Basics
Baseball Player Wins and Losses
The job of a Major League Baseball player is to help his team win games, for the ultimate purpose of making the playoffs and winning the World Series. Since the early history of Major League Baseball, pitchers have been credited with Wins and Losses as official measures of the effectiveness of their pitching. Of course, Pitcher Wins are a fairly crude measure of how well a pitcher did his job, as wins are the product of the performance of the entire team - batters, baserunners, and fielders, in addition to pitchers.
While the implementation of Pitcher Wins as a measure of pitcher effectiveness is less than ideal, nevertheless the concept is perfectly sound. The ultimate measure of a player's contribution - be he a pitcher, a hitter, a baserunner, or a fielder - is in how much he contributes to his team's wins.
Using play-by-play data compiled from Retrosheet, I have constructed a set of Player won-lost records that attempt to quantify the precise extent to which individual players contribute directly to wins and losses in Major League Baseball on the baseball field.
The purpose of this article is to provide a general overview of Player wins. Links to additional writings by me about Player won-lost records can be found here.
Basic Calculations
The starting point for my construction of Player wins and losses is context-dependent player wins and losses - pWins and pLosses - and the starting point for constructing pWins and pLosses is Win Probabilities. The concept of Win Probability was first developed by Eldon and Harlan Mills in 1969 and published in their book, Player Win Averages.
The basic concept underlying win probability systems is elegantly simple. At any point in time, the situation in a baseball game can be uniquely described by considering the inning, the number and location of any baserunners, the number of outs, and the difference in score between the two teams. Given these four things, one can calculate a probability of each team winning the game. Hence, at the start of a batter's plate appearance, one can calculate the probability of the batting team winning the game. After the completion of the batter's plate appearance, one can once again calculate the probability of the batting team winning the game. The difference between these two probabilities, typically called the Win Probability Advancement or something similar, is the value added by the offensive team during that particular plate appearance (where such value could, of course, be negative).
If we assume that the two teams are evenly matched, then the initial probability of winning is 50% for each team. At the end of the game, the probability of one team winning will be 100%, while the probability of the other team winning will be 0%. The sum of the Win Probability advancements for a particular team will add up to exactly 50% for a winning team (100% minus 50%) and exactly -50% for a losing team (0% minus 50%). Hence, Win Probability Advancement is a perfect accounting structure for allocating credit for team wins and losses to individual players.
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.
I convert these Player Game Points into context-dependent Player Wins and Losses, which I call pWins and pLosses. Given a set of pWins and pLosses for a season, I then also construct a set of context-neutral Player Wins and Losses, called eWins and eLosses as well, which can be compared to pWins and pLosses, 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 decisions, two adjustments are made to these results to move from initial player game points to Player won-lost records.
1. Normalizing Component Won-Lost Records to 0.500
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.
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 won-loss records to ensure that the total number of player wins is exactly equal to the number of player losses 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.
2. Normalizing Player Won-Loss Records by Game
The total number of player game points accumulated in an average major-league game is around 3.3 per team. This number varies tremendously game-to-game, however, with some teams earning 2 wins in some team victories while some other teams may earn 6 wins in team losses. At the end of the day (or season), however, all wins are equal. Hence, in my work, I have chosen to assign each team one player win and one player loss for each team game. In addition, the winning team earns a second full win, while the losing team earns a second full loss. Ties are allocated as 1.5 wins and 1.5 losses for both teams. Context-neutral player decisions (eWins and eLosses) are also normalized to average three Player decisions per game. For eWins and eLosses, this normalization is done at the season level, rather than the game level, so that different numbers of context-neutral player decisions will be earned in different games.
Technically, the second normalization here undoes some of the first normalization. When I first constructed Player won-lost records, I assumed that any such asymmmetries introduced by the second normalization would be random and would be likely to balance out over time. In fact, however, the normalization of games to exactly two pWins per team win (and two pLosses per team loss) led to systematic asymmetries for some components. To correct this, I iterate through these two normalizations three times. That is, I normalize the results so that winning percentages by component and sub-component are equal to 0.500. I then normalize player decisions to tie to team wins and losses. I then take those results, and re-normalize the results by component and sub-component. I then re-normalize those re-normalized results to again tie back to team wins and losses. I then repeat the last two steps two more times.
The result are a set of pWins which tie exactly to team wins (two pWins and one pLoss in team wins, one pWin and two pLosses in team losses) and for which pWin winning percentages are approximately 0.500 for every component and sub-component.
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,
Bryce Harper
led the major leagues in 2015 with
26.3
pWins, while
Jose Altuve
led the majors with
20.9
pLosses.
In comparison, Jake Arrieta led all major league pitchers in 2015 with 22 wins (Arrieta amassed
17.7
pWins) while Shelby Miller (13.9
pLosses) led the major leagues with 17 losses. Over the entire Retrosheet Era, the most pWins accumulated by a player in a single season was
31.4 by Babe Ruth in 1927 (against 14.8 pLosses).
The most single-season pLosses were accumulated by
Leo Norris in 1936 with 23.6 pLosses (and 17.3
pWins).
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 pWins in games which his team won and only credit pLosses in games which his team lost. I have chosen instead to give players some pWins even in team losses and some pLosses 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 (1916 - 2019), 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 a typical 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 pWins in team losses (or pLosses in team wins). That's simply too much lost information 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, bad Major League Baseball teams are not that much worse than good Major League Baseball teams. Surely, we can all remember a time when a first-place team lost two out of three games (or maybe even three out of three games) to a last-place team. Something like this happens pretty much every season.
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 (in a league with no slaughter rule) is for the winning team to do some things that reduce its chances of winning: it has to make 3 outs per inning for at least 8 innings (not counting rain-shortened games). Likewise, a losing team is guaranteed to do some things that increase its chance of winning: it must get the other team out 3 times per inning.
My pWins and pLosses will still reward players, however, 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 can subtract 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 .500 players will be a .500 team (of course), but, for example, a team of .510 players (e.g., 248 - 238) will be a .530 team (86 - 76 in a 162-game season), and a team of .550 players (e.g., 267 - 219) will be a .650 team (105 - 57). At the other extreme, a team of .400 players (e.g., 194 - 292) will be a .200 team (32 - 130).