Baseball Player Wins and Losses
Player WinsPlayer wins are calculated such that the players on a team earn 3 Player decisions per game. I calculate two sets of Player wins: pWins are tied to team wins - the players on a winning team earn 2 pWins and 1 pLoss, the players on a losing team earn 1 pWin and 2 pLosses - while eWins attempt to control for the context in which they were earned, as well as controlling for the abilities of a player's teammates.
|300 pGame Winners of the Retrosheet Era|
|Pete Rose Sr.||438.0||391.6||0.528||12.4||55.2|
|Joe L. Morgan||364.3||283.4||0.562||45.9||79.0|
|Ken Griffey Jr.||337.1||298.0||0.531||16.6||47.3|
|Tony Gwynn Sr.||322.0||289.5||0.527||5.1||33.9|
|Luis 'Gonzo' Gonzalez||319.0||295.2||0.519||2.1||32.3|
|Tim Raines Sr.||314.2||274.4||0.534||11.9||39.5|
Wins over Positional AverageIn constructing Player wins and losses, 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.
|Top 50 Players in Wins over Positional Average|
|Joe L. Morgan||364.3||283.4||0.562||45.9||79.0|
|Randy 'Big Unit' Johnson||282.4||222.2||0.560||37.9||65.0|
|Pedro J. Martinez||194.5||138.7||0.584||33.3||51.8|
|J. Kevin Brown||205.8||166.8||0.552||25.4||45.5|
|Pee Wee Reese||211.1||168.2||0.557||24.1||45.5|
Wins over Replacement LevelReplacement 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.
|Top 50 Players in Wins over Replacement Level|
|Joe L. Morgan||364.3||283.4||0.562||45.9||79.0|
|Randy 'Big Unit' Johnson||282.4||222.2||0.560||37.9||65.0|
|Pete Rose Sr.||438.0||391.6||0.528||12.4||55.2|
|Pedro J. Martinez||194.5||138.7||0.584||33.3||51.8|
Wins vs. WOPA vs. WORLThe choice 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 have also written a separate article which looks at various factors that one might consider in constructing such a statistic.
Replicating WARProbably 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 = (Net Wins over Average) + Wrep
WORL = WOPA + Wrep
WAR = 2*WOPA + (WORL - WOPA) = WOPA + WORLHence, one can calculate the pWin or eWin-based equivalent of WAR by adding WOPA plus WORL.
Changing Replacement LevelIt 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.
|(1)||WORL - WOPA||=||.050*(Player Decisions)|
|(2)||Wins - WORL||=||.450*(Player Decisions)|
Wins over 0.480 = WOPA + 0.4*(WORL - WOPA) = 0.6*WOPA + 0.4*WORL
Wins over 0.350 = WORL + (2/9)*(Wins - WORL) = (7/9)*WORL + (2/9)*Wins
1. Normalizing Component Won-Lost Records to 0.500A key implicit assumption underlying my Player Won-Loss Records is that Major League Baseball players will have a combined winning percentage of 0.500. While this is trivially true at the aggregate level, almost regardless of what you do, it should also be true at finer levels of detail as well.
2. Normalizing Player Game Points by GameThe total number of Player Game Points accumulated in an average Major League Baseball game is around 3.3 per team. This number varies tremendously game-to-game, however, with some teams earning 2 wins in some team victories while some other teams may earn 6 wins in team losses. At the end of the day (or season), however, all wins are equal. Hence, in my work, I have chosen to assign each team one Player Win and one Player Loss for each team game. In addition, the winning team earns a second full Win, while the losing team earns a second full Loss. Ties are allocated as 1.5 Wins and 1.5 Losses for both teams. Context-neutral player decisions (eWins and eLosses) are also normalized to average three Player decisions per game. For eWins and eLosses, this normalization is done at the season level, rather than the game level, so that different numbers of context-neutral player decisions will be earned in different games.
Why 3 Player Decisions per Game?
The choice of three Player Decisions per game here is largely arbitrary. I chose three because the resulting Player Won-Lost records end up being on a similar scale to traditional pitcher won-lost records, with which most baseball fans are quite familiar. For example, expressed in this way, Jayson Werth led the major leagues in 2010 with 23.5 (Context-Dependent) Player Wins, while Ichiro Suzuki led the majors with 21.7 losses.
In comparison, C.C. Sabathia and Roy Halladay led all major league pitchers in 2010 with 21 wins (Sabathia amassed 16.2 Player Wins, while Halladay had 17.1 ) while Joe Saunders (14.5 Player losses) led the major leagues with 17 losses. The relationship between team-dependent wins and traditional Pitcher Wins is explored elsewhere. Over the entire Retrosheet Era, the most pWins accumulated by a player in a single season was 29.1 by Willie Mays in 1962 (against 18.4 pLosses). The most single-season pLosses were accumulated by Vladimir Guerrero in 2001 with 23.2 pLosses (and 25.5 pWins).
