**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

The Uber-Weights page provides 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. It is not possible (for now) to select a non-continuous range of seasons.

*above* positional average.

One can enter any numbers one wishes in these three boxes.

That is, suppose one chose a weight of 0.75 for pWins (vs. eWins), 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. It is not possible (for now) to select a non-continuous range of seasons.

As with most of the stat pages on my website, one can choose the time period over which positional averages are calculated. This is an option on most stat pages. Options for positional averages are 0.500 for all positions, or position-specific averages calculated over one year, nine years (the year of interest plus four years prior and four years after, if available), or all seasons for which Player won-lost records are calculated (currently 1916 to 2019). For pitchers, one can also choose how to calculate positional averages for starting vs. relief pitchers (0.500 for both, empirical - i.e., overall record for all starters vs. overall record for all relievers, or empirical only for those pitchers who did both in the same season). Positional averages are discussed in more detail here.Positional Averages

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. Replacement Level is set one standard deviation below positional average. Wins over Star (WO*) are wins over "Star Level". Star Level is set one standard deviationWins vs. WOPA vs. WORL vs. WO*

One can enter any numbers one wishes in these three boxes.

Approximately half of all WOPA and a majority of WO* values will be negative, by construction. It is also possible for WORL to be negative for a season. If a "y" is entered in any of these boxes, negative seasonal values for WORL, WOPA, and/or WO* will be treated as zeroes in calculation. A value of "n" will rely upon raw WORL, WOPA and/or WO* 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 for 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. Wins over Star are not calculated for postseason records.Weights for Postseason

That is, suppose one chose a weight of 0.75 for pWins (vs. eWins), 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 1928, 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.Extrapolate 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 final table of players. 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.

In 2018, I self-published a book

The rest of this article looks in some more detail at the factors that I allow someone to weight and identifies the default weights if one simply goes to the Uber Leaders page. Positional averages are discussed in more detail here.

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. Because of this, my default weights are equal to 0.5 each 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

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.

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 1928. The exact games missing by season and by team are detailed here.Missing Play-by-Play Data

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 basic 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). For my Uber-Stat, I have added a fourth number, WO*, or Wins over Star Level.

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 192.4 career pWins rank a fairly low 486^{th} in the Retrosheet Era, while his 62.6 pWOPA rank a much more impressive 27^{th}, or Mariano Rivera, whose 125.9 pWins rank even lower than Pedro's (1228^{th}) but who ranks 31^{st} in career pWOPA with 61.4.

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 0.443 (0.450 for non-pitchers, and 0.430 for pitchers). A team of 0.443 players would have an expected winning percentage of 0.329 (53 - 109 over a 162-game season).

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

*Baseball Player Won-Lost Records: 150 Players, 50 Years* which looks at the top 150 players of the 50 years from 1961 - 2010 as measured by an uber-stat which I created at that time. For that work, I created a fourth "wins" measure, Wins over Star, or WO*.

In my work, replacement level is set equal to one standard deviation below positional average. I set "star level" equal to one standard deviation above positional average. The idea is that, while WORL will give value to players who are below-average but not necessarily terrible, WO* was intended to only give value to players who are not merely above average, but are "stars". The purpose of introducing WO* was to provide a means of giving players credit for their peak performance above and beyond the extent to which a strong peak translates into strong career numbers.

The idea behind WO* is that, in certain situations (such as, perhaps, Hall of Fame voting) there may be no value in a player merely being average or even slightly above average. The Hall of Fame, the idea would go, is for "stars". I once read somebody make the argument against Omar Vizquel's Hall-of-Fame candidacy as "If a player wasn't a Hall-of-Famer at his best, he can't become a Hall-of-Famer just by playing a long time." I'm not taking a position for or against that view, I'm just explaining why I've included WO* as an option here.

