Looking at the above table, is there any obvious break-point where the data seem to indicate that below a certain roster spot players are “replacement-level”? To me, the answer is “Sort of.”

Below the first 12 or so roster spots, roster spots 13 – 23 hover just below 0.500, in a relatively narrow range between 0.480 and 0.492. Changes in winning percentage by roster spot are somewhat erratic in this area of the roster, suggesting that differences in player decisions at this level are the result of differences in decisions earned across positions moreso than differences in the quality of the players occupying the various spots (e.g., outfielders tend to earn more decisions than infielders even though there’s no reason to think that outfielders are better players than infielders on average). This might suggest that, in fact, setting “replacement level” as the level just below roster spot 23 - which ends up being very close to just off the 25-man roster - may have some merit. If players at roster spots below 23 are viewed as “replacement-level”, this would put replacement level at approximately 0.459. Another possibility could be three positions lower as roster spots 25 and 26 appear fairly interchangeable, with a more pronounced downward trend starting at row 27. Setting replacement level below roster spot 26 would put replacement level at approximately 0.449.

This ends up being fairly close to the result setting replacement level one standard deviation below Positional Average, 0.454.
Winning Percentages by Position
I noted above that some people like to calculate unique Replacement Levels by position. This is an idea worth at least examining.

To do so, I looked at what a one-standard-deviation standard would imply regarding unique replacement levels by player position. Standard deviations for winning percentage by position are shown below calculated in two ways. The numbers on the left were calculated based on basic context-neutral, teammate-adjusted records. The numbers on the right also incorporate Expected Team Win Adjustments.

Standard Deviations for Positional Winning Percentages
Position Raw Wins Adjusted Wins
C 4.7%4.9%
1B 4.7%4.9%
2B 3.8%4.0%
3B 4.3%4.5%
SS 3.7%3.9%
LF 4.5%4.6%
CF 4.0%4.2%
RF 4.2%4.4%
DH 7.2%7.3%
PH 15.6%15.6%
PR 26.4%26.5%
Pitcher (Offense) 10.9%11.1%
Starting Pitcher 4.4%5.3%
Relief Pitcher 6.7%7.1%


A few comments about this table. First, the positions of DH, PH, PR, and pitcher offense give somewhat odd results that don’t necessarily make a lot of sense and are likely plagued to some extent by small-sample problems, even over the 60+ year time period considered here.

The other problem with PH, PR, and pitcher offense, I think, is that the correlation between winning percentage and total games is likely weaker for these positions, especially pitcher offense, than for other positions. That is, better catchers will catch more games, which will serve to reduce the weighted standard deviation of catcher winning percentage. Pitchers, on the other hand, are chosen almost exclusively for their pitching ability, not their hitting ability. As a result, there is likely to be very little correlation between the number of batting decisions earned by a pitcher and his hitting ability. The same is probably due, albeit to a lesser extent, for pinch hitting and pinch running. In many cases, a team's best pinch-hitting option on a particular day will be the best-hitting regular who has the day off, but, for any given regular, the number of times when that will be him will be very small; if he had too many days off, he'd no longer be a regular.

Excluding these positions, the results are actually quite stable across positions. For non-pitchers at fielding positions, the standard deviation for basic wins averages out to 3.9%, with a fairly narrow range across positions (3.7% - 4.7%). For pitchers, the standard deviation for basic wins averages out to 4.6%.

The gap between the standard deviations for position players and pitchers is even greater when expected intra-game win adjustments are taken into consideration. As I explain elsewhere, expected team win adjustments adjust for the fact that player differences from .500 will tend to have an exaggerated impact on leading to team wins; the reverse is true of below-average players as well. Being a little bit better than average has a multiplicative impact on a team's winning percentage. Because of this effect, when one adjusts basic player winning percentages for this expected team win adjustment, this will have the effect of increasing the spread of player winning percentages: player winning percentages above 0.500 will move farther above 0.500, while player winning percentages below 0.500 will move farther below 0.500. As a result, the standard deviation of player winning percentages is greater when expected team win adjustments are accounted for.

This effect of players on team wins is stronger for pitchers than it is for non-pitchers, because pitchers concentrate their performance into fewer team games. Adding, for example 0.3 player wins in one game will have more of an impact on a team than adding 0.1 player wins in each of three separate games. Because of this, when one incorporates expected team win adjustments for pitchers, especially starting pitchers, this has a much more significant impact on their standard deviation - which rises from 4.4% to 5.3% - than is the case for non-pitchers.

Overall, non-pitcher fielders see their average standard deviation increase from 3.9% to 4.1%. Pitchers, on the other hand, see their average standard deviation increase of 4.6% to 5.3%. This increased separation in the standard deviations of winning percentages for pitchers and non-pitchers further strengthens my decision to calculate separate standard deviations for these two groups.

Even with these adjustments, the differences in standard deviation across fielding positions, however, are still very narrow - ranging from 3.9% to 4.9%. Because of this, I have chosen to calculate a single standard deviation for calculating Replacement Levels for all non-pitchers.

Final Results
Putting all of this together, these results lead to my final decision to set Replacement Level at one standard deviation below Positional Average with standard deviations calculated separately for non-pitchers and pitchers. Over the Retrosheet era as a whole, this works out to an average Replacement Level for non-pitchers of 0.463, and for pitchers of 0.439. Going back to the table by roster level, this puts Replacement Level at about the level of players below the 27th-best player on an average major-league roster, with Replacement-Level players accounting for maybe 4% of all Player decisions.

Combining these, a team of replacement-level players would have an expected winning percentage of around 0.362 (59 - 103 over a 162-game season).

For an individual player, Wins over Replacement Level (pWORL, eWORL) are equal to Player Wins minus (Player Decisions times Replacement Level). I compare my wins over replacement level (WORL) to Baseball-Reference's Wins above Replacement Level (WAR) in a separate article.

Wins vs. WOPA vs. WORL

The choice by an analyst between Wins, WOPA, and WORL will likely depend on exactly what one is looking for. And there's no reason to limit oneself to just one of these three. To help with this, I've created a page that allows one to create a customized statistic using whatever weights one would like.

I look briefly next at a few possible sets of weights that might have some appeal.

Replicating WAR
Probably the most popular "uber-stat" for measuring baseball players' value is Wins above Replacement (WAR). Measures of WAR are presented on player pages at both Baseball-Reference.com as well as at Fangraphs.com. I compare my eWORL to Baseball-Reference's version of WAR in a separate article.

WAR are built up from net wins while WORL are built up from wins over 0.500. I discuss the difference between these two concepts in a separate article. Basically, a 20-10 record is 10 net wins (20 minus 10) but 5 wins over 0.500 (15-15), so net wins are double the magnitude of wins over 0.500. WAR and WORL agree, however, in their calculation of the number of wins between average and replacement (what Baseball-Reference calls Rrep (replacement runs). Putting it into formula form,

WAR = (Net Wins over Average) + Wrep
WORL = WOPA + Wrep

where Wrep is Rrep, converted to wins (replacement wins).

(Net Wins over Average) is basically two times WOPA (which is basically wins over 0.500). From the second equation, we get that Wrep is equal to (WORL - WOPA). Plugging these two facts into the first equation, then, we can express WAR as a function WOPA and WORL as follows:

WAR = 2*WOPA + (WORL - WOPA) = WOPA + WORL

Hence, one can calculate the pWin or eWin-based equivalent of WAR by adding WOPA plus WORL. The top 100 players in career (eWOPA + eWORL) for the years over which I have calculated Player won-lost records (1934 - 2013) are shown below.

