**Calculating Customized Value Statistics**

Many people (including me) like to distill player values down to a single number, so that they can create lists and rankings of players. The ability to express player values in a single number is a frequent feature of Hall-of-Fame debates, MVP discussions, and trade evaluations. It forms the core of putting together alternate Halls-of-Fame.

Despite my affinity for this type of list-making and ranking, I think the real value of my player won-lost records is the fact that they do

Having said that, I think there is definitely a place for trying to condense everything down to one single number. And when condensing everything down to one number, I think there's a lot to be said for having some flexibility and letting people construct their one number however they want to. To facilitate this, I have created a page which allows people to choose their own weights to create their own uber-stat.

+–Using the Uber-Stat Page

At the top of my "Creat Your Own Customized Statistic" page are a series of options for various choices that one can make in constructing one's statistic.

Simply enter the first and last season over which you would like to construct your stat in the two boxes on this line. The earlier season goes to the left. You can calculate your statistic over a single season by simply entering the same season in both boxes.

That is, suppose one chose a weight of 0.75 for pWins (vs. eWins), for 0.25 for Wins (vs. WOPA vs. WORL) and a weight of 2 for postseason wins. The combined weight, then, for postseason pWins would be 0.75*0.25*2 = .375 (vs. a weight for regular-season pWins of 0.75*0.25 = .1875).

Entering "y" in this box, a player's Player won-lost records for these seasons will be blown up in proportion to his actual games played. So, for example, if a player actually played in 110 games in a particular season, but I only have data for 83 of his games, his record for the season will be multiplied by (110/83) = 1.325. Entering "n" in the box, player statistics will be based only on games for which Retrosheet has released play-by-play data.

After filling in any boxes of interest, press the "Go" button and the table will populate itself. Any boxes which are left blank will retain their most recent value.

The first option is the range of seasons over which the statistic will be calculated. One can only choose seasons for which I have calculated Player won-lost records of course (actually, you could choose seasons for which I haven't calculated records; everybody's records would just all be 0 - 0, by construction).Season Range

Simply enter the first and last season over which you would like to construct your stat in the two boxes on this line. The earlier season goes to the left. You can calculate your statistic over a single season by simply entering the same season in both boxes.

I calculate Player won-lost records two ways: pWins are tied to team records while eWins control for context. One can enter any numbers one wishes in the two boxes on this line.pWins vs. eWins

Wins are simply raw wins - a pure counting stat. WOPA stands for Wins over Positional Average and measures value relative to average. WORL stands for Wins over Replacement Level. One can enter any numbers one wishes in these three boxes.Wins vs. WOPA vs. WORL

Approximately half of all WOPA values will be negative, by construction. It is possible, although fairly rare, for WORL to also be negative. If a "y" is entered in either of these boxes, negative seasonal values for WOPA and/or WORL will be treated as zeroes in calculation. A value of "n" will rely upon raw WOPA and WORL values, regardless of sign.Zero Out Negative Values?

There are 14 separate positions to which one can apply distinct weights: the 8 fielding positions, designated hitter, pinch hitter, pinch runner, a pitcher's offensive contributions, starting pitching, and relief pitching. One can enter any numbers one wishes in these fourteen boxes.By Position

Player won-lost records are calculated for postseason games exactly the same way as they are calculated for regular-season games. One can assign whatever weights one would like to postseason wins, WOPA, and WORL. The weights chosen earlier for pWins vs. eWins and for Wins vs. WOPA vs. WORL will be applied to postseason records as well.Weights for Postseason

That is, suppose one chose a weight of 0.75 for pWins (vs. eWins), for 0.25 for Wins (vs. WOPA vs. WORL) and a weight of 2 for postseason wins. The combined weight, then, for postseason pWins would be 0.75*0.25*2 = .375 (vs. a weight for regular-season pWins of 0.75*0.25 = .1875).

Entering a positive number, p, in this box will normalize all team seasons to p games. So, for example, if a player played in 120 of his team's 162 games in a season and p was set equal to 100, the player's statistics would be scaled down by (100/162), which would reduce the player's effective games played to 74 games (120*[100/162]). Leaving this box blank, or entering the number zero, would use the actual number of team games for all seasons.Normalize seasons to _ Games

For seasons before 1944, Retrosheet is missing play-by-play data for some games. In these cases, Player won-lost records are calculated only for games for which Retrosheet has released play-by-play data.Exprapolate missing player games?