This normalization process has no effect on the relative ordering of players – if pWins and pLosses were normalized to be equal to 6 per game, Jayson Werth would have continued to lead the major leagues in wins in 2010, he simply would have had twice as many of them. Nor does it affect player winning percentages, as pWins and pLosses are scaled proportionally.
One consequence of my choice of three Player Decisions per team game is that, as a result of this normalization process, total Player Wins for a league as a whole will be equal to total Win Shares as constructed by Bill James. Hence, one might think of Player Won-Lost records as calculated here as measuring “true” win shares.
Because the players on a team receive only two team-dependent wins for each team win, however, the total number of team-dependent wins will be less than the total number of Win Shares for teams with winning records. On the other hand, because the players on a team receive one team-dependent win for each team loss, the total number of team-dependent wins will be greater than the total number of Win Shares for teams with losing records. The comparison between team-dependent wins and Win Shares is explored elsewhere.
Why Do Players Get Wins in Games Their Team Loses?
If one is interested in assigning credit to players for team wins or blame to players for team losses, one might think that it would make sense to only credit a player with Player wins in games which his team won and only credit Player losses in games which his team lost. I have chosen instead to give players some wins even in team losses and some losses even in team wins. I do this for a couple of reasons.
Most simply put, baseball players do tons of positive things in team losses and baseball players do tons of negative things in team wins. Throwing away all of those things based solely on the final score of the game leads, in my opinion, to too much valuable data simply being lost. It makes the results too dependent on context.
As I noted above, in the average major-league baseball game of the Retrosheet Era (1947 - 2012), the average team amasses 3.3 Player Game Points. The win probability for the winning team goes from 50% at the start of the game to 100% at the end, so that the winning team will amass exactly 0.5 more positive Player Game Points than negative Player Game Points by construction. This means that the players on an average winning team will amass a combined record of something like 1.9 - 1.4 in an average game. That works out to a 0.576 winning percentage, or about 93 wins in a 162-game schedule (93-69). Put another way, more than 40% of all Player Game Points (1 - 0.576) would be zeroed out in a system that credited no Player wins in team losses (or Player losses in team wins). That's simply too much for me to be comfortable making such an adjustment.
There are two reasons why such a large percentage of plays do not contribute to victory. First, it is indicative, I think, of the fairly high level of competitive balance within Major-League Baseball. Put simply, even very bad Major-League Baseball teams are not that much worse than very good Major-League Baseball teams.
But the other reason why such a large percentage of plays do not contribute to victory, and why I assign player wins even in team losses and vice-versa, is because of the rules of baseball. Because there is no clock in baseball, the only way for a game to end is for even the winning team to do some things that reduce its chances of winning: it has to make 3 outs per inning for at least 8 innings (not counting rain-shortened games). Likewise, a losing team is guaranteed to do some things that increase its chance of winning: it must get the other team out 3 times per inning.
My system still rewards players who do positive things that contribute to wins more favorably than players who do positive things that lead to losses. As I noted above, an average team will amass a player winning percentage of approximately 0.576 in team wins (and 0.424 in team losses). By assigning 2 wins and only 1 loss in team wins, however, players will amass a 0.667 player winning percentage in team wins (and 0.333 in team losses). So, player wins that lead to team wins will still be more valuable than player wins that happen in team losses. The latter are simply not worthless.
Relationship of Player Decisions to Team Decisions
Under my system, to move from players’ team-dependent won-lost records (pWins and pLosses) to a team won-lost record, one subtracts out what I call “background wins” and “background losses.” One-third of a player’s decisions are background wins and one-third of a player’s decisions are background losses. Mathematically, then, if the sum of the team-dependent won-lost records of the players on a team is W wins and L losses, then the team’s won-lost record will be as follows:
Team Wins = W – (W + L) / 3; Team Losses = L – (W + L) / 3What this means is that a team of, say, .450 players will not play .450 ball, but will instead play something closer to .350 ball. Consider, for example, the 2011 Houston Astros. The 2011 Astros finished with a record of 56-106 (a .346 wining percentage). I view them as having been essentially a replacement-level team. The players on the 2011 Astros earned a total of -0.3 pWORL. The combined winning percentage of the Astros' players, however, was not the .346 winning percentage the Astros amassed, but, instead, was 0.449.
|Team Wins||Team Win Pct.||Player Wins||Player Win Pct.|
pWins vs. Win Probability Advancements (WPA)As noted above, the central building block in calculating pWins and pLosses is the concept of Win Probability.