With my recalculation of WOPA in July 2019, the concept of WO*, as I had been calculating it, became somewhat problematic - WO* values have become considerably more extreme to a degree to which I am not entirely comfortable. In addition, while I like the idea behind WO* - for Hall-of-Fame debates, do we even want to give credit to a player for being merely average - I am not convinced that WO* provides new information above and beyond WOPA and WORL (e.g., if one simply uses WOPA as one's Hall-of-Fame measure, then one will not give credit to a player for being merely average). Because of this, I have removed WO* from my Player pages and, initially, I eliminated it as a potential input into my Uber-Stat calculations in my initial July 2019 re-release.

At the request of some users of my website, I have put WO* back as an option in calculating user-defined uber-stats. In doing so, however, I would give two cautions. First, I would argue strongly that one should zero out negative WO* values. Failing to do so will lead to reducing a player's uber-stat not merely for below-replacement or even for below-average seasons but for seasons which were above average but simply not*enough* above average. Second, I would be conservative in assigning a weight to WO*. While I do think that WO* has some analytical value, I think the additional information provided by WO* over and above WOPA and WORL is probably limited.

That said, the purpose of my uber-stats page is to allow people to create their own uber-statistics based on their own personal preferences. And I think it best that this includes allowing people to set their own personal weight on WO* (and to choose whether or not to zero out negative values).

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

*Baseball Player Won-Lost Records: 150 Players, 50 Years*, the weights I chose for these four values were based on the 300th-best career value in each of these four statistics over the 50 seasons from 1961 through 2010.

Using this same 50-season time period, the next table shows various measures for these four statistics - weighting pWins and eWins at 50% each and zeroing out negative values for all four statistics. The second table normalizes the values in the first table such that the weight on WORL is equal to one by construction (i.e., the WORL values in the first table are all divided by the various other values to construct the weights in the second table). One could use the second table here to perhaps construct weights which attempted to give equal weight to a player's performance across all four measures of value.

As noted above, my replacement level works out to around 0.443. Wins over positional average (WOPA) works out to 0.500 on average. Knowing this, we can make two general statements:

Doing some simple algebra to isolate (Player Decisions) on the right side of the equations, then, we get:

Suppose you wanted to set replacement level at 0.480. You want to add 0.020*(Player Decisions) to WOPA. Plugging equation (1) above into that, 0.020*(Player Decisions) equals 0.020*(1/0.058)*(WORL - WOPA), which simplifies to 0.345*(WORL - WOPA), i.e.,

Suppose you wanted to set replacement level at 0.342. You want to add 0.100*(Player Decisions) to WORL, or, from (2) above: (.1/.442)*(Wins - WORL), i.e.,

One word of caution: my player-level replacement levels are not team-level replacement levels. Because I assign two pWins and one pLoss to the winning team in every game, team winning percentage and player winning percentage are related by the following formula:

When I initially put together Player won-lost records, my eWins over positional average (eWOPA) were approximately half as large as wins above average (WAA) as used by Baseball-Reference and Fangraphs in constructing their WAR values, i.e.,

The only difference, then, conceptually, between my wins over replacement level (WORL) and the two most popular versions of WAR (bWAR and fWAR) now is the replacement level.

Both bWAR and fWAR are calculated setting team replacement level at .294 (approximately 48-114 over a 162-game season). In contrast, my player-level replacement level is approximately 0.443. As I explain elsewhere, a player-level replacement level of 0.443 works out to a team-level replacement level of 0.329. Converting eWORL from a team-level replacement level of 0.329 to .294 (to match bWAR and fWAR) can be done as follows:

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 for both of these statistics.

Player wins are calculated such that the players on a team earn three Player decisions per game. I calculate two sets of Player wins: pWins are tied to team wins - the players on a winning team earn two pWins and one pLoss, the players on a losing team earn one pWin and two 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 192.4 career pWins rank a fairly low 486

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 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 0.443 (0.450 for non-pitchers, and 0.430 for pitchers). A team of 0.443 players would have an expected winning percentage of 0.329 (53 - 109 over a 162-game season).