Entering "y" in this box, a player's Player won-lost records for these seasons will be blown up in proportion to his actual games played. So, for example, if a player actually played in 110 games in a particular season, but I only have data for 83 of his games, his record for the season will be multiplied by (110/83) = 1.325. Entering "n" in the box, player statistics will be based only on games for which Retrosheet has released play-by-play data.

The number entered in this box will be the number of players presented in the table below. The table is constructed on the fly and the larger the number entered here, the longer the table may take to be built. Please be patient.Show top _ players

After filling in any boxes of interest, press the "Go" button and the table will populate itself. Any boxes which are left blank will retain their most recent value.

The rest of this article looks in some more detail at the factors that I allow someone to weight.

I calculate two measures of Player won-lost records: pWins & pLosses - which are tied to team wins - and eWins & eLosses - which control for the quality of a player's teammates and the context in which he performed.

The choice between pWins and eWins will likely depend on one's purposes in putting together a list. One could think of pWins as measuring what actually happened, while eWins perhaps measure what*should have* happened. Personally, I think both of these measures provide us with useful and interesting information.

For that reason, my default weights are equal to 0.5 for both pWins and eWins.

The choice between pWins and eWins will likely depend on one's purposes in putting together a list. One could think of pWins as measuring what actually happened, while eWins perhaps measure what

For that reason, my default weights are equal to 0.5 for both pWins and eWins.

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.

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.

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:

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.

In a separate article, I compare Roger Clemens and Greg Maddux. Determining which of these two pitchers had the more valuable career depends, in part, on how one accounts for the 1994-95 strike.

Missing games are not uniform, but are worse for some teams than others. For example, for the 1940s (1940 - 1949), Retrosheet is missing data for only 1% of the games that were played by the Brooklyn Dodgers, but Retrosheet is missing data for 27% of the games that were played by the Chicago White Sox over these same seasons.

The aforementioned Dodgers and White Sox of the 1940s provide an excellent example of the impact of these missing team games on player valuation. Both the Dodgers and White Sox played most of the 1940's with a Hall-of-Fame shortstop. The next table compares the raw Player won-lost records of Luke Appling and Pee Wee Reese from 1940 - 1949 based on the games for which I have complete play-by-play data.

Based on that comparison, it looks like Luke Appling barely played in the first half of the 1940s, while Pee Wee Reese played almost every Dodgers game beginning in 1941. In fact, however, Appling played 139 or more games in 7 seasons over this time period: 1940 - 1943, 1946 - 1948 (both Appling and Reese missed time because of World War II).

The next table extrapoloates the Player won-lost records for for Reese and Appling from 1940 - 1949 based on their Player won-lost records from games for which Retrosheet has play-by-play data.

While extrapolating Player won-lost records in this way can be helpful to try to get a general sense of how players might compare, the resulting numbers are, of course, merely an estimate, based on an implicit assumption that the player(s) performed exactly as well in the missing games as in games for which play-by-play data are available. Nevertheless, I think that this can be a helpful addition to my Player comparison tools.

My default adjustments are to normalize all seasons to 162 games and to extrapolate missing player games.

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).162-Game Season

Second, there have been regular-season games missed due to labor strikes during four seasons 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 exactly 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.Labor Stoppages

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 |
---|---|

1979 | 6 |

1980 | 15 |

1981 | 88 |

1982 | 156 |

1983 | 156 |

1984 | 160 |

1985 | 150 |

1986 | 151 |

1987 | 139 |

1988 | 109 |

1989 | 145 |

1990 | 130 |

1991 | 155 |

1992 | 144 |

1993 | 115 |

1994 | 100 |

1995 | 133 |

1996 | 59 |

1997 | 74 |

1998 | 109 |

1999 | 58 |

2001 | 51 |

2002 | 97 |

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 |
---|---|

1979 | 6 |

1980 | 15 |

1981 | 132 |

1982 | 156 |

1983 | 155 |

1984 | 161 |

1985 | 151 |

1986 | 152 |

1987 | 139 |

1988 | 108 |

1989 | 145 |

1990 | 130 |

1991 | 155 |

1992 | 144 |

1993 | 115 |

1994 | 143 |

1995 | 149 |

1996 | 59 |

1997 | 74 |

1998 | 109 |

1999 | 58 |

2001 | 51 |

2002 | 97 |

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

In a separate article, I compare Roger Clemens and Greg Maddux. Determining which of these two pitchers had the more valuable career depends, in part, on how one accounts for the 1994-95 strike.