pWins vs. WPA, Example 1: How Many Wins can One Player Get in One Game?Win Probability Advancements are structured such that net Win Probability Advancements (WPA+ minus WPA-) sum to exactly 0.5 for every team win and exactly -0.5 for every team loss. Hence, team wins are equal to exactly two times WPA. In Game 6 of the 2011 World Series, David Freese and Lance Berkman accumulated a combined WPA of 1.8 (according to Baseball-Reference). In other words, Freese and Berkman combined to "win" 3.6 games that night - and their teammates (mostly their bullpen) combined to "lose" 2.6 games. But, of course, when Game 6 of the World Series was over, the Cardinals had only won 1 game, not 3.6, and they had certainly not lost 2.6 games.
pWins vs. WPA, Example 2: Solo Home Runs in 1-0 GamesIn a separate article, I look at how context can affect value as I measure it via Player won-lost records by comparing two games during the 2002 season which the Los Angeles Doders won at Dodger Stadium by a score of 1-0 with the only run of the game scoring on a solo home run.
|8/28/2002||Odalis Perez||2 out, bottom 5||0.1377||0.1691||0.2531||1.2287||1.4966||1.8388|
|9/27/2002||Paul LoDuca||Lead-off, bottom 10||0.1377||0.3617||0.3363||2.6271||0.9298||2.4428|
pWins vs. WPA, Example 3: Value of Breaking a Game Open Early vs. Coming up Clutch LateLater in this article, I compare the 2005 seasons of David Ortiz and Alex Rodriguez when they finished 1-2 in voting for the AL MVP award.
Context-Neutral Win ProbabilitiesTraditionally, win-probability systems are purely context-dependent. In fact, however, I do not think that this is necessarily the appropriate starting point for measuring player value. Rather, I am interested in beginning with an assessment of players’ performances in the absence of the contexts in which the players actually performed. That is, what would the expected won-lost record be for a player, given his actual performance, assuming that performance had come in a neutral context? To answer this question, I construct a set of context-neutral Player Game Points. Once these are constructed, I can then add back in the contextual information in a way that clearly identifies how players’ values were affected by the context in which they performed.
1. Independent EventsMost events can happen regardless of the base-out situation. One can strike out at any time, regardless of how many baserunners or outs there are. Similarly, a triple could happen at any time regardless of the number of baserunners. All batter results, except for double plays (which are base-state dependent), intentional walks, and bunts, fall into the category of independent events. Intentional walks and bunts are treated as purely contextual events, which are described below.
2. Base-State Dependent EventsSome events can only happen given certain baserunners or a certain number of outs. For example, one can only ground into a double play with at least one baserunner on and less than two outs. Any Player Game Points accumulated by a baserunner on third base can, of course, only be accumulated in a base-out state that includes a runner on third base.
3. Purely Contextual EventsWhile it is possible to remove much, if not all, of the context from most plays, there are certain plays which are, essentially, purely elective plays, and are therefore inextricably tied to the context in which they take place. In my opinion, it would be wrong to attempt to divorce these plays from their context.
Constructing eWins and eLosses from Context-Neutral Win ProbabilitiesContext-neutral Player Wins and Losses are normalized to be equal to aggregate Context-dependent Player Wins and Losses for each component and sub-component. Hence, the total number of Context-Neutral Player Wins accumulated for a particular type of event or sub-event – say, home runs – will equal the total number of Context-Dependent Player Wins accumulated over the same set of events. This normalization is done at the season/league level. At the game or team level, however, the total number of context-neutral player decisions need not be equal to the number of context-dependent decisions, either at the component level or in the aggregate.
Expected ContextIn relating player wins and losses to team wins and losses, the context in which a player’s performance takes place matters. This is reflected in two context measures related to Context-Dependent player decisions: inter-game context and intra-game context.
Offense: Batting and BaserunningExpected contexts are calculated for four different positions: pinch hitter, pinch runner, pitcher, and other. For each of these positions, expected context is set equal to the average context for the position for the league and season in question.
PitchingStarting pitchers have an average inter-game context of 0.998 and an average intra-game context of 1.080, a combined average context of 1.078. For relief pitchers, the numbers are 1.005, 0.825, and 0.829, respectively. Expected contexts for starting pitchers are set equal to the average context for starting pitchers for the relevant league and season. The same is true for relief pitchers: expected context is set equal for all relief pitchers – closers, setup men, mopup men – regardless of their actual context.
FieldingOver the Retrosheet Era, there is no obvious relationship between context and fielding position. Hence, expected context is set equal to 1 for all fielding player decisions.
Final ResultsExpected context for a player is calculated by taking the weighted average of the expected contexts for the player’s offensive, pitching, and fielding decisions.