Top 100 Players in (eWOPA + eWORL)
Player eWins eLosses eWOPA eWORL eWOPA+
eWORL
Barry Bonds452.8309.658.588.6147.1
Roger Clemens318.4234.648.076.5124.5
Mickey Mantle354.4233.749.374.7124.0
Greg Maddux332.2270.746.675.2121.8
Willie Mays436.7323.244.176.9121.0
Joe L. Morgan360.5284.045.572.7118.3
Hank Aaron475.9360.339.376.0115.3
Warren Spahn341.5288.339.268.0107.2
Alex Rodriguez343.3271.540.965.1105.9
Mike Schmidt334.2241.339.662.8102.4
Ted Williams292.7190.739.661.3100.8
Frank Robinson389.5291.633.263.796.9
Randy 'Big Unit' Johnson273.1224.532.557.890.3
Carl Yastrzemski447.5363.426.362.488.7
Rickey Henderson423.1350.228.559.788.2
Gaylord Perry327.6287.029.458.387.7
Stan Musial342.7257.030.557.087.4
Tom Seaver303.4267.529.755.184.7
Eddie Mathews303.9232.730.053.183.1
Reggie Jackson356.4284.026.455.581.9
Mike Mussina226.6175.729.451.180.5
Cal Ripken366.6339.726.053.879.9
J. Kevin Brown212.9165.130.249.379.5
Harmon Killebrew301.7222.227.550.878.4
Bob Gibson258.6225.127.749.677.3
Pedro J. Martinez185.1135.830.247.077.2
Al Kaline377.3302.523.353.376.6
Tom Glavine288.8267.725.051.676.6
Tommy John290.8257.325.250.775.9
Robin Roberts306.7283.023.050.373.3
Chipper Jones313.2251.425.447.572.9
Ken Griffey Jr.345.6292.823.649.072.6
Jim Thome267.2201.625.347.272.5
Don Sutton321.5300.422.150.272.3
Duke Snider280.1213.025.046.671.6
Bobby Grich249.3210.726.245.171.3
Pee Wee Reese281.7244.823.547.671.1
John Smoltz225.0193.525.345.771.0
Derek Jeter333.7307.522.847.770.5
Bert Blyleven301.4271.321.548.870.4
Frank E. Thomas248.1184.823.746.370.0
Albert Pujols258.9186.526.043.569.5
Manny Ramirez304.0244.323.346.169.4
Dwight Evans334.7277.321.747.268.9
Steve Carlton328.8318.119.748.167.8
Ron Santo290.6236.722.445.367.7
Curt Schilling209.2177.024.143.667.7
Carlton Fisk248.4212.123.842.966.8
Juan Marichal227.8200.223.442.766.2
Lou Whitaker283.4252.722.143.465.5
Willie Stargell288.6220.521.843.765.5
Robin Yount357.0338.118.646.665.3
Johnny Bench237.4190.523.541.665.2
George Brett324.1277.219.545.264.7
Jim Palmer236.2202.521.942.864.7
Willie McCovey278.6206.521.742.864.5
Barry Larkin272.3238.422.142.264.2
Alan Trammell273.3254.921.442.563.9
Tim Hudson182.8149.323.640.363.9
Larry Walker275.5213.721.841.463.1
Gary Sheffield333.5279.318.744.062.7
Billy Williams342.2279.417.344.962.2
Andy Pettitte212.1181.420.541.461.9
Joe DiMaggio206.4151.022.539.361.8
Darrell Evans303.0249.918.942.361.2
Ernie Banks300.6256.318.542.561.0
Ryne Sandberg283.7245.220.040.560.4
Roy Halladay174.7140.021.938.360.2
Jim Kaat285.2271.716.742.859.5
Wade Boggs291.5253.218.940.559.4
Jim Edmonds250.8206.420.138.358.5
Toby Harrah255.8227.419.239.058.2
Edgar Martinez208.6164.318.739.558.2
Nolan Ryan328.1318.314.044.258.2
Whitey Ford208.0184.419.838.057.8
Jeff Bagwell266.3198.719.538.157.6
Early Wynn255.7240.417.340.257.5
Mark McGwire212.6152.321.435.757.1
Dick Allen230.9173.919.737.156.8
Bret Saberhagen161.3125.521.235.556.7
Jackie Robinson186.8141.421.035.356.3
C.C. Sabathia176.5145.119.636.656.2
Reggie Smith269.4216.717.738.556.2
Craig Biggio340.6312.115.140.755.8
Mike Piazza199.5164.220.335.455.7
Paul Molitor305.3272.614.041.555.5
Jimmy Wynn268.8218.917.238.355.5
Fred Lynn255.1214.618.237.255.4
Yogi Berra216.3181.418.836.255.0
Orel Hershiser200.5180.518.536.655.0
Bobby Bonds266.5215.617.137.955.0
Carlos Beltran279.3238.917.137.254.3
Roberto Alomar289.9266.116.138.154.1
Bob Lemon189.5166.418.335.153.4
Claude Osteen219.9204.216.736.152.8
Rod Carew290.9260.914.537.952.4
Gary Carter237.6205.217.235.052.2
Sammy Sosa317.4268.614.238.052.2
Todd Helton261.5201.217.135.052.0
Dave Winfield375.8333.311.140.952.0


Changing Replacement Level
It may be the case that somebody doesn't like my choice for replacement level. One could approximate an alternate replacement level by weighting Wins, WOPA, and/or WORL.

As I mentioned above, my replacement level works out to around 0.450. Wins over positional average (WOPA) works out to 0.500 on average. Knowing this, we can make two general statements:

(1)WORL - WOPA=.050*(Player Decisions)
(2)Wins - WORL=.450*(Player Decisions)


Suppose you wanted to set replacement level at 0.480. You want to add 0.020*(Player Decisions) to WOPA, or, from (1) above: 0.4*(WORL - WOPA), i.e.,

Wins over 0.480 = WOPA + 0.4*(WORL - WOPA) = 0.6*WOPA + 0.4*WORL



Suppose you wanted to set replacement level at 0.350. You want to add 0.100*(Player Decisions) to WORL, or, from (2) above: (.1/.45)*(Wins - WORL), i.e.,

Wins over 0.350 = WORL + (2/9)*(Wins - WORL) = (7/9)*WORL + (2/9)*Wins

Some Analyses of Player Positions

Differences in Career Values by Position
In addition to differences in winning percentages across positions, there are also differences in the raw number of wins (and losses) earned by players depending on the position they play. The next table shows the distribution of Player decisions (pWins, pLosses) by player position. It also shows the distribution of Player wins over replacement level (pWORL).


Position
Total Decisions
pWins + pLosses

pWORL
Catcher 4.2%4.0%
First Base 7.4%7.0%
Second Base 8.8%8.1%
Third Base 8.5%7.9%
Shortstop 9.5%8.8%
Left Field 10.3%8.8%
Center Field 10.8%9.0%
Right Field 10.5%9.0%
Designated Hitter 1.7%2.0%
Pinch Hitter 0.9%0.5%
Pinch Runner 0.1%0.0%
Pitcher Offense 1.8%2.5%
Starting Pitcher 22.0%28.3%
Relief Pitcher 3.6%4.2%


What Do These Numbers Mean?
So, what do these numbers mean? Focusing only on non-pitcher fielding positions, the first thing that I notice is that the distribution of pWORL is fairly uniform across fielding positions - ranging between 8.8% and 9.5% of total pWORL - with two exceptions: Firstbasemen, who earn 7.0% of all pWORL, and Catchers, who earn 4.0% of all pWORL.

