Baseball Player Wins and Losses
1. Normalizing Component Won-Lost Records to 0.500A key implicit assumption underlying my Player Won-Loss Records is that Major League Baseball players will have a combined winning percentage of 0.500. While this is trivially true at the aggregate level, almost regardless of what you do, it should also be true at finer levels of detail as well.
2. Normalizing Player Game Points by GameThe total number of Player Game Points accumulated in an average Major League Baseball game is around 3.3 per team. This number varies tremendously game-to-game, however, with some teams earning 2 wins in some team victories while some other teams may earn 6 wins in team losses. At the end of the day (or season), however, all wins are equal. Hence, in my work, I have chosen to assign each team one Player Win and one Player Loss for each team game. In addition, the winning team earns a second full Win, while the losing team earns a second full Loss. Ties are allocated as 1.5 Wins and 1.5 Losses for both teams. Context-neutral player decisions (eWins and eLosses) are also normalized to average three Player decisions per game. For eWins and eLosses, this normalization is done at the season level, rather than the game level, so that different numbers of context-neutral player decisions will be earned in different games.
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 25.8 (Context-Dependent) Player Wins, while Jay Bruce led the majors with 21.1 losses.Why 3 Player Decisions per Game?
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.Why Do Players Get Wins in Games Their Team Loses?
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:Relationship of Player Decisions to Team Decisions
Team Wins = W – (W + L) / 3; Team Losses = L – (W + L) / 3As 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).
Basic Results: pWinsPlayer wins are calculated such that the players on a team earn 3 Player decisions per game. I calculate two sets of Player wins: pWins are tied to team wins - the players on a winning team earn 2 pWins and 1 pLoss, the players on a losing team earn 1 pWin and 2 pLosses - while eWins attempt to control for the context in which they were earned, as well as controlling for the abilities of a player's teammates.
|300 pGame Winners of the Retrosheet Era*|
|Pete Rose Sr.||437.9||394.8||0.526||11.1||44.1|
|Joe L. Morgan||374.0||292.3||0.561||46.2||72.7|
|Ken Griffey Jr.||339.3||300.7||0.530||16.5||42.0|
|Tony Gwynn Sr.||318.3||288.1||0.525||3.9||27.4|
|Luis 'Gonzo' Gonzalez||317.9||293.5||0.520||2.4||26.5|
|Tim Raines Sr.||313.2||275.9||0.532||10.7||33.9|
|Pee Wee Reese||300.7||238.7||0.558||35.2||57.0|
Comparing Players across Positions: Wins over Positional Average (WOPA)Player won-lost records are an excellent overall measure of player value. When context and the effects of teammates are controlled for, Player won-lost records can also, in my opinion, serve as an excellent starting point for measuring player talent. As a means of comparing players who play different positions, however, raw Player won-lost records are not necessarily an ideal comparative tool.
|Top 50 Players in Wins over Positional Average*|
|6||Joe L. Morgan||374.0||292.3||0.561||46.2||72.7|
|15||Randy 'Big Unit' Johnson||281.3||221.0||0.560||38.5||64.3|
|19||Pee Wee Reese||300.7||238.7||0.558||35.2||57.0|
|23||Pedro J. Martinez||193.7||137.5||0.585||33.9||51.4|
|44||J. Kevin Brown||204.6||164.7||0.554||26.4||45.2|
Wins over Replacement Level: WORLReplacement Level is the level of performance which a team should be able to get from a player who they can find easily on short notice – such as a minor-league call-up or a veteran waiver-wire pickup. The theory here is that major league baseball players only have value to a team above and beyond what the team could get from basically pulling players off the street. That is, there’s no real marginal value to having a third baseman make routine plays that anybody who’s capable of playing third base at the high school or college level could make, since if a major-league team were to lose its starting third baseman, they would fill the position with somebody and that somebody would, in fact, make at least those routine plays at third base. This is similar to the economic concept of Opportunity Cost.
|Top 50 Players in Wins over Replacement Level*|
|8||Joe L. Morgan||374.0||292.3||0.561||46.2||72.7|
|13||Randy 'Big Unit' Johnson||281.3||221.0||0.560||38.5||64.3|
|24||Pee Wee Reese||300.7||238.7||0.558||35.2||57.0|
|38||Pedro J. Martinez||193.7||137.5||0.585||33.9||51.4|
Contextual FactorsAs explained above, I calculate two measures of Player won-lost records: [pWins & pLosses] and [eWins & eLosses]. Comparing the results for these two sets of Player records, it is possible to isolate and identify the specific contextual factors that affect how player performance translates into team wins.
Context refers to the importance of a specific play in terms of determining team victories relative to a play of average importance. Differences in context will affect the total number of player decisions, so that, for example, a player who performed in an above-average context (>1) will earn more context-dependent player decisions (pWins + pLosses) than context-neutral player decisions (eWins + eLosses).Context and Win Adjustments can both differ across two dimensions: inter-game or intra-game.
Win Adjustments measure differences in a player's player winning percentage across different situations, i.e., the increase in a team's probability of victory relative to the average increase in win probability associated with a particular event. So, for example, a player who hits better in the clutch than at other times may have a higher winning percentage when measured using pWins and pLosses than based on eWins and eLosses. The player's "win adjustment" would be the difference between these two winning percentages.
Inter-game refers to differences in the relative importance of situations within a single game.Here are a few specific examples of players whose pWins differ from their eWins and why.
Intra-game refers to differences in the relative importance of situations across different games.
Trevor Hoffman, for example, earned 46.2 more pWins than eWins in his career (85%) mostly because the actual context in which he performed was 66% greater than his expected context.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.