Expected Win AdjustmentsOne of the key implications of my work is that the difference between winning and losing is very small in Major-League Baseball. In an average Major-League Baseball game during the Retrosheet Era, for example, the winning team accumulated around 1.9 positive Player Game Points – the building block of Player Wins – and 1.4 negative Player Game Points – the building block of Player Losses. In other words, the average winning team compiled a team winning percentage of 1.000 (by definition), but the Players on that team compiled a combined winning percentage of something like 0.576, which works out to about an 93-69 record in a 162-game schedule.
Trevor Hoffman, for example, earned 45.9 more pWins than eWins in his career (83%) mostly because the actual context in which he performed was 68% greater than his expected context.Certainly, some people may feel that some of these differences are more "real" than others. In theory, one could adjust player records based on individual contextual factors. I have not allowed for that possibility (yet) on my custom-weight page. I do, however, allow one to assign different weights to pWins and eWins.
Derek Jeter has earned 10.7 more pWins than eWins in his career largely because he has had the good fortune to play with above-average teammates, so that Jeter's positive contributions have been more likely to contribute to victories than would have been expected. This is reflected in what I call Jeter's intra-game win adjustment, which has raised his pWinning percentage by 0.021 (to 0.539) over Jeter's expected winning percentage (accounting for 13.3 additional wins).
David Ortiz earned 2.3 more pWins than eWins in 2005 mostly because of the timing of his hits (i.e., Big Papi was a great clutch hitter that year). The timing of Ortiz's hits, which I call his inter-game win adjustment, increased his winning percentage by 0.037, adding 1.2 wins to Ortiz's record.
Component 1: BasestealingFor components where Player decisions are shared across multiple players (e.g., pitchers and fielders in Component 5), I divide credit between players based on the extent to which player winning percentages within the particular component persist over time. I describe this process in more detail in a separate article.
Player Decisions are assessed to baserunners, pitchers, and catchers for stolen bases, caught stealing, pickoffs, and balks.
Component 2: Wild Pitches and Passed Balls
Player Decisions are assessed to baserunners, pitchers, and catchers for wild pitches and passed balls.
Component 3: Balls not in Play
Player Decisions are assessed to batters and pitchers for plate appearances that do not involve the batter putting the ball in play: i.e., strikeouts, walks, and hit-by-pitches.
Component 4: Balls in Play
Player Decisions are assessed to batters and pitchers on balls that are put in play, including home runs, based on how and where the ball is hit.
Component 5: Hits versus Outs on Balls in Play
Player Decisions are assessed to batters, pitchers, and fielders on balls in play, based on whether they are converted into outs or not.
Component 6: Singles versus Doubles versus Triples
Player Decisions are assessed to batters, pitchers, and fielders on hits in play, on the basis of whether the hit becomes a single, a double, or a triple.
Component 7: Double Plays
Player Decisions are assessed to batters, baserunners, pitchers, and fielders on ground-ball outs in double-play situations, based on whether or not the batter grounds into a double play.
Component 8: Baserunner Outs
Player Decisions are assessed to batters, baserunners, and fielders on the basis of baserunner outs.
Component 9: Baserunner Advancements
Player Decisions are assessed to batters, baserunners, and fielders on the basis of how many bases, if any, baserunners advance on balls in play.
Breakdowns of Player Game Points by Component: 1947 - 2012
Distribution of Player Decisions
|Percentage of Component Decisions Allocated to Player Decisions|
|Percent of Total||Batters||Baserunners||Pitchers||Fielders|
|Total Off. / Def. Decisions||91.4%||8.6%||64.2%||35.8%|
|Total Player Decisions||45.7%||4.3%||32.1%||17.9%|
Basic Player Wins and Losses
|pWins||pLosses||pWin Pct.||pWOPA||pWORL|||||eWins||eLosses||eWin Pct.||eWOPA||eWORL|
Context-Neutralized, Teammate-Adjusted Won-Lost Records by FactorThe initial building blocks for Player Won-Lost records are context-neutralized and teammate-adjusted won-lost records by component. These component Player Won-Lost records are summed up by factor: batting, baserunning, pitching, and fielding. These figures, summed across all nine components, for Dontrelle Willis are as follows:
Context-Neutralized, Teammate-Adjusted, Won-Lost Records by Factor
Adjustments to Basic Player Won-Lost RecordsBasic context-neutral player records are adjusted five ways to tie Player won-lost records to team wins and losses.
Context: Inter-Game and Intra-Game
The first two of these are Context multipliers which adjust the player’s total games based on the relative importance of the timing of his performance.
Inter-game context measures the importance of a player’s performance at the time at which it took place. This is analogous to the sabermetric concept of Leverage (the linked article also has parts two and three). Dontrelle Willis’s inter-game context in 2005 was 0.8716.