In theory, one might think that every (non-pitcher fielding) position should be equally valuable. All fielding positions have to be filled at all times on defense, and every fielding position must take its place in the lineup. On the other hand, it makes sense that weaker-hitting positions might earn fewer offensive player decisions as players at these positions (C, 2B, SS) will be more likely to hit lower in the lineup and be pinch-hit for more often. On the defensive side, outfielders and middle infielders field more balls than corner infielders and catchers, and hence accumulate more fielding decisions.

The position for which both of these factors work against it, of course, is catchers, who tend to be poor hitters who therefore bat lower in the lineup and are pinch-hit for more often, but who also handle very few defensive plays.

One could, perhaps, make some adjustments to player value based on the above table, if one were so inclined. Personally, I am not so inclined.

Relationship between Player Position and Career Length
When evaluating a player's career, it can be important to put career length into perspective. One thing that can affect the length of a player's career is what position(s) he played. The table below shows the distribution of pWORL by player position for three sets of players: everybody for whom Player won-lost records have been calculated, the top 100 players in career pWORL, and the top 1,000 players in career pWORL.

Position Total WORL Top 100 Players Top 1000 Players
Catcher 4.0%2.8%3.3%
First Base 7.0%7.2%7.5%
Second Base 8.1%7.2%7.7%
Third Base 7.9%8.7%8.3%
Shortstop 8.8%8.6%9.4%
Left Field 8.8%9.8%9.0%
Center Field 9.0%10.7%9.3%
Right Field 9.0%8.3%9.5%
Designated Hitter 2.0%3.4%2.4%
Pinch Hitter 0.5%0.3%0.4%
Pinch Runner 0.0%0.0%0.0%
Pitcher Offense 2.5%2.6%2.4%
Starting Pitcher 28.3%29.6%28.7%
Relief Pitcher 4.2%0.7%2.1%


Looking at the top 100 players, the two positions which appear to be the most under-represented are catcher (2.8%) and relief pitcher (0.7%). In fact, there are no players in the top 100 in career pWORL who were exclusively relief pitchers (Dennis Eckersley clocks in at number 74, although his top 3 seasons in pWORL were 1977, 1978, and 1979, when he was still a starting pitcher; Mariano Rivera's 42.5 place him 73rd).

The two positions which appear to perhaps be over-represented in the top 100 are third base (8.7%) and shortstop (8.6%). By my count, the top 100 players in pWORL include 9 third basemen, 11 shortstops, and Alex Rodriguez, who could go into either group. The list also includes several players who played some 3B early in their career before moving to 1B (Harmon Killebrew, Jim Thome, Tony Perez, et al.). This all could suggest that thirdbasemen and/or shortstops are perhaps over-valued in terms of career pWORL. Or it could simply be due to the relatively small sample size of 100 players.

To get a somewhat larger sample size, while still focusing on the best and longest overall careers, I also look at the top 1,000 players in career pWORL in the above table. My choice of the number 1,000 was somewhat arbitrary, but was chosen with the idea that it should capture the vast majority of players who have amassed worthwhile careers over the past 60 years.

Extending out to the top 1,000 players, shortstops and (especially) third basemen are no longer remarkable. Catchers are still somewhat under-represented in the top 1,000 list (3.3%), although less than in the top 100 list. The largest under-representation remains relief pitchers (2.1%)
Weighting Player Value by Position(s) Played
I have created a page which allows a user to enter their own weights and thereby create their own personalized ranking of players for whom I have estimated Player won-lost records. One of the weighting options offered on that page are to assign different weights to players based on the position(s) they played.

The default weights used on that page were chosen by me as follows. First, I set aside non-fielding positions - DH, PH, PR, and Pitcher Offense. The default weights for all of these are set equal to one (although the page allows one to vary these weights as well, if desired - heck, you could even zero out all DH games if you hate the designated hitter enough). Next, I re-calculated the percentages above so that they summed to 100% for the remaining positions.

The resulting percentages are shown in the table below.

Position Total WORL Top 1000 Players
Catcher 4.2%3.5%
First Base 7.3%7.9%
Second Base 8.6%8.1%
Third Base 8.3%8.8%
Shortstop 9.2%9.9%
Left Field 9.2%9.5%
Center Field 9.4%9.9%
Right Field 9.4%10.0%
Starting Pitcher 29.8%30.3%
Relief Pitcher 4.4%2.2%


Using the numbers in the first column (total pWORL by position) as benchmarks, I then divided both columns by the corresponding benchmark for each position. Note that doing so makes the first column (pWORL) exactly equal to one for every position, by construction. The results are shown in the next table. The last column is just a simple average of the previous two columns.

Position pWORL Top 1000 Average
Catcher 11.2041.102
First Base 10.9310.965
Second Base 11.0531.026
Third Base 10.9520.976
Shortstop 10.9350.967
Left Field 10.9710.986
Center Field 10.9580.979
Right Field 10.9450.973
Starting Pitcher 10.9830.992
Relief Pitcher 11.9921.496


Basically, there are two numbers here that strike me as noteworthy: catchers and relief pitchers. For the customized leaders page, I use the numbers in the last column for these two categories: 1.10 for catchers and 1.50 for relief pitchers. The default weights for all other positions are set exactly equal to one. Of course, these weights are all customizable, so you can feel free to set these weights however you'd like on this page.
Hitting Positions vs. Fielding Positions
One way to compare Player Won-Lost records across defensive positions is to normalize Fielding Winning Percentages so that they are based around a 0.500 average across all defensive positions, as opposed to being based around a 0.500 average at each individual position. Doing this earlier in this article produced the following normalized winning percentage for average fielders by fielding position, excluding pitchers and catchers:

1B 0.474
2B 0.501
3B 0.505
SS 0.510
LF 0.489
CF 0.516
RF 0.500



Combining these results with average offensive winning percentages by position yields the following average winning percentages by defensive position:

1B 0.521
2B 0.492
3B 0.507
SS 0.488
LF 0.512
CF 0.514
RF 0.516



Looking at total player game points by position for non-catchers reveals an interesting contrast. First basemen and outfielders turn out to be better than 0.500 on average (0.515 to be exact) while second basemen, third basemen, and shortstops turn out to be slightly below average as a group (0.496). So, is this a mistake? Not necessarily. One possible explanation for this that I have seen suggested is the fact that, in major league baseball, left-handed throwers are only employed as pitchers, first basemen, and outfielders. Because other defensive positions are limited to those who throw right handed, however, these positions draw from a more limited pool of candidates. Is this really a sufficient explanation?

One way to think about it is that, if you were to add average members of the 1B/OF pool (0.515) to the infielder pool (0.496), you would have to add enough 1B/OFers such that 22% of the combined pool were 1B/OFers to get a combined winning percentage of .500. The percentage of the population that is left-handed is approximately 10%. If 10% of the combined 1B/OF and 2B/3B/SS pools are also left-handed, this would suggest that approximately 17% of the 1B/OF pool are left-handed (given that 0% of the 2B/3B/SS pool is left-handed*). If 22% of the 1B/OF pool was shifted to the infielder pool (which, as noted above, would bring the overall winning percentage of the infielder pool up to 0.500), this would raise the percentage of the infielder pool that is left-handed up from 0% to 4%, which is certainly closer to the overall proportion of the population in general.
*The term "left-handed" is somewhat fuzzy. Really, the requirement for non-1B infielders is that they throw right-handed. Brooks Robinson, as one example, does everything left-handed except for batting and throwing a baseball during his 23-year Hall-of-Fame career at third base.