Derek Jeter earned 14.9 more pWins than eWins in his career largely because he had the good fortune to play with above-average teammates, so that Jeter's positive contributions have been more likely to contribute to victories than would have been expected. This is reflected in what I call Jeter's intra-game win adjustment, which has raised his pWinning percentage by 0.019 (to 0.534) over Jeter's expected winning percentage (accounting for 13.3 additional wins).
David Ortiz earned 3.0 more pWins than eWins in 2005 mostly because of the timing of his hits (i.e., Big Papi was a great clutch hitter that year). The timing of Ortiz's hits, which I call his inter-game win adjustment, increased his winning percentage by 0.041 that year, adding 1.3 wins to Ortiz's record.
Components of Player Wins and LossesPlayer Wins and Losses are calculated using a nine-step process, each step of which assumes average performance in all subsequent steps. Each step of the process is associated with a Component of Player Wins and Losses (Player Decisions). These nine components are outlined briefly below. There are four basic positions from which a player can contribute toward his baseball team’s probability of winning: Batter, Baserunner, Pitcher, and Fielder. Player Decisions are allocated to each of these four positions, as appropriate, within each of the following nine Components.
Component 1: BasestealingFor components where Player decisions are shared across multiple players (e.g., pitchers and fielders in Component 5), I divide credit between players based on the extent to which player winning percentages within the particular component persist over time.
Player Decisions are assessed to baserunners, pitchers, and catchers for stolen bases, caught stealing, pickoffs, and balks.
Component 2: Wild Pitches and Passed Balls
Player Decisions are assessed to baserunners, pitchers, and catchers for wild pitches and passed balls.
Component 3: Balls not in Play
Player Decisions are assessed to batters and pitchers for plate appearances that do not involve the batter putting the ball in play: i.e., strikeouts, walks, and hit-by-pitches.
Component 4: Balls in Play
Player Decisions are assessed to batters and pitchers on balls that are put in play, including home runs, based on how and where the ball is hit.
Component 5: Hits versus Outs on Balls in Play
Player Decisions are assessed to batters, pitchers, and fielders on balls in play, based on whether they are converted into outs or not.
Component 6: Singles versus Doubles versus Triples
Player Decisions are assessed to batters, pitchers, and fielders on hits in play, on the basis of whether the hit becomes a single, a double, or a triple.
Component 7: Double Plays
Player Decisions are assessed to batters, baserunners, pitchers, and fielders on ground-ball outs in double-play situations, based on whether or not the batter grounds into a double play.
Component 8: Baserunner Outs
Player Decisions are assessed to batters, baserunners, and fielders on the basis of baserunner outs.
Component 9: Baserunner Advancements
Player Decisions are assessed to batters, baserunners, and fielders on the basis of how many bases, if any, baserunners advance on balls in play.
Breakdowns of Player Game Points by Component: 1921 - 2017
Distribution of Player Decisions
|Percent of Offensive/Defensive Component Decisions Allocated to Player Decisions|
|Percent of Total||Batters||Baserunners||Pitchers||Fielders|
|Component 1: Stolen Bases, etc.||2.2%||0.0%||100.0%||50.8%||49.2%|
|Component 2: Wild Pitches, Passed Balls||1.3%||0.0%||100.0%||73.3%||26.7%|
|Component 3: Balls Not in Play||14.7%||100.0%||0.0%||100.0%||0.0%|
|Component 4: Balls in Play||34.8%||100.0%||0.0%||100.0%||0.0%|
|Component 5: Hit vs. Out||33.0%||100.0%||0.0%||29.2%||70.8%|
|Component 6: Single v. Double v. Triple||3.5%||100.0%||0.0%||27.4%||72.6%|
|Component 7: Double Plays||2.2%||84.2%||15.8%||16.4%||83.6%|
|Component 8: Baserunner Outs||2.3%||40.7%||59.3%||0.0%||100.0%|
|Component 9: Baserunner Advancements||6.0%||46.7%||53.3%||0.0%||100.0%|
|Total Offensive/Defensive Decisions||91.6%||8.4%||62.5%||37.5%|
|Total Player Decisions||45.8%||4.2%||31.2%||18.8%|
1.   Run-Scoring EnvironmentRuns are more valuable in a lower run-scoring environment. Scoring one run is more likely to lead to winning in an environment where 1-0 victories are fairly common than in an environment where the average final score is 8-6. This is why Player won-lost records control for the run-scoring environment, both for the season and league in which the game took place as well as for the ballpark in which the game was played.
2.   Timing of EventsThe timing of events within a game can affect the value of those events. Hits which drive in runners on base can be viewed as more valuable than hits with the bases empty which do not produce runs. Home runs are more valuable in tie games than when the score is 15-0 (in either direction).
3.   Retrospective ContextThe value of a win is greater than the value of a loss. Retrospectively, one can argue that this means that the value of events are greater if they contribute to a win than if they contribute to a loss.
Value versus True TalentSo what is the difference between "value" and "true talent"? The key difference, as I see it, is that "value" can be directly observed, while "true talent" can only be inferred. Going one step farther, "true talent" can only be inferred from value. Hence, to my mind, measuring value is a necessary first step to being able to assess true talent.
So What's the Point of Context-Neutral Wins and Losses (eWins, eLosses)?So, if context is a necessary condition of measuring player value, then what is the point of the context-neutral wins and losses that I calculate, eWins and eLosses? By constructing wins and losses that are stripped of context, it becomes possible to distinguish the value of what players do (eWins, eLosses) from when players do these things via the Contextual Factors that relate eWins and eLosses to pWins and pLosses.
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