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

In 2018, I self-published a bookWO*

In my work, replacement level is set equal to one standard deviation below positional average. I set "star level" equal to one standard deviation above positional average. The idea is that, while WORL will give value to players who are below-average but not necessarily terrible, WO* was intended to only give value to players who are not merely above average, but are "stars". The purpose of introducing WO* was to provide a means of giving players credit for their peak performance above and beyond the extent to which a strong peak translates into strong career numbers.

The idea behind WO* is that, in certain situations (such as, perhaps, Hall of Fame voting) there may be no value in a player merely being average or even slightly above average. The Hall of Fame, the idea would go, is for "stars". I once read somebody make the argument against Omar Vizquel's Hall-of-Fame candidacy as "If a player wasn't a Hall-of-Famer at his best, he can't become a Hall-of-Famer just by playing a long time." I'm not taking a position for or against that view, I'm just explaining why I've included WO* as an option here.

With my recalculation of WOPA in July 2019, the concept of WO*, as I had been calculating it, became somewhat problematic - WO* values have become considerably more extreme to a degree to which I am not entirely comfortable. In addition, while I like the idea behind WO* - for Hall-of-Fame debates, do we even want to give credit to a player for being merely average - I am not convinced that WO* provides new information above and beyond WOPA and WORL (e.g., if one simply uses WOPA as one's Hall-of-Fame measure, then one will not give credit to a player for being merely average). Because of this, I have removed WO* from my Player pages and, initially, I eliminated it as a potential input into my Uber-Stat calculations in my initial July 2019 re-release.

At the request of some users of my website, I have put WO* back as an option in calculating user-defined uber-stats. In doing so, however, I would give two cautions. First, I would argue strongly that one should zero out negative WO* values. Failing to do so will lead to reducing a player's uber-stat not merely for below-replacement or even for below-average seasons but for seasons which were above average but simply not

That said, the purpose of my uber-stats page is to allow people to create their own uber-statistics based on their own personal preferences. And I think it best that this includes allowing people to set their own personal weight on WO* (and to choose whether or not to zero out negative values).

The choice between wins, WORL, WOPA, and WO* 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, WORL, WOPA, and WO*

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

In the past, I have set my default weights for Wins, WORL, WOPA, and WO* in such a way that the N-th-best career value in each statistic over a particular time period would be worth the same value. So, for example, in my book,Relative Weights for Wins, WORL, WOPA, and WO*

Using this same 50-season time period, the next table shows various measures for these four statistics - weighting pWins and eWins at 50% each and zeroing out negative values for all four statistics. The second table normalizes the values in the first table such that the weight on WORL is equal to one by construction (i.e., the WORL values in the first table are all divided by the various other values to construct the weights in the second table). One could use the second table here to perhaps construct weights which attempted to give equal weight to a player's performance across all four measures of value.

Player # | Wins | WORL | WOPA | WO* |

Total | 309,926.7 | 44,133.6 | 21,358.8 | 7,998.9 |

1 | 464.8 | 169.6 | 131.8 | 94.9 |

100 | 260.5 | 55.1 | 32.3 | 15.3 |

300 | 189.1 | 31.7 | 16.7 | 6.6 |

500 | 150.9 | 23.6 | 11.3 | 4.0 |

1000 | 100.0 | 13.3 | 5.8 | 1.6 |

Player # | Wins | WORL | WOPA | WO* |

Total | 0.1424 | 1.0000 | 2.0663 | 5.5174 |

1 | 0.3650 | 1.0000 | 1.2872 | 1.7870 |

100 | 0.2113 | 1.0000 | 1.7028 | 3.6002 |

300 | 0.1678 | 1.0000 | 1.8997 | 4.7801 |

500 | 0.1566 | 1.0000 | 2.0943 | 5.8393 |

1000 | 0.1335 | 1.0000 | 2.2967 | 8.2077 |

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 at my uber-stat page.Changing Replacement Level