The third potential issue with games played is unique to Player won-lost records, rather than to the actual seasons played. 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 seasons prior to 1944. The exact games missing by season and by team are detailed here.Missing Play-by-Play Data

Missing games are not uniform, but are worse for some teams than others. For example, for the 1940s (1940 - 1949), Retrosheet is missing data for only 1% of the games that were played by the Brooklyn Dodgers, but Retrosheet is missing data for 27% of the games that were played by the Chicago White Sox over these same seasons.

The aforementioned Dodgers and White Sox of the 1940s provide an excellent example of the impact of these missing team games on player valuation. Both the Dodgers and White Sox played most of the 1940's with a Hall-of-Fame shortstop. The next table compares the raw Player won-lost records of Luke Appling and Pee Wee Reese from 1940 - 1949 based on the games for which I have complete play-by-play data.

Luke Appling | Pee Wee Reese | |||||||||||

Season |
Games |
pWins |
pLoss |
Win Pct. |
pWOPA | pWORL | Games |
pWins | pLoss | Win Pct. |
pWOPA | pWORL |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1940 | 67 | 9.3 | 7.9 | 0.540 | 0.9 | 1.6 | 84 | 11.7 | 9.8 | 0.543 | 1.2 | 2.1 |

1941 | 55 | 8.5 | 6.7 | 0.562 | 1.1 | 1.8 | 152 | 19.4 | 17.5 | 0.526 | 1.2 | 3.1 |

1942 | 46 | 5.4 | 5.7 | 0.484 | -0.1 | 0.4 | 151 | 21.4 | 17.2 | 0.555 | 2.3 | 4.0 |

1943 | 20 | 2.8 | 2.5 | 0.528 | 0.2 | 0.4 | ||||||

1944 | ||||||||||||

1945 | 18 | 2.1 | 2.3 | 0.480 | -0.0 | 0.1 | ||||||

1946 | 149 | 21.0 | 18.8 | 0.527 | 1.3 | 3.0 | 152 | 22.3 | 15.8 | 0.585 | 3.5 | 5.0 |

1947 | 139 | 17.3 | 16.4 | 0.513 | 0.4 | 1.8 | 142 | 19.0 | 14.0 | 0.576 | 2.5 | 3.8 |

1948 | 139 | 16.0 | 16.1 | 0.499 | -0.2 | 1.1 | 151 | 20.3 | 16.7 | 0.548 | 2.0 | 3.5 |

1949 | 142 | 17.7 | 16.5 | 0.519 | 0.9 | 2.3 | 155 | 23.0 | 16.3 | 0.585 | 3.6 | 5.2 |

------ | ------ | ------ | ------ | ------ | ------ | ------ | ------ | ------ | ------ | ------ | ------ | ------ |

CAREER RECORDS | 775 | 100.2 | 92.8 | 0.519 | 4.4 | 12.6 | 987 | 137.1 | 107.3 | 0.561 | 16.2 | 26.8 |

Based on that comparison, it looks like Luke Appling barely played in the first half of the 1940s, while Pee Wee Reese played almost every Dodgers game beginning in 1941. In fact, however, Appling played 139 or more games in 7 seasons over this time period: 1940 - 1943, 1946 - 1948 (both Appling and Reese missed time because of World War II).

The next table extrapoloates the Player won-lost records for for Reese and Appling from 1940 - 1949 based on their Player won-lost records from games for which Retrosheet has play-by-play data.

Luke Appling | Pee Wee Reese | |||||||||||

Season |
Games |
pWins |
pLoss |
Win Pct. |
pWOPA | pWORL | Games |
pWins | pLoss | Win Pct. |
pWOPA | pWORL |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1940 | 150 | 20.7 | 17.6 | 0.540 | 2.0 | 3.7 | 84 | 11.7 | 9.8 | 0.543 | 1.2 | 2.1 |

1941 | 154 | 23.9 | 18.6 | 0.562 | 3.0 | 5.1 | 152 | 19.4 | 17.5 | 0.526 | 1.2 | 3.1 |

1942 | 142 | 16.6 | 17.7 | 0.484 | -0.4 | 1.2 | 151 | 21.4 | 17.2 | 0.555 | 2.3 | 4.0 |