Intra-game context adjusts Player Won-Lost records so that the total number of Player games is the same in all games. Dontrelle Willis’s intra-game context in 2005 was 1.3213.
Inter-game and intra-game contexts are somewhat negatively correlated as games with higher-than-average inter-game context (i.e., lots of high-leverage situations) will generate more Player wins and losses than games with fewer high-context situations. One can see this negative correlation between inter-game and intra-game context in the case of Dontrelle Willis in 2005.
Willis’s inter-game context was fairly low at 0.872 (i.e. 12.8% below average). This is a fairly common (if slightly low) context level for a starting pitcher. In very close games, particularly extra-inning games, starting pitchers are long gone by the highest-context moments late in these games. Pitcher plate appearences (of which Willis had 101 in 2005) tend to be extremely low-context, since (a) in high-context plate appearances with runners on base, pitchers tend to bunt and I treat bunts as purely context-dependent, which caps the context of these plate appearances at one, and (b) in later-inning high-context plate appearances, pitchers are typically pinch-hit for.
In contrast, Willis’s intra-game context is quite high (1.321 – 32.1% above average) because a large number of his games were extremely one-sided games which, consequently, had very low inter-game context and, hence, led to very few Player wins and losses. In approximately one-third of Willis’s starts (11), for example, the final run differential was 6 or more runs. In Willis’s first two starts of 2005, the Marlins scored single runs in the bottom of the first and second inning and never trailed as Willis won back-to-back complete-game shutouts 9-0 and 4-0. The average intra-game context for those two games was 2.317.
The combined effect of the inter-game and intra-game context multipliers ( 0.8716*1.3213 = 1.1516) is to increase Willis’s Player Games by 15.2% (to 30.3).
Win Adjustments: Inter-Game and Intra-Game
The next two adjustments modify a player’s winning percentage based on the timing of his performance. As with Context, the two considerations here are inter-game performance, and intra-game performance. Inter-game performance measures, in effect, clutch performance. A player who performs better in high-context situations than in low-context situations will have a positive inter-game win adjustment, while a player who performs better in low-context situations than in high-context situations will have a negative inter-game win adjustment. Dontrelle Willis performed very well in the clutch in 2005, as reflected by his inter-game win adjustment which serves to increase his winning percentage by 2.2%. As one example of the “clutchiness” of Willis’s performance, of the 11 home runs allowed by Willis in 2005, only 3 occurred with a runner on base and none occurred with any runners in scoring position. With the bases loaded, batters were 0-for-10 against Willis with one walk and one sacrifice fly.
Intra-game win adjustment adjusts for how Willis’ performance coincided with Marlins’ wins versus losses. Dontrelle Willis had an Intra-Game Win Adjustment of 2.8%. Overall, the Florida Marlins were 23-11 in Willis’s 34 starts. In the 23 Marlins wins, Willis pitched 173-1/3 innings with a 1.40 ERA. In the 11 Marlins losses in which Willis pitched, he pitched 64 innings with a 5.91 ERA. Willis’s performance was more valuable than average to the Florida Marlins in 2005 because he concentrated the best of his performance into games that the Marlins ended up winning.
The final adjustments to tie Player won-lost records to team decisions are teammate adjustments. These are the number of additional wins that a player is credited with because of his teammates based on shared offensive plays and shared defensive plays. In this case, Dontrelle Willis’s total teammate adjustment is -0.10. That is, Willis loses 0.10 wins because his teammates did a poorer-than-average job of playing behind him: e.g., advancing fewer bases than an average baserunner would have or converting fewer balls-in-play into outs than expected. The relationship between teammates on shared Player wins and losses is described here.
Adjustments to Context-Neutral Player Won-Lost Records: Expected Context, Expected Team Win-Normalization
The adjustments described above are not necessarily randomly distributed. Instead, some of these adjustments can be predicted, to some extent, based on either the position played or the performance of the player.
Context (inter-game and intra-game combined) can be predicted as a function of player position. On offense, pitchers tend to bat in below-average contexts, while pinch hitters and pinch runners perform in above-average contexts. On defense, starting pitchers tend to perform in a higher average context than relief pitchers (due to a higher intra-game context). Dontrelle Willis’s expected context in 2005 was 1.0576. This is about 8% lower than Willis’s actual context of 1.1516.
Expected Team Win Adjustment is an adjustment to the Player’s won-lost record to recognize the decentralizing influence of player wins on team wins. That is, a team of players who are each slightly over 0.500 will, in fact, win the overwhelming majority of their games. Expected team win adjustments are the intra-game win adjustment that would be expected on a team that was average with the exception of the particular player. Above-average players will have positive expected team win adjustments and below-average players will have negative expected team win adjustments. Dontrelle Willis had an Expected Intra-Game Win Adjustment of 2.5% in 2005. As noted above, Willis’s actual Intra-Game Win Adjustment was 2.8%, somewhat better than expectations.