To be honest, I'm pretty sure I way overthought the math in that last paragraph, but the general concept makes at least some sense to me: first basemen and outfielders might be better, on average, than non-1B infielders (and catchers), because they are drawn from a larger population.

That said, in terms of "value" as opposed to talent, the fact remains that a team has to play a 2B, a 3B, and a SS, and (right or wrong), these players have to throw right-handed. This is why I evaluate player value relative to positional averages rather than attempting to estimate whether some positions are, in fact, more "valuable" than others.

Center Fielders vs. Corner Outfielders
Over the Retrosheet Era, total Fielding Decisions (Player wins plus Player losses) for each of the three outfield positions were as follows:

Component 5 Component 6 Component 8 Component 9 Total Fielding
Left Field 12,2683,6912,2174,79222,968
Center Field 11,5282,8612,0255,32721,741
Right Field 12,1063,1432,2764,88822,413


At first glance, this looks quite curious. Why do left fielders and right fielders accumulate more fielding decisions than center fielders? What does this mean, exactly? Is a good defensive right fielder more valuable than a good defensive center fielder? Arguably. Should teams play their best defensive outfielder in right field rather than center field? Probably not.

The reason for this apparent anomaly is not because corner outfielders are better, or even necessarily more valuable, than center fielders. Rather, this is the result of two issues that are worth thinking about with respect to Player Won-Lost records. First, there is a wider range of fielding talent across corner outfielders than across center fielders, and, second (and somewhat related), there is a greater range of possible outcomes on balls hit to left or right field than on balls hit to center field.

The table below shows the number of plays in the 2007 American League (i.e., games played at AL ballparks) for which the various outfielders are the fielder of record (i.e., are the first fielder to touch the ball):

Total Plays Total Outs Singles* Doubles Triples % Outs % XBH
Left Field 10,252 4,611 3,965 1,618 58 45.0% 29.8%
Center Field 11,667 5,996 4,421 1,060 190 51.4% 22.1%
Right Field 9,609 4,527 3,629 1,278 175 47.1% 28.7%

*“Singles” include batters reaching on error.

For simplicity, suppose that singles have a net fielding win value of -0.0364 and extra-base hits have a net fielding win value of -0.0625 (these are reasonably close to the average net win values for these plays in recent seasons).* Let’s also normalize the above numbers to be per 100 plays.

*Base hits will likely not have the exact same value to all fields because of differences in baserunner advancement. The numbers here should therefore be thought of as illustrative, not definitive.

Total Plays Outs Singles Extra-Base Hits
Left Field 100.00 44.98 38.68 16.35
Center Field 100.00 51.39 37.89 10.71
Right Field 100.00 47.11 37.77 15.12


So, for example, left fielders allow 38.68 singles per 100 plays. At -0.0364 wins per play that works out to -1.41 wins for left fielders on singles allowed. Full numbers are shown in the table below.



Net Wins on: Singles Extra-Base Hits Total Losses Total Wins Wins per Out
Left Field -1.4078 -1.0218 -2.4295 2.4295 0.0540
Center Field -1.3793 -0.6696 -2.0489 2.0489 0.0399
Right Field -1.3747 -0.9451 -2.3198 2.3198 0.0492


Let me walk through the numbers briefly. As noted above, left fielders allow 38.68 singles per 100 plays with a value of -0.0364 wins (0.0364 losses) per single, for a total of -1.4078 wins (1.4078 losses). Left fielders allow 16.35 extra-base hits per 100 plays with a value of -0.0625 wins per extra-base hit, for a total of -1.0218 wins on extra-base hits. Adding these together, left fielders accumulate approximately 2.43 losses per 100 plays. Since fielding wins and losses are set to be equal in the aggregate for every position by construction, this means that left fielders also accumulate 2.43 wins per 100 plays, which works out to 0.0540 wins per out by the left fielder.

Note what this shows. Plays made by the left fielder are worth more player decisions on average – 0.049 decisions per play* – than plays made by right fielders – 0.046 – than plays made by center fielders – 0.041. This is true for two reasons. First, center fielders allow fewer extra-base hits than corner outfielders – 10.7 per 100 plays vs. 15.8 per 100 plays for corner outfielders, and extra-base hits have the highest value in terms of total player decisions per play. Second, center fielders allow fewer hits than corner outfielders – 48.6 per 100 plays vs. 54.0 per 100 plays – which makes outs to center field less valuable – because they’re more common – than outs to the corners. The overall result is that an average play made by a left fielder is worth about 19% more player decisions than an average play made by a center fielder, which is more than enough difference to offset the fact that center fielders were involved in 14% more plays than left fielders (in the 2007 American League).
*2.4295 wins plus 2.4295 losses equals 4.86 total decisions per 100 plays, or 0.0486 decisions per play.

The primary reason for this, I believe, is that there is a much wider range in the abilities of corner outfielders as compared to center fielders. Mathematically, this can be measured by looking at the standard deviation of winning percentages by corner outfielders. Over the Retrosheet Era, the standard deviation of season-level winning percentages for center fielders (fielding only) is 4.0%, versus 4.7% for right fielders and 4.9% for left fielders. In other words, the spread in winning percentages for corner outfielders (which can be taken as an approximation of the spread in the fielding talent of corner outfielders) is approximately 19% greater than the spread in center-fielder winning percentages (fielding talent).

In words, virtually all center fielders are good fielders, whereas, while some corner outfielders are excellent fielders (e.g., Ichiro Suzuki), others are notoriously bad fielders (e.g., Manny Ramirez). The result is that the relative value of a corner outfielder who is capable of converting balls in play into outs and in preventing extra-base hits is greater than the value of a center fielder that can do the same, because such a corner outfielder is rarer. Curious, but I think it’s true.

Pinch Hitting and Designated Hitting: Is There a DH/PH Penalty?
In The Book, Tango, Lichtman, and Dolphin studied player performances pinch hitting and DHing. Their conclusions were as follows:

“A player is significantly less effective as a pinch hitter than he is as a starter…. Players also lose effectiveness when being used as a designated hitter; the DH penalty is about half that of the PH penalty.” (Tango, Lichtman, and Dolphin, The Book: Playing the Percentages in Baseball, page 113)
I decided to undertake a similar analysis using Player Won-Lost records. Across all of the seasons for which I have estimated Player won-lost records, 33,360 players amassed offensive Player decisions as a pinch hitter as well as while playing a fielding position (i.e., excluding DH and pinch-running appearances as well as PH appearances) . Using the harmonic mean of the players' offensive Player decisions as a PH and as a position player for weights, the weighted average winning percentage of these players as pinch hitters was 0.478. The weighted average offensive winning percentage for the same players when playing the field was 0.484. So, on average, a player’s offensive winning percentage is 0.007 less as a pinch-hitter than as a non-PH. Overall, 58.6% of these players (19,541) had a worse offensive winning percentage as pinch hitters than as position players. So, I generally find the same result as The Book: players hit somewhat worse as pinch hitters than when they are playing a regular fielding position.

Doing the same thing for designated hitters (DHs), I find a weighted average offensive winning percentage as a DH of 0.512 and as position players (again, excluding PH and PR appearances) of 0.522 for the players who have done both in a single season. This works out to a DH “penalty” of 0.010. Overall, 58.8% of these players (3,445) had a worse offensive winning percentage as designated hitters than as position players, very similar to the PH penalty that I found above. This differs somewhat from The Book, which found a much smaller "DH penalty" than "PH penalty".

