The starting point for my construction of Player Wins and Losses is context-dependent Player wins and losses and the starting point for constructing context-dependent wins and losses is Win Probabilities.

Changes in Win Probabilities are credited to the individual players responsible for these changes. These contributions are called Player Game Points here. Positive changes in Win Probabilities are credited as Positive Player Game Points, while negative changes in Win Probabilities are credited as Negative Player Game Points.

Player Game Points are assigned to both offensive and defensive players on each individual play. Anything which increases the probability of the offensive team winning is credited as Positive Points to the offensive player(s) involved and as Negative Points to the defensive player(s) involved. Anything which increases the probability of the defensive team winning is credited as Positive Points to the defensive player(s) involved and as Negative Points to the offensive player(s) involved. Within any individual game, the number of Positive Player Game Points by offensive players on one team will be exactly equal to the number of Negative Player Game Points by defensive players on the other team and vice versa. Similarly, the number of Positive Player Game Points collected by members of the winning team will exactly equal the number of Negative Player Game Points accumulated by the losing team (and, again, vice versa).

Player Game Points assigned in this way provide a perfect accounting structure for assigning 100% of the credit for all changes in Win Probability to players on both teams involved in a game. The sum of the Positive Player Game Points minus the sum of the Negative Player Game Points for one team in one game will always be the same for any team win (0.5) or loss (-0.5). Most Win Probability systems which I have seen focus on a single number, which is (more or less) the difference between Positive Player Game Points and Negative Player Game Points, and define this number as something like Win Probability Advancements or Game State Wins, or the like. For such systems, this is where the process stops, with final results being expressed as some measure of net Win Probability added, although Fangraphs does show what it calls "+WPA" and "-WPA" separately.

Personally, I find such a construction unsatisfactory. To my mind, net Win Probabilities added don’t reveal the full context in which a player’s performance took place. From my perspective, 9 wins and 2 losses is a different performance than 15 wins and 8 losses, and that difference needs to be maintained. Moreover, expressing Win Probability Added (WPA) as a single number does not enable one to isolate the specific contextual factors underlying that performance, thereby assessing the extent to which a player’s performance was influenced by the performances of his teammates and the specific timing of his performance.

Hence, I convert these Player Game Points into Context-Dependent Player Wins and Losses, which I call pWins and pLosses. I simultaneously construct Context-Neutral Player Wins and Losses, called eWins and eLosses as well, which can be compared to Context-Dependent Player Wins and Losses to identify the contextual factors affecting players’ performances and how those contextual factors affect the translation of Player Wins and Losses into team wins and losses.

For both Context-Dependent and Context-Neutral Player Games, two adjustments are made to these results to move from initial Player Game Points to Player Won-Lost records.

So, for example, if Player Won-Loss records are calculated correctly, the total number of wins accumulated by baserunners on third base for advancing on wild pitches and passed balls should be exactly equal to the total number of losses accumulated by baserunners on third base for failing to advance on wild pitches or passed balls. Likewise, the total number of wins accumulated by second basemen for turning double plays on ground balls in double-play situations should be exactly equal to the total number of losses accumulated by second basemen for failing to turn double plays on ground balls in double-play situations.

To ensure this symmetry, therefore, I normalize Player Game Points to ensure that the total number of Positive Player Game Points is exactly equal to the number of Negative Player Game Points for every Component of Player Game Points as well as by sub-component, at the finest level of detail which makes logical sense in each case.

Changes in Win Probabilities are credited to the individual players responsible for these changes. These contributions are called Player Game Points here. Positive changes in Win Probabilities are credited as Positive Player Game Points, while negative changes in Win Probabilities are credited as Negative Player Game Points.

Player Game Points are assigned to both offensive and defensive players on each individual play. Anything which increases the probability of the offensive team winning is credited as Positive Points to the offensive player(s) involved and as Negative Points to the defensive player(s) involved. Anything which increases the probability of the defensive team winning is credited as Positive Points to the defensive player(s) involved and as Negative Points to the offensive player(s) involved. Within any individual game, the number of Positive Player Game Points by offensive players on one team will be exactly equal to the number of Negative Player Game Points by defensive players on the other team and vice versa. Similarly, the number of Positive Player Game Points collected by members of the winning team will exactly equal the number of Negative Player Game Points accumulated by the losing team (and, again, vice versa).

Player Game Points assigned in this way provide a perfect accounting structure for assigning 100% of the credit for all changes in Win Probability to players on both teams involved in a game. The sum of the Positive Player Game Points minus the sum of the Negative Player Game Points for one team in one game will always be the same for any team win (0.5) or loss (-0.5). Most Win Probability systems which I have seen focus on a single number, which is (more or less) the difference between Positive Player Game Points and Negative Player Game Points, and define this number as something like Win Probability Advancements or Game State Wins, or the like. For such systems, this is where the process stops, with final results being expressed as some measure of net Win Probability added, although Fangraphs does show what it calls "+WPA" and "-WPA" separately.