For the most part, differences between a player’s expected team win adjustment and his actual intra-game win adjustment will reflect the overall talent of the player’s teammates – a player who plays for an above-average team will tend to have a better intra-game win adjustment than expected and vice-versa. The 2005 Florida Marlins had an above-average offense, finishing second in the National League in park-adjusted OPS (106), third in the NL in runs scored per game on the road (4.60), and, in fact, even managing to finish ninth in the NL in total runs scored despite playing in the second-best pitching park in the National League. Given that, it’s not too surprising that Dontrelle Willis’s intra-game win adjustment was slightly better than expected.
Dontrelle Willis’s final Context-Neutral won-lost record is calculated by taking his basic record of 14.9 - 11.3 and adjusting it in two ways. First, Willis’s total number of Player decisions is adjusted by multiplying his basic number of decisions (26.3) by his expected context (1.0576), giving him a total of 27.8 context-neutral player decisions. Willis’s context-neutral winning percentage is adjusted by taking his basic winning percentage (0.569) and adding his expected team-win adjustment (0.025) to produce a final context-neutral winning percentage of 0.594.
Multiplying Dontrelle Willis’s total context-neutral decisions (27.8) times his context-neutral winning percentage (0.594) produces 16.5 context-neutral wins for Dontrelle Willis. Subtracting this from his total decisions yields 11.3 context-neutral losses. So, Dontrelle Willis’s final context-neutralized, teammate-adjusted won-lost record in 2005 (eWins, eLosses) was 16.5 - 11.3.
Context-Dependent, Teammate-Dependent, Win-DependentCombining basic context-neutral Player wins and losses with the context multipliers and win adjustments outlined above produce a final set of context-dependent, teammate-dependent, win-dependent player wins and losses, pWins and pLosses. These won-lost records are constructed such that the sum of player wins for a team will be equal to team games plus team wins and the sum of player losses for a team will be equal to team games plus team losses. The rationale and methodology for tying player wins and losses to team wins and losses was described earlier.
(1) Adjust basic player wins using teammate adjustment
The teammate adjustment is added to basic context-neutral wins by factor. In the case of Dontrelle Willis, this produces 1.7 offensive wins plus 13.2 defensive wins plus a teammate adjustment of (-0.1) for a total of 14.8 teammate-adjusted wins and a teammate-adjusted winning percentage of 0.565.
(2) Adjust total player decisions for inter-game and intra-game context
Basic player decisions (26.3 for Willis in 2005) are multiplied by inter-game (0.8716) and intra-game (1.3213) context to calculate total context-dependent player decisions. For Dontrelle Willis, this works out to 30.3 total context-dependent games.
(3) Adjust player winning percentage with inter-game and intra-game win adjustments
Dontrelle Willis’s teammate-adjusted winning percentage, calculated above, 0.565, is adjusted by adding Willis’s inter-game win adjustment (2.2%) and his intra-game win adjustment (2.8%), to yield a final context-dependent winning percentage of 0.614.
(4) Calculate total player wins and losses
Dontrelle Willis’s final ‘Context-Dependent’ wins total is then simply equal to games (30.3) times winning percentage (0.614), 18.6 wins. Player losses are equal to Games (30.3) minus Wins (18.6), in this case, 11.7. So Dontrelle Willis's final won-lost record in 2005 (pWins, pLosses) was 18.6 - 11.7
Comparing Players Across Positions: Positional Averages and Positional Replacement LevelsWhile Player Won-Lost Records are (in my opinion) an excellent overall measure of player value, raw Player Won-Lost records are not really an effective tool for comparing players across positions. In constructing Player Won-Lost records, all events are measured against expected, or average, results across the event.
1. Basic Offensive StatisticsAlex Rodriguez and David Ortiz put up similar offensive statistics in 2005. Their traditional statistics are shown below.
|Basic Offensive Statistics, 2005|
|Advanced Offensive Statistics, 2005|
|Player Won-Lost Record: Batting, Context-Neutral|
|eWins||eLosses||eWinPct||eWins over .500|
2. Everything ElseThere’s more to playing baseball than simply batting, of course.
David Ortiz is a rather notoriously slow baserunner with 11 career stolen bases. Alex Rodriguez stole nearly twice as many bases in 2005 alone (21). Even beyond stolen bases, Rodriguez is, in general, a much better baserunner than David Ortiz. The context-neutral baserunning Player Game Points accumulated by each of them are shown below.
|Player Won-Lost Record: Baserunning, Context-Neutral|
|eWins||eLosses||eWinPct||eWins over .500|
David Ortiz is a poor-fielding first baseman who played a total of 78 innings in the field in 2005. Alex Rodriguez is a former Gold-Glove winning shortstop who played 1,390 innings in the field in 2005.