Out of curiosity, I did the same thing for pinch runners, comparing baserunning winning percentages for pinch runners as pinch runners versus when they reached base as a batter. Pinch runners have a weighted average baserunning winning percentage of 0.495 as pinch runners versus 0.521 for the same players otherwise for the 16,449 players who did both in a single season. This works out to a PR penalty of 0.026. Overall, 53.8% of these players (8,843) had a worse baserunning winning percentage as pinch runners.

Finally, I looked at players who earned player decisions as both a DH and a pinch hitter in the same season. There were a total of 5,598 such players. The weighted average of their winning percentage as a DH was 0.510 vs. 0.456 as a pinch hitter, implying a "PH penalty" of 0.054.

In calculating positional averages (which serve as the baseline from which I calculate positional replacement levels), I use the actual average winning percentage for these positions. Hence, these positional penalties are implicitly adjusted for in the calculation of these positional averages and replacement levels.

Starting Pitching vs. Relief Pitching
In evaluating Player won-lost records, I consider starting pitcher and relief pitcher to be two separate positions. Some differences between starting pitchers and relief pitchers are explored here.

Pitcher Contexts
Over the entire Retrosheet Era, the overall Player won-lost records of starting pitchers and relief pitchers were as follows:

Context-Neutral Context Win Adjustments
Pitcher - Role Decisions Win Pct. Inter-Game Intra-Game Combined Inter-Game Intra-Game
Starting Pitcher 187,8570.5001.0001.0771.078-0.0020.004
Relief Pitcher 81,1050.5020.9990.8210.8200.0040.006
Non-Save Situations 51,7650.5000.4371.0190.4460.001-0.030
Save Situations* 17,0340.5102.0280.8101.643-0.0010.065
Tie Games 12,3060.4991.9380.6481.2560.007-0.044

*Save situations are defined here as situations in which the winning or tying run is either on base, at bat, or on deck. This excludes saves earned by pitching at least three innings in a win, regardless of situation, or by pitching at least one inning with a 3-run lead. This also includes what would be classified as "holds" instead of saves.

There are several comparisons that I find interesting here. The first one is that relief pitchers compiled a slightly higher overall winning percentage than starting pitchers: 0.502 to 0.500. As a general rule, pitchers tend to perform better – lower ERA, more strikeouts, better context-neutral winning percentage – as relief pitchers than as starters. In fact, however, the difference in context-neutral winning percentages actually understates the impact of this. This is because, in general, (with many exceptions, of course) starters tend to be better pitchers than relievers, especially non-closers. To some extent, many, if not most, relief pitchers are failed starters.

A better way to determine the extent to which pitching in relief would be expected to improve one’s player winning percentage, then, is to focus on pitchers who both started and relieved within the same season and compare these player’s winning percentages. Among all seasons for which I have estimated Player won-lost records (1947 – 2011), a total of 13,474 player-seasons included both starting pitching and relief pitching. Weighting each of these players’ performances by the harmonic mean of their starting and relief pitching Player Decisions, these pitchers compiled a weighted average winning percentage of 0.476 as starting pitchers and 0.496 as relief pitchers. Using the Matchup Formula to re-center these winning percentages around 0.500, the average winning percentage for these pitchers as starters was 0.493 and for these pitchers as relievers was 0.517. Looked at in this way, the positional average for starting pitchers appears to be about 2.4% (0.024) lower than for relief pitchers. This difference forms the basis for calculating Positional Averages and Positional Replacement Levels.

The second comparison above is the difference in contexts. Inter-game context is slightly higher for relief pitchers, 0.999, than for starting pitchers, 1.000. This difference is entirely centered around save situations*, 2.028, and tie games, 1.938. Relief appearances in non-save situations have an average inter-game context less than half as big as that of starting pitchers (0.437).
*As noted above, "save situations" here do not include saves earned by closers for pitching the ninth inning with a 3-run lead.

The story is exactly the opposite for intra-game context. Starting pitchers have an average intra-game context of 1.077 vs. 0.821 for relief pitchers. This is because average intra-game context is highest in the early innings of games. The relationship of inter-game and intra-game context across innings is described here.

Combining inter-game and intra-game context, starting pitchers have a combined average context of 1.078 vs. 0.820 for relief pitchers. This difference in combined overall context is taken account of in my construction of final Context-Neutral player won-lost records through the calculation of an Expected Context. Of course, the use of relief pitchers has changed considerably over the 60+ years over which I have estimated Player won-lost records. The same results since 2000 are shown in the next table.

Context-Neutral Context Win Adjustments
Pitcher - Role Decisions Win Pct. Inter-Game Intra-Game Combined Inter-Game Intra-Game
Starting Pitcher 45,5040.4970.9891.0921.080-0.002-0.001
Relief Pitcher 23,3830.5071.0220.8270.8450.0030.013
Non-Save Situations 14,9300.5060.4191.0320.432-0.000-0.016
Save Situations 4,9760.5162.1390.8181.749-0.0000.067
Tie Games 3,4770.5002.0110.6571.3220.006-0.050



The general relationships identified above are all still true. More recently, however, there has been a somewhat greater spread in winning percentages between starting pitchers and relief pitchers. Relief pitchers have also seen a somewhat higher average inter-game context in recent years than for earlier years.

Changes in Relief Pitcher Roles over Time
The next table shows a breakdown of context-neutral pitching decisions by pitcher role by decade from the 1950s to the 2000s (2000 - 2013).

Breakdown of Context-Neutral Pitching Decisions by Role
Pitcher-Role 1950s 1960s 1970s 1980s 1990s 2000s
Starting Pitcher 72.7%71.3%72.3%69.7%67.3%66.1%
Relief Pitcher 27.3%28.7%27.7%30.3%32.7%33.9%
Non-Save Situations 18.6%18.5%17.4%18.3%20.4%21.7%
Save Situations 4.9%5.7%5.9%7.1%7.4%7.2%
Tie Games 3.9%4.6%4.4%4.9%4.9%5.0%


From the 1950s through the 1970s, the overall percentage of (context-neutral) pitching decisions earned by relief pitchers was relatively constant. This relatively constant overall usage masked underlying changes in relief pitcher usage, however. Specifically, over this time period, the use of relief pitchers declined by 1.2% in non-save situations, but rose 1.0% in save situations.

The 1980s saw the greatest increase in overall relief pitcher decisions of any decade (2.5%). This increase in relief-pitcher usage spanned all three roles shown here, with the use of relief pitchers in non-save situations returning to 1950s - 60s levels, while the share of total pitcher decisions earned by relief pitchers in save situations and tie games increased by a combined 1.7%.

The 1990s and 2000s have seen a continuing increase in overall relief pitcher usage. Interestingly (to me), however, the increase in relief pitcher usage over the past 20 years appears to be almost entirely centered on increased relief pitcher usage in non-save situations*.
*The definition of "save situations" which I use here does not include saves earned by closers for pitching the ninth inning with a 3-run lead. I suspect the number of such saves has increased over this time period, which may be part of the apparent increase in what I am identifying as "non-save situations".

To get a better feel for how the changing roles of relief pitchers have interacted with changing usage, the final table here shows a breakdown of context-dependent pitching decisions by pitcher role by decade from the 1950s to the 2000s (2000 - 2013).