As noted above, my replacement level works out to around 0.443. Wins over positional average (WOPA) works out to 0.500 on average. Knowing this, we can make two general statements:

(1) | WORL - WOPA | = | .058*(Player Decisions) |

(2) | Wins - WORL | = | .442*(Player Decisions) |

Doing some simple algebra to isolate (Player Decisions) on the right side of the equations, then, we get:

(1) | (1/0.058)*(WORL - WOPA) | = | (Player Decisions) |

(2) | (1/0.442)*(Wins - WORL) | = | (Player Decisions) |

Suppose you wanted to set replacement level at 0.480. You want to add 0.020*(Player Decisions) to WOPA. Plugging equation (1) above into that, 0.020*(Player Decisions) equals 0.020*(1/0.058)*(WORL - WOPA), which simplifies to 0.345*(WORL - WOPA), i.e.,

Wins over 0.480 = WOPA + 0.345*(WORL - WOPA) = 0.655*WOPA + 0.345*WORL

Suppose you wanted to set replacement level at 0.342. You want to add 0.100*(Player Decisions) to WORL, or, from (2) above: (.1/.442)*(Wins - WORL), i.e.,

Wins over 0.342 = WORL + (.226)*(Wins - WORL) = (.774)*WORL + (.226)*Wins

One word of caution: my player-level replacement levels are not team-level replacement levels. Because I assign two pWins and one pLoss to the winning team in every game, team winning percentage and player winning percentage are related by the following formula:

Team Win Pct. = (pWinPct - (1/3)) / (1/3)

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 (hereafter bWAR) as well as at Fangraphs.com (hereafter fWAR).Replicating WAR

When I initially put together Player won-lost records, my eWins over positional average (eWOPA) were approximately half as large as wins above average (WAA) as used by Baseball-Reference and Fangraphs in constructing their WAR values, i.e.,

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

I have recently changed my calculation of of eWOPA (and pWOPA), however, so that it is now on the same scale as WAA.The only difference, then, conceptually, between my wins over replacement level (WORL) and the two most popular versions of WAR (bWAR and fWAR) now is the replacement level.

Both bWAR and fWAR are calculated setting team replacement level at .294 (approximately 48-114 over a 162-game season). In contrast, my player-level replacement level is approximately 0.443. As I explain elsewhere, a player-level replacement level of 0.443 works out to a team-level replacement level of 0.329. Converting eWORL from a team-level replacement level of 0.329 to .294 (to match bWAR and fWAR) can be done as follows:

(1) Calculate the Player win percentage that corresponds to a team winning percentage of .294,Using the formula shown above, a team-level replacement level of .294 would work out a player replacement level of .431. To set player-level replacement level at .431, you want to subtract 0.012*(Player Decisions) from WORL, or, from above: (0.012/0.443)*(Wins - WORL), i.e.,

(2) Adjust the replacement level underlying WORL as outlined above.

Wins over 0.431 = WORL + 0.027*(Wins - WORL) = 0.027*Wins + 0.973*WORL

My default weights for the Uber-Statistics page on the website are zero for wins, 1.5 for WOPA and 1.0 for WORL. These are purely subjective and, of course, can be changed to whatever numbers one desires.Default Weights

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 for both of these statistics.

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 16.9 - 12.4, good for 7.5 pWORL. If he had pitched the no-hitter against the Reds two days earlier, in the regular season, his record would have instead been 17.8 - 12.6, 8.3 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 (eWins, eLosses) by player position. It also shows the distribution of Player wins over replacement level (eWORL).

One fairly interesting result is that pitchers earn a significantly higher percentage of wins over replacement level (eWORL) - 43.4% - than raw decisions - 34.0%. I believe this is true for two reasons, which are expounded upon somewhat in other articles.