Let’s see how they compare.
|Player Won-Lost Record: Fielding, Context-Neutral|
|eWins||eLosses||eWinPct||eWins over .500|
|Player Won-Lost Record: Context-Neutral|
|eWins||eLosses||eWinPct||eWins over .500|
• Inter-Game Adjustments: Performance in the Clutch
Inter-game contextual factors adjust for the relative importance of a player's performance within the context of a given game. In other words, hitting a home run in the bottom of the ninth inning of a tie game is worth more than hitting a home run leading off the top of the 5th inning of a game in which the player's team is already leading 12-1.
There are two inter-game adjustments to Player won/lost records: Context and Win Adjustments.
• Inter-Game Context
Inter-game context is basically what some other people refer to as Leverage. This measures the relative importance of situations within the context of a single game. In 2005, Alex Rodriguez performed in an average inter-game context of 0.989, about 1.1% below average. This serves to lower A-Rod's total player decisions by 0.5 games.
In contrast, David Ortiz performed in an average inter-game context of 1.035, about 3.5% above average, which increased Papi's total player decisions by 1.1 games.
• Inter-Game Win Adjustment
Of course, the issue in not simply how many high-leverage situations a player performs in, but how well he does in those situations. The MVP argument for David Ortiz was not simply that he had a lot of high-leverage at-bats (which, as we just saw, he did), but that he rose to the occasion in those situations, performing even better in those high-leverage situations than his already-excellent self.
In this regard, David Ortiz excelled. Overall, in 2005, Ortiz batted .300/.397/.604. With runners in scoring position, he improved that to .352/.462/.580. With two outs and runners in scoring position, he batted .368/.507/.719. When the score was tied, Ortiz batted .289/.405/.583. In "late and close" situations, Ortiz batted .346/.447/.846. No matter how you slice the data, Papi delivered big-time in the clutch in 2005. Because of this, his effective winning percentage was better than his context-neutral winning percentage of 0.582. In fact, his inter-game win adjustment increased his winning percentage by 0.037 to an inter-game adjusted winning percentage of 0.620.
Alex Rodriguez, on the other hand, while not as "un-clutch" as maybe some people thought at the time, performed almost exactly the same regardless of the inter-game context, so that his inter-game win adjustment was 0.000.
Taking inter-game context and inter-game win adjustments into account, the comparison between Alex Rodriguez and David Ortiz looks thus.
Player Won-Lost Records, Inter-Game Adjusted: 2005
|Wins||Losses||WinPct||Wins over .500|
• Intra-Game Adjustments: Performance in Team Wins versus Team Losses
In addition to adjusting for inter-game context, I also adjust for intra-game context. As with inter-game adjustments, I adjust for two factors here: Context and Win Adjustments.
• Intra-Game Context
Intra-game context adjusts player wins and losses to normalize the total number of player decisions per game to be equal to exactly three decisions per team per game.
Alex Rodriguez played in an average Intra-Game context of 1.072 about 7.2% above average. This increased Rodriguez's total player decisions by 2.9.
David Ortiz had an average Intra-Game context of 1.015 (1.5% above average), increasing his total player decisions by 0.5.
The intra-game context adjustment basically gives A-Rod as much of an edge in player decisions over Ortiz as the inter-game context adjustment gave to Papi. This is because intra-game context is somewhat negatively correlated to inter-game context. This is because games with lots of high-leverage plays will tend to generate more raw Player Game Points than games with relatively few high-leverage plays. But, at the end of the day, all games count exactly the same in the standings: a team can only win a game once no matter how many clutch hits its players managed to get.
• Intra-Game Win Adjustment
There is one final adjustment that I make to Player Won-Lost records. This adjusts player wins and losses such that the players on a team earn exactly two player wins in any team win and exactly one win in any team loss, and that players earn exactly two player losses in any team loss and exactly one loss in any team win. In this adjustment, positive events which contributed to wins are weighted more heavily than positive events which happened in team losses, while negative events which contributed to team losses get more weight than negative events which happened in team wins.
This final adjustment improves David Ortiz's player winning percentage by 0.006 and A-Rod's winning percentage by 0.023.
This final adjustment benefits both Rodriguez and Ortiz, as they both tended to perform better in games which their teams won than they did in games which their teams lost. Of course, this is true of most players (that’s why their teams win those games after all). Rodriguez and Ortiz were both also helped by the fact that their teams won 95 games apiece.
While this adjustment helped both players, the help to Ortiz was fairly minimal, an extra 0.2 wins (and a reduction of 0.2 losses). Rodriguez, on the other hand, gained more than 5 times as many wins as Ortiz (1.0) by virtue of having produced better in Yankee victories than in Yankee losses.