1943 | 155 | 22.0 | 19.7 | 0.528 | 1.5 | 3.3 | ||||||

1944 | ||||||||||||

1945 | 18 | 2.1 | 2.3 | 0.480 | -0.0 | 0.1 | ||||||

1946 | 149 | 21.0 | 18.8 | 0.527 | 1.3 | 3.0 | 152 | 22.3 | 15.8 | 0.585 | 3.5 | 5.0 |

1947 | 139 | 17.3 | 16.4 | 0.513 | 0.4 | 1.8 | 142 | 19.0 | 14.0 | 0.576 | 2.5 | 3.8 |

1948 | 139 | 16.0 | 16.1 | 0.499 | -0.2 | 1.1 | 151 | 20.3 | 16.7 | 0.548 | 2.0 | 3.5 |

1949 | 142 | 17.7 | 16.5 | 0.519 | 0.9 | 2.3 | 155 | 23.0 | 16.3 | 0.585 | 3.6 | 5.2 |

------ | ------ | ------ | ------ | ------ | ------ | ------ | ------ | ------ | ------ | ------ | ------ | ------ |

CAREER RECORDS | 1,188 | 157.4 | 143.6 | 0.523 | 8.4 | 21.6 | 987 | 137.1 | 107.3 | 0.561 | 16.2 | 26.8 |

My customized uber-stat page allows two types of adjustments based on season length. First, one can normalize the number of team games to adjust for differences between 154-game and 162-game schedules and to account for games lost due to strikes. Second, one can extrapolate missing player records for games for which Retrosheet has not yet released play-by-play data.Adjustments Based on Season Length

While extrapolating Player won-lost records in this way can be helpful to try to get a general sense of how players might compare, the resulting numbers are, of course, merely an estimate, based on an implicit assumption that the player(s) performed exactly as well in the missing games as in games for which play-by-play data are available. Nevertheless, I think that this can be a helpful addition to my Player comparison tools.

My default adjustments are to normalize all seasons to 162 games and to extrapolate missing player games.

I calculate three numbers that could be thought of as expressing player value in a single number: Wins, Wins over Positional Average (WOPA), and Wins over Replacement Level (WORL).

Player wins end up being on a similar scale to traditional pitcher wins: 20 wins is a good season total, 300 wins is an excellent career total.

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.

In order to compare players across positions, it is therefore necessary to normalize players' records relative to an average player at the position(s) a player played.

Focusing on players' wins above average helps to highlight players who had relatively short but brilliant careers, players like Pedro Martinez, whose 194.0 career pWins rank a fairly low 395^{th} in the Retrosheet Era, while his 33.4 pWOPA rank a much more impressive 20^{th}, or Mariano Rivera, whose 126.7 pWins rank even lower than Pedro's (1038^{th}) but who ranks 32^{nd} in career pWOPA with 29.5.

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 0.455 (0.464 for non-pitchers, and 0.439 for pitchers). A team of 0.455 players would have an expected winning percentage of 0.366 (59 - 103 over a 162-game season).

Measuring against replacement level instead of average helps to weed out pure compilers such as Rusty Staub while showing a mix of short excellent careers (e.g., Pedro Martinez) together with long, more modestly above-average careers, such as Don Sutton.

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

As discussed in my aforementioned article, eWins over positional average (eWOPA) does not relate to team wins over .500 on a one-to-one basis (as bWAA and fWAA do), but on something closer to a two-to-one basis, i.e.,

Except for one detail: bWAR and fWAR are both calculated setting team replacement level at .294 (approximately 48-114 over a 162-game season). In contrast, my player-level replacement level is approximately 0.455. As I explain elsewhere, a player-level replacement level of 0.455 works out to a team-level replacement level of 0.366. Converting eWORL from a team-level replacement level of 0.366 to .294 (to match bWAR and fWAR) can be done as follows:

If player replacement level works out to 0.455 and wins over positional average (WOPA) work out to 0.500 (on average), then we can make two general statements:

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:

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.,

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.,

My default weights are equal to 0.14 for Wins, 2.05 for WOPA, and 1 for WORL. These weights are chosen to give roughly equal weight to each of these three measures; the specific weights for wins and WOPA here are set approximately equal to the ratio of the 100th highest career totals across these three values (approximately 278 pWins, 19 pWOPA, and 38 pWORL).

I also give the option of zeroing out negative seasonal values of WOPA and/or WORL. In my default calculations, I zero out negative values of WORL, but do not zero out negative WOPA values.