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 (1.8%) and relief pitcher (0.5%). There are no players in the top 100 in career eWORL who were exclusively a relief pitcher (Mariano Rivera's 61.4 place him 103^{rd}).

The position which perhaps appears to be most strongly represented in the top 100 is first base (9.4%).

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 eWORL 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 (3.1%), although less than in the top 100 list. The largest under-representation remains relief pitchers (2.1%)*Baseball Player Won-Lost Records: 150 Players, 50 Years*, I assigned unique weights for positions based on a variation of the above table. For the website, I have simplified the default weights considerably: 1.15 for catchers and 1.0 for all other positions.

Of course, the entire point of this sheet is that 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 (eWins, eLosses) by player position. It also shows the distribution of Player wins over replacement level (eWORL).

Total Decisions |
||

Position | eWins + eLosses | eWORL |
---|---|---|

Catcher | 5.9% | 5.1% |

First Base | 6.9% | 5.9% |

Second Base | 8.0% | 6.8% |

Third Base | 7.7% | 6.6% |

Shortstop | 8.1% | 6.9% |

Left Field | 8.7% | 7.5% |

Center Field | 8.4% | 7.2% |

Right Field | 8.6% | 7.3% |

Designated Hitter | 1.6% | 1.6% |

Pinch Hitter | 1.8% | 1.6% |

Pinch Runner | 0.1% | 0.1% |

Pitcher Offense | 1.9% | 2.2% |

Starting Pitcher | 24.3% | 28.4% |

Relief Pitcher | 7.8% | 12.7% |

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 (eWORL) - 43.4% - than raw decisions - 34.0%. 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.Shifting the focus, then, to non-pitcher fielding positions, the first thing that I notice is that the distribution of eWORL is fairly uniform across fielding positions - ranging between 6.6% and 7.5% of total eWORL - with two exceptions: First Basemen, who earn 5.9% of all eWORL, and Catchers, who earn 5.1% of all eWORL.

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 0.430 over the Retrosheet Era) than for non-pitchers (average replacement level of 0.450).

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 eWORL by player position for three sets of players: everybody for whom Player won-lost records have been calculated, the top 100 players in career eWORL, and the top 1,000 players in career eWORL.Relationship between Player Position and Career Length

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

Catcher | 5.1% | 1.8% | 3.1% |

First Base | 5.9% | 9.4% | 8.9% |

Second Base | 6.8% | 7.2% | 7.5% |

Third Base | 6.6% | 9.3% | 9.1% |

Shortstop | 6.9% | 8.8% | 8.2% |

Left Field | 7.5% | 12.4% | 10.6% |

Center Field | 7.2% | 9.8% | 8.9% |

Right Field | 7.3% | 11.5% | 11.4% |

Designated Hitter | 1.6% | 3.8% | 2.8% |

Pinch Hitter | 1.6% | 0.8% | 0.9% |

Pinch Runner | 0.1% | 0.0% | 0.0% |

Pitcher Offense | 2.2% | 1.8% | 2.0% |

Starting Pitcher | 28.4% | 23.2% | 24.5% |

Relief Pitcher | 12.7% | 0.5% | 2.1% |

Looking at the top 100 players, the two positions which appear to be the most under-represented are catcher (1.8%) and relief pitcher (0.5%). There are no players in the top 100 in career eWORL who were exclusively a relief pitcher (Mariano Rivera's 61.4 place him 103

The position which perhaps appears to be most strongly represented in the top 100 is first base (9.4%).

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 eWORL 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 (3.1%), although less than in the top 100 list. The largest under-representation remains relief pitchers (2.1%)

In my book,Weighting Player Value by Position(s) Played

Of course, the entire point of this sheet is that 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, follow me on Twitter, and/or subscribe to my YouTube channel.

Baseball player won-lost records have been constructed by Tom Thress. Feel free to contact me by e-mail, follow me on Twitter, and/or subscribe to my YouTube channel.