Breakdown of Context-Dependent Pitching Decisions by Role
Pitcher-Role 1950s 1960s 1970s 1980s 1990s 2000s
Starting Pitcher 79.2%77.1%77.6%74.4%72.3%71.3%
Relief Pitcher 20.8%22.9%22.4%25.6%27.7%28.7%
Non-Save Situations 8.9%8.4%7.7%8.1%9.0%9.4%
Save Situations 7.3%8.9%9.3%11.4%12.4%12.6%
Tie Games 4.6%5.6%5.4%6.1%6.3%6.7%



Player Comparisons: Some Examples

I have written several articles which compare players. Such articles include career comparisons of Roger Clemens vs. Greg Maddux, Jim Rice vs. Dale Murphy, and single-season comparisons of David Ortiz vs. Alex Rodriguez (2005), and Stan Javier vs. Aubrey Huff (2001). In December of 2012, I wrote a series of articles on the players who appeared on the 2013 Hall-of-Fame ballot. Several of these involved player comparisons, including Jeff Bagwell (vs. Frank Thomas), Craig Biggio (vs. Ken Griffey, Jr.), Kenny Lofton (vs. Manny Ramirez and Albert Belle), Don Mattingly (vs. Keith Hernandez), Mike Piazza (vs. Ivan Rodriguez), and Bernie Williams (vs. Kirby Puckett).

When comparing players, there is a natural tendency to compare players who played the same, or at least similar, positions (e.g. Maddux and Clemens, Rice and Murphy, Puckett and Williams, etc.). But I think that sometimes it can be more fun and interesting to compare players at different positions and with very different skill sets. When doing so with Player won-lost records, though, it is important to keep in mind that different players have different positional averages against which they need to be judged.

The next part of this article shares two such comparisons: Roger Clemens vs. Mickey Mantle (which I wrote about in the article on Clemens in my 2013 Hall-of-Fame ballot series) and Ozzie Smith vs. Frank Thomas.

Roger Clemens vs. Mickey Mantle
If you look at the top players as measured by Player won-lost records, the player closest to Roger Clemens in Player wins over positional average (pWOPA) and replacement level (pWORL) is Mickey Mantle. Here is how Roger Clemens and Mickey Mantle compare in pWins.

Roger Clemens Mickey Mantle
Age Games pWins pLoss Win Pct. pWOPA pWORL Games pWins pLoss Win Pct. pWOPA pWORL
19
 
9613.29.30.5871.72.7
20
 
14221.914.80.5973.24.7
21
217.25.50.5640.9
1.5
12720.612.90.6153.34.8
22
155.94.50.5680.8
1.4
14523.914.80.6163.75.4
23
3317.610.30.6313.9
5.2
14725.614.30.6424.96.6
24
3618.812.40.6033.5
5.1
15026.815.50.6334.96.7
25
3518.412.30.5993.2
4.7
14426.112.60.6736.07.6
26
3515.313.00.5401.3
2.7
15023.816.50.5912.94.5
27
3116.99.10.6494.1
5.4
14421.215.30.5822.44.0
28
3517.111.40.6003.0
4.5
15324.513.90.6394.56.1
29
3216.110.40.6083.1
4.5
15327.215.30.6395.27.1
30
2913.213.00.5050.2
1.5
12320.911.70.6414.15.4
31
2410.98.20.5721.4
2.5
659.75.20.6542.12.7
32
239.06.90.5671.3
2.1
14322.113.60.6193.75.2
33
3413.711.50.5441.4
2.8
12214.012.40.5310.31.4
34
3418.89.90.6544.7
6.4
10813.011.40.5330.41.4
35
3316.29.50.6293.6
5.0
14417.112.30.5821.52.8
36
3013.312.70.5120.5
1.9
14415.110.90.5811.32.5
37
3214.212.30.5371.2
2.6
38
3314.49.20.6112.9
4.2
39
2911.69.40.5521.3
2.4
40
3313.911.30.5511.5
2.9
41
3315.411.00.5843.0
4.4
42
3214.410.20.5872.8
3.9
43
197.34.90.5961.5
2.1
44
186.25.70.5170.3
1.0
45
 
------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------
CAREER RECORDS709325.7234.60.58151.7
80.5
2,400366.9232.70.61255.981.8

The shape of Mantle's and Clemens's careers are somewhat different, with Mantle having a higher pWORL than Clemens's career-best in 4 different seasons. Clemens makes up for Mantle's better peak, however, by putting together an incredible string of 24 consecutive above-average seasons.

As I noted above, Mantle and Clemens are very close to each other in career pWOPA and pWORL. Interestingly, they are even closer in pLosses (1.9). But Mickey Mantle accumulated 41.2 more pWins than Roger Clemens and, consequently, had a higher career winning percentage.

What then brings Clemens back up to Mickey Mantle's level in pWOPA and pWORL is an offsetting difference in the two players' positional average.

In his career, players who played the same position(s) as Mickey Mantle (mostly CF) amassed an average Player winning percentage of 0.519. Mickey Mantle spent his entire career in leagues in which pitchers batted. Because pitchers are well below-average offensively, everybody else - including, of course, center fielders - is above average offensively, basically by definition. This serves to raise the positional average against which Mickey Mantle is compared in his career.

In contrast, players who played the same position(s) as Roger Clemens (i.e., starting pitchers) amassed an average Player winning percentage of 0.489. On average, starting pitchers are, of course, well below average offensively. In addition, as outlined above, starting pitchers have a lower average winning percentage than relief pitchers. Both of these factors serve to lower the positional average against which Roger Clemens is compared in his career.

As explained above, I set replacement level one weighted standard deviation below positional average, with separate standard deviations calculated for pitchers and non-pitchers. The standard deviation for non-pitcher winning percentage during Mantle's career is 0.043, leading to a positional replacement level for Mantle of 0.475. In contrast, the standard deviation for pitchers over Clemens's career was 0.051, for a replacement level for Clemens of 0.438.

Put it all together and we get two very different players with very similar career values.

Ozzie Smith vs. Frank Thomas
There might not be two more different great position players than Ozzie Smith and Frank Thomas. Ozzie Smith was elected to the Hall-of-Fame in his first year of eligibility in 2002 with 91.7% of the vote. His Hall-of-Fame case rested almost entirely on being the greatest fielding shortstop in major-league history. To the extent he had any offensive value at all (and he actually had some respectable seasons on offense especially later in his career), it was focused in speed (580 career stolen bases, 22nd alltime) and "small ball" (214 career sacrifice bunts, 73rd all-time).

Frank Thomas was nicknamed "The Big Hurt" based on what he did in the batter box. In his younger days, some people would speculate about whether he was the greatest right-handed hitter ever. In terms of baserunning, Frank Thomas was 6'5", weighed at least 240 lbs (that's what Baseball-Reference says), and ran about as well as you'd expect a guy that size to run. As for fielding, Frank Thomas was a born DH, a position that became his regular position at age 30.

Ozzie Smith had 548 more stolen bases, 214 more sacrifice bunts, and 13 more Gold Gloves than Frank Thomas (who had 0 sacrifice bunts and 0 Gold Gloves in his career). Frank Thomas hit 493 more home runs than Ozzie Smith, beat him in career OBP by .092 and in career SLG by .227.

Weighing all of those factors against each other, how do Frank Thomas and Ozzie Smith compare? As the next table shows, they actually end up with remarkably similar overall career value, achieved in very different ways.