Personally, I find such a construction unsatisfactory. To my mind, net Win Probabilities added don’t reveal the full context in which a player’s performance took place. From my perspective, 9 wins and 2 losses is a different performance than 15 wins and 8 losses, and that difference needs to be maintained. Moreover, expressing Win Probability Added (WPA) as a single number does not enable one to isolate the specific contextual factors underlying that performance, thereby assessing the extent to which a player’s performance was influenced by the performances of his teammates and the specific timing of his performance.

Hence, I convert these Player Game Points into Context-Dependent Player Wins and Losses, which I call pWins and pLosses. I simultaneously construct Context-Neutral Player Wins and Losses, called eWins and eLosses as well, which can be compared to Context-Dependent Player Wins and Losses to identify the contextual factors affecting players’ performances and how those contextual factors affect the translation of Player Wins and Losses into team wins and losses.

For both Context-Dependent and Context-Neutral Player Games, two adjustments are made to these results to move from initial Player Game Points to Player Won-Lost records.

A key implicit assumption underlying my Player Won-Loss Records is that Major League Baseball players will have a combined winning percentage of 0.500. While this is trivially true at the aggregate level, almost regardless of what you do, it should also be true at finer levels of detail as well.1. Normalizing Component Won-Lost Records to 0.500

So, for example, if Player Won-Loss records are calculated correctly, the total number of wins accumulated by baserunners on third base for advancing on wild pitches and passed balls should be exactly equal to the total number of losses accumulated by baserunners on third base for failing to advance on wild pitches or passed balls. Likewise, the total number of wins accumulated by second basemen for turning double plays on ground balls in double-play situations should be exactly equal to the total number of losses accumulated by second basemen for failing to turn double plays on ground balls in double-play situations.

To ensure this symmetry, therefore, I normalize Player Game Points to ensure that the total number of Positive Player Game Points is exactly equal to the number of Negative Player Game Points for every Component of Player Game Points as well as by sub-component, at the finest level of detail which makes logical sense in each case.

The total number of Player Game Points accumulated in an average Major League Baseball game is around 3.3 per team. This number varies tremendously game-to-game, however, with some teams earning 2 wins in some team victories while some other teams may earn 6 wins in team losses. At the end of the day (or season), however, all wins are equal. Hence, in my work, I have chosen to assign each team one Player Win and one Player Loss for each team game. In addition, the winning team earns a second full Win, while the losing team earns a second full Loss. Ties are allocated as 1.5 Wins and 1.5 Losses for both teams. Context-neutral player decisions (eWins/eLosses) are also normalized to average three Player decisions per game. For eWins and eLosses, this normalization is done at the season level, rather than the game level, so that different numbers of context-neutral player decisions will be earned in different games.2. Normalizing Player Game Points by Game

**Why 3 Player Decisions per Game?**

The choice of three Player Decisions per game here is largely arbitrary. I chose three because the resulting Player Won-Lost records end up being on a similar scale to traditional pitcher won-lost records, with which most baseball fans are quite familiar.
For example, expressed in this way,
Jayson Werth
led the major leagues in 2010 with
23.5
(Context-Dependent) Player Wins, while
Ichiro Suzuki
led the majors with
21.7
losses.

In comparison, C.C. Sabathia and Roy Halladay led all major league pitchers in 2010 with 21 wins (Sabathia amassed
16.2
Player Wins, while Halladay had
17.1
) while Joe Saunders (14.4
Player losses) led the major leagues with 17 losses.
The relationship between team-dependent wins and traditional Pitcher Wins is explored elsewhere.
Over the entire Retrosheet Era, the most pWins accumulated by a player in a single season was
31.0 by Babe Ruth in 1927 (against 15.1 pLosses).
The most single-season pLosses were accumulated by
Vladimir Guerrero in 2001 with 23.2 pLosses (and 25.5
pWins).

This normalization process has no effect on the relative ordering of players – if pWins and pLosses were normalized to be equal to 6 per game,
Jayson Werth
would have continued to lead the major leagues in wins in 2010, he would simply would have had twice as many of them. Nor does it affect player winning percentages, as pWins and pLosses are scaled proportionally.

One consequence of my choice of three Player Decisions per team game is that, as a result of this normalization process, total Player Wins for a league as a whole will be equal to total Win Shares as constructed by Bill James. Hence, one might think of Player Won-Lost records as calculated here as measuring “true” win shares.