Player 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.Wins

Player wins end up being on a similar scale to traditional pitcher wins: 20 wins is a good season total, 300 wins is an excellent career total.

In 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.Wins over Positional Average (WOPA)

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.

In order to compare players across positions, it is therefore necessary to normalize players' records relative to an average player at the position(s) a player played.

Focusing on players' wins above average helps to highlight players who had relatively short but brilliant careers, players like Pedro Martinez, whose 194.0 career pWins rank a fairly low 395

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.Wins over Replacement Level (WORL)

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 0.455 (0.464 for non-pitchers, and 0.439 for pitchers). A team of 0.455 players would have an expected winning percentage of 0.366 (59 - 103 over a 162-game season).

Measuring against replacement level instead of average helps to weed out pure compilers such as Rusty Staub while showing a mix of short excellent careers (e.g., Pedro Martinez) together with long, more modestly above-average careers, such as Don Sutton.

The 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.Combining Wins, WOPA, and WORL

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

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 systematically compare my Player won-lost records to WAR in two separate articles.Replicating WAR

As discussed in my aforementioned article, eWins over positional average (eWOPA) does not relate to team wins over .500 on a one-to-one basis (as bWAA and fWAA do), but on something closer to a two-to-one basis, i.e.,

(Wins over .500) ~ bWAA ~ 2*eWOPA

But the difference between WAA (Wins above Average) and WAR (Wins above Replacement) and the difference between WOPA (Wins over Positional Average) and WORL (Wins over Replacement Level) are on the same scale, i.e.,(bWAR - bWAA) ~ (eWORL - eWOPA)

Hence, one can calculate the pWin or eWin-based equivalent of WAR by adding WOPA plus WORL.Except for one detail: bWAR and fWAR are both calculated setting team replacement level at .294 (approximately 48-114 over a 162-game season). In contrast, my player-level replacement level is approximately 0.455. As I explain elsewhere, a player-level replacement level of 0.455 works out to a team-level replacement level of 0.366. Converting eWORL from a team-level replacement level of 0.366 to .294 (to match bWAR and fWAR) can be done as follows:

If player replacement level works out to 0.455 and wins over positional average (WOPA) work out to 0.500 (on average), then we can make two general statements:

(1) WORL - WOPA = 0.045*(Player Decisions)

(2) Wins - WORL = 0.455*(Player Decisions)

Wins over 0.431 = WORL + 0.053*(Wins - WORL) = 0.053*Wins + 0.947*WORL

Combining the earlier result, then, that WAR ~ WOPA + WORL, we can get the Player won-lost version of WAR - eWAR - by fitting the following formula:"eWAR" = 0.053*eWins + eWOPA + 0.947*eWORL

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.Changing Replacement Level

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

My default weights are equal to 0.14 for Wins, 2.05 for WOPA, and 1 for WORL. These weights are chosen to give roughly equal weight to each of these three measures; the specific weights for wins and WOPA here are set approximately equal to the ratio of the 100th highest career totals across these three values (approximately 278 pWins, 19 pWOPA, and 38 pWORL).

I also give the option of zeroing out negative seasonal values of WOPA and/or WORL. In my default calculations, I zero out negative values of WORL, but do not zero out negative WOPA values.

In 2010, Roy Halladay made his 33^{rd} start of the season in the Philadelphia Phillies' 157^{th} 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 34^{th} 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 17.0 - 12.5, 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 17.9 - 12.7, 4.8 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 183.6 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).

My default weights are equal to 1 for each of postseason wins, postseason WOPA, and postseason WORL.

In his next start, Roy Halladay threw a no-hitter against the 91-win Cincinnati Reds. That start was not, however, Halladay's 34

Most baseball statistics - both conventional (e.g., Hank Aaron's 755 career home runs) and sabermetric (e.g., Babe Ruth's 183.6 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).

My default weights are equal to 1 for each of postseason wins, postseason WOPA, and postseason WORL.

I take the position(s) played by a player into account when I calculate wins over average and replacement level. The position(s) that a player plays can also affect his career value. Alternately, one's purpose in putting together a list may prompt one to weight some positions more highly than others, or even to exclude some positions altogether. For example, to produce a list of only position players, one could set the weights for starting and relief pitchers equal to zero. If somebody hates the designated hitter rule strongly enough, he or she can assign a weight of zero to the DH position.