Ozzie Smith Frank E. Thomas
Age Games pWins pLoss Win Pct. pWOPA pWORL Games pWins pLoss Win Pct. pWOPA pWORL
22
 
607.04.80.5920.91.3
23
15920.420.10.5040.9
2.6
15818.212.00.6032.64.2
24
15616.618.30.475-0.1
1.3
16021.515.80.5772.23.6
25
15820.521.00.4940.7
2.4
15320.814.00.5972.74.1
26
11012.515.60.444-1.0
0.1
11315.09.30.6192.33.4
27
14019.216.30.5422.1
3.5
14515.812.60.5571.02.4
28
15919.918.20.5221.3
2.7
14116.213.20.5500.92.1
29
12417.515.20.5351.9
3.2
14618.012.30.5932.13.5
30
15821.517.70.5492.7
4.2
16015.012.50.5460.72.4
31
15318.216.40.5271.5
2.8
13513.610.90.5540.92.2
32
15821.717.40.5562.7
4.3
15917.511.80.5982.44.2
33
15321.717.50.5542.4
3.9
201.21.40.448-0.20.0
34
15520.118.00.5281.5
2.9
14812.211.70.510-0.11.5
35
14315.717.00.481-0.3
1.0
15316.912.30.5791.83.6
36
15020.417.30.5411.9
3.3
747.44.60.6151.32.0
37
13218.116.50.5231.2
2.5
342.92.00.5870.40.7
38
14118.117.40.5100.7
2.1
13714.710.40.5871.73.3
39
9810.512.00.466-0.5
0.4
15513.611.90.5330.41.9
40
444.55.40.451-0.4
0.0
715.96.30.484-0.30.4
41
827.36.70.5200.4
1.0
------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------
CAREER RECORDS2,573324.4304.00.51619.6
44.3
2,322253.6190.10.57223.646.7

Frank Thomas crushes Ozzie Smith in career Player winning percentage, 0.572 to 0.516. But first basemen and designated hitters are expected to be above-average hitters, while shortstops are not, so Frank Thomas's record is compared to a positional average of 0.518 while Ozzie Smith is compared to a positional average of 0.485.

Even being compared to the higher average, however, Frank Thomas still ends up slightly ahead of Ozzie Smith in career pWins over positional average (pWOPA). Compared to replacement level, however, Smith, because he played more games in the field, and played them at a more important position, beats Thomas in career pWORL, on the strength of having accumulated 185 more Player decisions (pWins + pLosses) than Thomas.

Player Comparison Tool

One of the options on the front page of my website is a Player Comparison tool. You can enter the names of two players and compare their Player won-lost records.

The comparison page defaults to a comparison of pWins by age (like the Clemens-Mantle and Smith-Thomas comparisons above). In addition, I allow one to vary the comparison parameters in several ways.

First, one can change how the players' seasons line up: by age, by experience, or by year. You don't have to type the full words in the box here (although you can): you can simply type "a" for Age, either "e" or "x" for experience, and "y" for year (without the quotation marks in all cases).

Second, one can vary the records compared. There are six options. The first two of these are overall records: pWins, which tie to team wins, or eWins, which are adjusted to neutralize context and control for teammate-ability. These comparisons show Player wins, losses, winning percentage, and wins over positional average (WOPA) and replacement level (WORL), the calculations of which were described earlier in this article.

In addition to total Player won-lost records, one can also compare player won-lost records in the four key factors in which player wins are earned: Batting, Baserunning, Pitching, and Fielding. The numbers shown here are context-neutral and teammate-adjusted.

In addition to wins, losses, and winning percentages, the comparisons for Batting, Baserunning, Pitching, and Fielding also show normalized wins over average measures as follows.

For Batting and Baserunning, the Player Comparison tool shows what it calls "WOPA_b". WOPA_b measures (batting or baserunning) wins relative to a league-average non-pitcher. This allows one to compare players in DH leagues (where non-pitcher league average will be 0.500) with players in non-DH leagues, whose raw offensive winning percentages are boosted by having their offense be compared, in part, to pitchers' offense.

For Pitching, the Player Comparison tool shows wins over positional average, WOPA, where separate positional averages are calculated for starting pitchers and relief pitchers.

For Fielding, the Player Comparison tool shows what it calls "WORL_f". This measures Fielding wins over a player's overall replacement level. The purpose of this comparison is to enable one to compare fielders at different positions: i.e., to address an issue I raised near the beginning of this article, "who was a better fielder – the below-average fielder at the more difficult position or the above-average fielder at the easier position." Players at more difficult defensive positions will tend to have lower replacement values against which they are compared. For this comparison, I use replacement level instead of positional average to highlight the idea that, for example, a below-average defensive shortstop is nevertheless providing his team with positive value merely by playing shortstop. A player with a positive value of WORL_f (as most players do) is a player who is more valuable playing the field (if one uses WORL as one's measure of player value) than not. On the other hand, it is possible for a player to be such a poor fielder that his fielding value "over replacement" may actually be negative, suggesting that such a player would be more valuable as a DH (or PH) than by trying to play a defensive position. For his career, Frank Thomas was actually an example of such a player. Here is a fielding comparison of Frank Thomas and Ozzie Smith.

Ozzie Smith Frank E. Thomas
Age Games eWins eLoss Win Pct. WORL_f Games eWins eLoss Win Pct. WORL_f
22
 
600.70.90.434-0.1
23
1596.76.30.514
1.0
1580.70.90.459-0.0
24
1567.06.00.539
1.3
1602.62.80.4830.0
25
1587.97.10.526
1.3
1531.62.40.407-0.3
26
1105.24.90.514
0.8
1131.21.30.4850.0
27
1407.35.80.558
1.5
1451.31.30.4940.1
28
1597.56.40.538
1.2
1411.62.00.454-0.1
29
1246.36.00.514
1.0
1461.31.50.475-0.0
30
1587.56.40.537
1.3
1600.30.40.417-0.0
31
1535.35.00.513
0.7
1350.60.80.438-0.0
32
1586.14.80.561
1.2
1590.40.40.5340.1
33
1536.25.20.543
1.0
200.00.10.263-0.0
34
1555.55.10.522
0.7
1480.10.10.328-0.0
35
1434.74.20.532
0.7
1530.30.30.437-0.0
36
1505.65.30.514
0.7
740.10.00.5450.0
37
1325.85.20.527
0.8
340.00.00.0
38
1415.55.40.503
0.6
1370.00.00.0
39
983.93.50.524
0.6
1550.00.00.0
40
441.61.60.511
0.2
710.00.00.0
41
822.11.90.520
0.3
------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------
CAREER RECORDS2,573107.596.00.528
16.9
2,32212.915.20.460-0.4

The Player Comparison tool accepts the following abbreviations for the six player record options: pw (for pWins), ew (for eWins), bat (for batting), r or run (for baserunning), pitch (for pitching), and f or field (for fielding).

Finally, there are two additional options: including postseason games and normalizing season lengths. These concepts are discussed in a bit more detail below.

Normalizing Season Length
My Player won-lost records are constructed on a game-by-game basis. In the case of pWins and pLosses, the number of total player decisions is exactly equal to three per team game. Hence, my work implicitly values each game the same. Rather than considering individual games to be of equal value, however, it might make more sense to think of individual seasons as being of equal value.

There are three primary reasons why season lengths might differ across the seasons for which I have estimated Player won-lost records.

First, prior to 1961 in the American League and 1962 in the National League, seasons were 154 games long. Since 1962 (1961 in the AL), seasons have been 162 games long. Eight games may not seem like much, but over the course of a 20-year career, an additional 8 games per season adds up to another full season (20*8 = 160).