Because the players on a team receive only two team-dependent wins for each team win, however, the total number of team-dependent wins will be less than the total number of Win Shares for teams with winning records. On the other hand, because the players on a team receive one team-dependent win for each team loss, the total number of team-dependent wins will be greater than the total number of Win Shares for teams with losing records. The comparison between team-dependent wins and Win Shares is explored elsewhere.

**Why Do Players Get Wins in Games Their Team Loses?**

If one is interested in assigning credit to players for team wins or blame to players for team losses, one might think that it would make sense to only credit a player with Player wins in games which his team won and only credit Player losses in games which his team lost. I have chosen instead to give players some wins even in team losses and some losses even in team wins. I do this for a couple of reasons.

Most simply put, baseball players do tons of positive things in team losses and baseball players do tons of negative things in team wins. Throwing away all of those things based solely on the final score of the game leads, in my opinion, to too much valuable data simply being lost. It makes the results too dependent on context.

As I noted above, in the average major-league baseball game of the Retrosheet Era (1922 - 2013), the average team amasses 3.3 Player Game Points. The win probability for the winning team goes from 50% at the start of the game to 100% at the end, so that the winning team will amass exactly 0.5 more positive Player Game Points than negative Player Game Points by construction. This means that the players on an average winning team will amass a combined record of something like 1.9 - 1.4 in an average game. That works out to a 0.576 winning percentage, or about 93 wins in a 162-game schedule (93-69). Put another way, more than 40% of all Player Game Points (1 - 0.576) would be zeroed out in a system that credited no Player wins in team losses (or Player losses in team wins). That's simply too much for me to be comfortable making such an adjustment.

There are two reasons why such a large percentage of plays do not contribute to victory. First, it is indicative, I think, of the fairly high level of competitive balance within Major-League Baseball. Put simply, even very bad Major-League Baseball teams are not that much worse than very good Major-League Baseball teams.

But the other reason why such a large percentage of plays do not contribute to victory, and why I assign player wins even in team losses and vice-versa, is because of the rules of baseball. Because there is no clock in baseball, the only way for a game to end is for even the winning team to do some things that reduce its chances of winning: it has to make 3 outs per inning for at least 8 innings. Likewise, a losing team is guaranteed to do some things that increase its chance of winning: it must get the other team out 3 times per inning.

My system still rewards players who do positive things that contribute to wins more favorably than players who do positive things that lead to losses. As I noted above, an average team will amass a player winning percentage of approximately 0.576 in team wins (and 0.424 in team losses). By assigning 2 wins and only 1 loss in team wins, however, players will amass a 0.667 player winning percentage in team wins (and 0.333 in team losses). So, player wins that lead to team wins will still be more valuable than player wins that happen in team losses. The latter are simply not worthless.

**Relationship of Player Decisions to Team Decisions**

Under my system, to move from players’ team-dependent won-lost records (pWins and pLosses) to a team won-lost record, one subtracts out what I call “background wins” and “background losses.” One-third of a player’s decisions are background wins and one-third of a player’s decisions are background losses. Mathematically, then, if the sum of the team-dependent won-lost records of the players on a team is W wins and L losses, then the team’s won-lost record will be as follows:

Team Wins = W – (W + L) / 3; Team Losses = L – (W + L) / 3

As some practical examples, a team of 0.500 players will be a 0.500 team (of course), but, for example, a team of 0.510 players (e.g., 248 – 238) will be a 0.530 team (86-76 in a 162-game season), and a team of 0.550 players (e.g., 267 – 219) will be a 0.650 team (105-57). At the other extreme, a team of 0.400 players (e.g., 194 – 292) will be a 0.200 team (32-130).

The relationship between pWins and team wins is explored in a bit more detail elsewhere. The impact of player winning percentage on team winning percentage has interesting implications in terms of optimal player valuation. This issue is expanded upon elsewhere. An example of the Player Won-Lost record for a player – Dontrelle Willis in 2005 - is here.

The top (and bottom) 100 players in career regular-season pWins (total as well as over positional average, and replacement level) can be found here.

As some practical examples, a team of 0.500 players will be a 0.500 team (of course), but, for example, a team of 0.510 players (e.g., 248 – 238) will be a 0.530 team (86-76 in a 162-game season), and a team of 0.550 players (e.g., 267 – 219) will be a 0.650 team (105-57). At the other extreme, a team of 0.400 players (e.g., 194 – 292) will be a 0.200 team (32-130).

The relationship between pWins and team wins is explored in a bit more detail elsewhere. The impact of player winning percentage on team winning percentage has interesting implications in terms of optimal player valuation. This issue is expanded upon elsewhere. An example of the Player Won-Lost record for a player – Dontrelle Willis in 2005 - is here.

The top (and bottom) 100 players in career regular-season pWins (total as well as over positional average, and replacement level) can be found here.