The basic premise of my calculation of wins over positional average (WOPA) is that players at different positions will generate different Player winning percentages. In addition to differences in winning percentages across positions, however, 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).

One fairly interesting result is that pitchers earn a significantly higher percentage of wins over replacement level (pWORL) - 43.8% - than raw decisions - 34.6%. I believe this is true for two reasons, which are expounded upon somewhat in other articles.

Shifting the focus, then, to non-pitcher fielding positions, the first thing that I notice is that the distribution of pWORL is fairly uniform across fielding positions - ranging between 6.8% and 7.3% of total pWORL - with two exceptions: First Basemen, who earn 6.5% of all pWORL, and Catchers, who earn 4.9% 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.

Looking at the top 100 players, the two positions which appear to be the most under-represented are catcher (2.4%) and relief pitcher (1.9%). There is one player in the top 100 in career pWORL who was exclusively a relief pitcher. Mariano Rivera's 42.2 place him 78^{th}; Dennis Eckersley clocks in at #77, although his top 3 seasons in pWORL were 1977, 1978, and 1979, when he was still a starting pitcher.

The position which perhaps appears to be most strongly represented in the top 100 is first base (8.5%).

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 70-80 years.

Extending out to the top 1,000 players, first basemen are no longer remarkable. Catchers are still somewhat under-represented in the top 1,000 list (3.9%), although less than in the top 100 list. The largest under-representation remains relief pitchers (4.9%)

The resulting percentages are shown in the table below.

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.

Two numbers here strike me as most noteworthy: catchers and relief pitchers.

Because the numbers average to 1.0 by construction, the fact that catchers and relief pitchers are "under"-represented means that, on average, all other positions are "over"-represented, by construction. There are, perhaps, some differences in the extent to which different positions are over-represented, most notably second basemen, who appear to be almost perfectly represented (1.002), and first basemen and shortstops, who appear to be the most over-represented (0.927). For the remaining fielding positions (third base and the three outfield positions), the average value in the last column here is equal to 0.962.

Based on these results, I use the following numbers for the customized leaders page: 1.121 for catchers, 0.927 for first basemen, shortstops, and designated hitters, 1.002 for second basemen, 0.962 for other fielding positions (and PH, PR), 0.977 for starting pitchers (and pitcher offense), and 1.522 for relief pitchers. Of course, these weights are all customizable, so you can feel free to set these weights however you'd like on this page.

The basic premise of my calculation of wins over positional average (WOPA) is that players at different positions will generate different Player winning percentages. In addition to differences in winning percentages across positions, however, 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).

Total Decisions |
||

Position | pWins + pLosses | pWORL |
---|---|---|

Catcher | 5.9% | 4.9% |

First Base | 7.0% | 6.5% |

Second Base | 7.8% | 7.2% |

Third Base | 7.7% | 7.0% |

Shortstop | 7.8% | 7.3% |

Left Field | 8.7% | 6.9% |

Center Field | 8.5% | 6.8% |

Right Field | 8.7% | 7.0% |

Designated Hitter | 1.7% | 2.2% |

Pinch Hitter | 1.5% | 0.6% |

Pinch Runner | 0.1% | 0.0% |

Pitcher Offense | 2.0% | 2.8% |

Starting Pitcher | 23.9% | 30.8% |

Relief Pitcher | 8.7% | 10.2% |

So, what do these numbers mean?What Do These Numbers Mean?

One fairly interesting result is that pitchers earn a significantly higher percentage of wins over replacement level (pWORL) - 43.8% - than raw decisions - 34.6%. I believe this is true for two reasons, which are expounded upon somewhat in other articles.

First, being a little above average helps a lot in producing team victories. This effect is more pronounced for pitchers than for position players, because pitchers concentrate their performance into fewer games.The percentage of wins over replacement level (pWORL) earned by pitchers, 43.8%, is similar to pitchers' share of major-league payroll (43.4% in 2014), which is encouraging to me as an economist, suggesting that my numbers here are generally reasonable.

Second, pitchers are somewhat harder to replace than position players, which is reflected in a somewhat lower replacement level for pitchers (an average replacement level of 0.439 over the Retrosheet Era) than for non-pitchers (average replacement level of 0.464).

Shifting the focus, then, to non-pitcher fielding positions, the first thing that I notice is that the distribution of pWORL is fairly uniform across fielding positions - ranging between 6.8% and 7.3% of total pWORL - with two exceptions: First Basemen, who earn 6.5% of all pWORL, and Catchers, who earn 4.9% 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.