Second, my Player won-lost records are only calculated based on games for which Retrosheet has play-by-play data. Unfortunately, Retrosheet is missing some games in several of the earliest seasons over which I have estimated Player won-lost records. This problem gets worse the farther back you go - e.g., my Player won-lost records for 1948 are calculated for only 0% of the games that were played that year - and is worse for some teams than others - from 1947 - 1950, Retrosheet has play-by-play data for every Dodgers and Indians game, but is missing -1,198 Pirates games.

Consider, for example, Robin Roberts vis-a-vis Juan Marichal.

Based on raw regular-season Player won-lost records, I calculate Juan Marichal to have accumulated 52.0 pWORL and Robin Roberts to have accumulated 53.1 pWORL.

The prime of Juan Marichal's career - 1962 - 1969 - was played in 162-game schedules. Retrosheet also has play-by-play data for every game of Juan Marichal's career. Normalizing Juan Marichal's Player won-lost records to 162-game seasons has virtually no effect on his career pWORL, changing his career pWORL from 52.03 to 52.10.

The prime of Robin Roberts's career happened roughly a decade before Marichal's - 1950 - 1955. In addition, Retrosheet is missing play-by-play data on 5 of Robin Roberts's 688 career games (1%). Normalizing for missing games* and the 154-game schedule during the bulk of Robin Roberts's career, Roberts's career pWORL increases to 54.6, moving his adjusted career pWORL ahead of Juan Marichal.
*The adjustment here adjusts for missing Phillies games, not specifically for games pitched by Roberts. That is, the adjustment here assumes that Roberts's record in missing Phillies games was proportional to his record in games for which Retrosheet has play-by-play data.

Third, there have been games missed due to labor strikes four times in Major-League history: 1972, 1981, 1994, and 1995. The first of these was relatively short, reducing season lengths by about 7 games on average (teams played 153 - 156 games that year). The last reduced season length by 18 games per team (teams played a 144-game schedule in 1995). The middle two were particularly bad, costing teams 50 or more games each season and, in the latter case, eliminating the postseason as well. There were no players whose careers were affected by all three (1994-95 was a single work stoppage) of these work stoppages, but even for players affected only by the 1994-95 strike, the lost games added up to nearly half a season. For players affected by both the 1981 and 1994-95 strikes, the lost games added up to nearly a full season.

One player for whom work stoppages significantly affect the perception of his career is Tim Raines, Sr., who was affected by work stoppages at both ends of his career as an everyday player. Tim Raines's games played by season are shown in the table below.

Year Games Played
19796
198015
198188
1982156
1983156
1984160
1985150
1986151
1987139
1988109
1989145
1990130
1991155
1992144
1993115
1994100
1995133
199659
199774
1998109
199958
200151
200297



Looking at the above table, without thinking about labor strikes, it appears that Tim Raines broke into the big leagues in 1979, but didn't become a regular until 1982, was a regular for 11 seasons, 1982 - 1992, missing significant time in one of those seasons (1988), along with less significant time missed in two other seasons (1987 and 1990), before transitioning into part-time play starting in 1993. Or, in one sentence, the above table makes it appear that Tim Raines's career consisted of maybe a decade as a regular (1982 - 92, less time missed in 1987, 1988, and 1990), followed by a decade of part-time play (1993 - 2002).

If you normalize Tim Raines's record to 162-game seasons, however, his games played look like this:

Year Games Played
19796
198015
1981132
1982156
1983155
1984161
1985151
1986152
1987139
1988108
1989145
1990130
1991155
1992144
1993115
1994143
1995149
199659
199774
1998109
199958
200151
200297



Now, we see that Tim Raines became a regular in 1981 and remained one through 1995, with two seasons with significant time missed (1988, 1993) and two seasons with less significant time missed (1987*, 1990). Raines was not a starter for a decade who then hung around for another decade; he was a starter for 15 seasons, before hanging around for another 6 seasons of part-time work. That seems like a fairly significant difference in narrative to me.
*Raines was also adversely affected by labor issues in 1987. That season, he was a victim of collusion which caused him to miss the first month (20 games) of that season. Adjusting for that as well, Raines played the equivalent of 140+ games 11 times and 150+ games 7 times.

Both my Player Comparison tool (found on my homepage) as well as my customized statistics page allow one to normalize season length if desired. In the case of the Player Comparison tool, season-normalization is a simple y/n option, with "y" normalizing to 162-game seasons and "n" using actual games played. On the customized statistics page, on the other hand, I allow one to specify the specific season length one wishes to normalize to (e.g., 162 games, 154 games, 100 games, or whatever you'd like).

Treatment of Postseason Games
In 2010, Roy Halladay made his 33rd start of the season in the Philadelphia Phillies' 157th team game. Halladay left that game healthy. Based on the 5-man rotation used that season by the Phillies, Halladay was in line to start the Phillies' final regular-season game of the season.

In his next start, Roy Halladay threw a no-hitter against the 91-win Cincinnati Reds. That start was not, however, Halladay's 34th regular-season start of the season. Instead, the Phillies held him back, so he could start game 1 of the playoffs. I calculate Roy Halladay's regular-season Player won-lost record for 2010 (pWins - pLosses) at 17.4 - 12.8, good for 4.4 pWORL. If he had pitched the no-hitter against the Reds two days earlier, in the regular season, his record would have instead been 18.3 - 13.0, 4.9 pWORL. It seems to me that Roy Halladay deserves full credit for that game when evaluating his 2010 season as well as his career.

Most baseball statistics - both conventional (e.g., Hank Aaron's 755 career home runs) and sabermetric (e.g., Babe Ruth's 178.3 career WAR) - tend to count only regular-season statistics, but do not include postseason numbers. This seems to be something of a mistake to me.

Roy Halladay really did throw that no-hitter against the Reds, and he did it in a game that was extremely important to both the Phillies and the Reds: so important that the Phillies adjusted their pitching rotation to be sure that Roy Halladay was available to pitch that game. It seems to me that this performance of Halladay's ought to "count" in his record.

I have calculated Player won-lost records, both pWins/pLosses as well as eWins and eLosses, for all postseason games in the seasons over which I have calculated these records. These are calculated in the same way as regular-season games.

In a nod to traditional baseball record-keeping, I report these results separately for the most part, so, for example, Roy Halladay's regular-season results are presented here while the details of his postseason exploits are presented here. I do, however, show combined career totals for regular-season and postseason records on players' main pages.

On my leaders page, I offer options for showing leaders in pWins (Losses, WOPA, and WORL) and eWins for regular-season only, for postseason only (combined as well as by round), as well as for the regular season and postseason combined.

On my custom statistic page, I allow one to weight postseason wins, WOPA, and WORL however one sees fit. Entering a value of zero for any of these weights will exclude postseason records from consideration; a value of one will treat postseason records identical to regular-season records; a value greater than one would weight postseason performance more heavily than regular-season performance. I allow one to weight postseason wins, WOPA, and WORL differently if desired. So, for example, one could include postseason wins in the calculation but exclude postseason WOPA and WORL as a way to ensure that the postseason can only add to a player's case but not subtract from it (since negative values are possible for WOPA and WORL, but not for wins).

Finally, in my Player Comparison tool (found on my homepage), I allow the option to include postseason games in the comparisons.

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The information used here was obtained free of charge from and is copyrighted by Retrosheet. Interested parties may contact Retrosheet at "www.retrosheet.org". Baseball player won-lost records have been constructed by Tom Thress. Feel free to contact me by e-mail or follow me on Twitter.