Does this make sense?
Well, here are A-Rod’s numbers.
|Alex Rodriguez's Batting Line in 2005|
|David Ortiz's Batting Line in 2005|
|Red Sox Wins||94||431||0.332||0.441||0.685||92||104|
|Red Sox Losses||65||282||0.253||0.330||0.490||27||44|
3. Comparing a Third Baseman to a Designated HitterTaking everything into account, here is where we stand with Alex Rodriguez and David Ortiz in 2005.
Final Player Won-Lost Records: 2005
|pWins||pLosses||pWinPct||Wins over .500|
• Positional Average
A player who hit (and ran) like an average third baseman given Alex Rodriguez’s batting opportunities, and fielded like an average third baseman given A-Rod’s fielding opportunities, would have been expected to compile a 0.501 winning percentage. In contrast, a player who hit (and ran) like an average DH/1B given David Ortiz’s batting opportunities, and fielded like an average first baseman given Ortiz’s fielding opportunities, would have been expected to compile a 0.515 winning percentage.
Using these figures for “average”, then, Alex Rodriguez’s final won-lost record was 4.1 pWins over Positional Average (pWOPA) while David Ortiz compiled a pWOPA of 3.6, a somewhat more decisive lead for A-Rod.
• Replacement Level
Alex Rodriguez earned 35% more Player decisions than Ortiz because he played so many more innings in the field than Ortiz. If Rodriguez had earned the same number of decisions as Ortiz (if, say, he missed 40 games to injury), is it likely that the Yankees could have found an average player (which, in Rodriguez’s case, means a 0.501 player) to make up those extra decisions? No, it is not. Instead, the most likely scenario is that the Yankees would have had to make up those Player decisions with a below-average player. Consider who the Yankees played at third base in April of 2009 while A-Rod recovered from a hip injury: Cody Ransom, who batted a robust .190/.256/.329 for the Yankees.
Hence, instead of comparing A-Rod and Papi to average players, a more relevant measure of the relative value contributed by Alex Rodriguez and David Ortiz is to measure how many Wins they contribute over Replacement Level (WORL). In my work, I set Replacement Level one standard deviation below positional average. The standard deviation of Player winning percentages for non-pitchers for 2005 was 4.7%, so that the relevant replacement level for Rodriguez is 0.454 (0.501 - 0.047) and for Ortiz is 0.467.
Wins over Replacement Level for Rodriguez and Ortiz are shown below.
Final Player Won-Lost Records: 2005
|Wins over Positional|
1.   Run-Scoring EnvironmentRuns are more valuable in a lower run-scoring environment. Scoring one run is more likely to lead to winning in an environment where 1-0 victories are fairly common than in an environment where the average final score is 8-6. This is why Player won-lost records control for the run-scoring environment, both for the season and league in which the game took place as well as for the ballpark in which the game was played.
2.   Timing of EventsThe timing of events within a game can affect the value of those events. Hits which drive in runners on base can be viewed as more valuable than hits with the bases empty which do not produce runs. Home runs are more valuable in tie games than when the score is 15-0 (in either direction).
3.   Retrospective ContextThe value of a win is greater than the value of a loss. Retrospectively, one can argue that this means that the value of events are greater if they contribute to a win than if they contribute to a loss.
Value versus True TalentSo what is the difference between "value" and "true talent"? The key difference, as I see it, is that "value" can be directly observed, while "true talent" can only be inferred. Going one step farther, "true talent" can only be inferred from value. Hence, to my mind, measuring value is a necessary first step to being able to assess true talent.
So What's the Point of Context-Neutral Wins and Losses (eWins, eLosses)?So, if context is a necessary condition of measuring player value, then what is the point of the context-neutral wins and losses that I calculate, eWins and eLosses? By constructing wins and losses that are stripped of context, it becomes possible to distinguish the value of what players do (eWins, eLosses) from when players do these things via the Contextual Factors that relate eWins and eLosses to pWins and pLosses.
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.
List of Shorter Articles on Topics Covered Here
Basic Calculation of pWins and pLosses
Basic Calculation of eWins and eLosses
Comparing Player Won-Lost Records across Positions
Wins over Replacement Level
Wins vs. WOPA vs. WORL
Context-Neutral Win Probabilities
pWins vs. eWins
Contextual Factors affecting Player Won-Lost Records
Relationship of pWins to Team Wins
pWins vs. Win Probability Advancements (WPA)
Allocation of Player Wins by Component
Division of Shared Credit between Teammates
Example of Player Won-Lost Records: Dontrelle willis, 2005
2005 AL MVP Race Redux: David Ortiz vs. Alex Rodriguez
Value vs. Talent
Seasons and Games over which Player Won-Lost Records are Calculated