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.Relationship between Player Position and Career Length

Position | Total WORL | Top 100 | Top 1,000 |
---|---|---|---|

Catcher | 4.9% | 2.4% | 3.9% |

First Base | 6.5% | 8.5% | 7.6% |

Second Base | 7.2% | 6.8% | 7.1% |

Third Base | 7.0% | 8.9% | 7.6% |

Shortstop | 7.3% | 7.3% | 8.4% |

Left Field | 6.9% | 7.8% | 7.3% |

Center Field | 6.8% | 7.6% | 7.0% |

Right Field | 7.0% | 8.4% | 8.0% |

Designated Hitter | 2.2% | 4.1% | 2.7% |

Pinch Hitter | 0.6% | 0.4% | 0.5% |

Pinch Runner | 0.0% | 0.0% | 0.0% |

Pitcher Offense | 2.8% | 2.8% | 2.8% |

Starting Pitcher | 30.8% | 33.2% | 32.1% |

Relief Pitcher | 10.2% | 1.9% | 4.9% |

Looking at the top 100 players, the two positions which appear to be the most under-represented are catcher (2.4%) and relief pitcher (1.9%). There is one player in the top 100 in career pWORL who was exclusively a relief pitcher. Mariano Rivera's 42.2 place him 78

The position which perhaps appears to be most strongly represented in the top 100 is first base (8.5%).

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 70-80 years.

Extending out to the top 1,000 players, first basemen are no longer remarkable. Catchers are still somewhat under-represented in the top 1,000 list (3.9%), although less than in the top 100 list. The largest under-representation remains relief pitchers (4.9%)

The default weights on my Uber-Leaders page were chosen by me as follows. First, I set aside non-fielding positions - DH, PH, PR, and Pitcher Offense. I tied the DH weight to that of first base, the weight for Pitcher Offense to starting pitching, and the PH/PR weights to the majority of fielding positions. (The page allows one to vary these weights, if desired - so, for example, one could zero out all DH games if one hates the designated hitter enough). Next, I re-calculated the percentages above so that they summed to 100% for the remaining positions.Weighting Player Value by Position(s) Played

The resulting percentages are shown in the table below.

Position | Total WORL | Top 1,000 |
---|---|---|

Catcher | 5.2% | 4.2% |

First Base | 6.8% | 8.1% |

Second Base | 7.6% | 7.6% |

Third Base | 7.4% | 8.1% |

Shortstop | 7.7% | 9.0% |

Left Field | 7.3% | 7.8% |

Center Field | 7.2% | 7.4% |

Right Field | 7.4% | 8.5% |

Starting Pitcher | 32.6% | 34.1% |

Relief Pitcher | 10.8% | 5.3% |

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 1,000 | Average |
---|---|---|---|

Catcher | 1 | 1.243 | 1.121 |

First Base | 1 | 0.844 | 0.922 |

Second Base | 1 | 1.003 | 1.002 |

Third Base | 1 | 0.915 | 0.958 |

Shortstop | 1 | 0.864 | 0.932 |

Left Field | 1 | 0.944 | 0.972 |

Center Field | 1 | 0.962 | 0.981 |

Right Field | 1 | 0.873 | 0.937 |

Starting Pitcher | 1 | 0.954 | 0.977 |

Relief Pitcher | 1 | 2.045 | 1.522 |

Two numbers here strike me as most noteworthy: catchers and relief pitchers.

Because the numbers average to 1.0 by construction, the fact that catchers and relief pitchers are "under"-represented means that, on average, all other positions are "over"-represented, by construction. There are, perhaps, some differences in the extent to which different positions are over-represented, most notably second basemen, who appear to be almost perfectly represented (1.002), and first basemen and shortstops, who appear to be the most over-represented (0.927). For the remaining fielding positions (third base and the three outfield positions), the average value in the last column here is equal to 0.962.

Based on these results, I use the following numbers for the customized leaders page: 1.121 for catchers, 0.927 for first basemen, shortstops, and designated hitters, 1.002 for second basemen, 0.962 for other fielding positions (and PH, PR), 0.977 for starting pitchers (and pitcher offense), and 1.522 for relief pitchers. Of course, these weights are all customizable, so you can feel free to set these weights however you'd like on this page.

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.

Baseball player won-lost records have been constructed by Tom Thress. Feel free to contact me by e-mail or follow me on Twitter.