Games = Player Wins plus Player Losses
CM stands for Context Multiplier, which measures the relative importance of the player’s performance compared to an average player
TmAdj is an adjustment for the player’s teammates, and is defined below
WinAdj is an adjustment to winning percentage to reflect the timing of the player’s performance
B stands for Basic context-neutral player games
e stands for Expected, measuring Context-Neutral won-lost records, adjusted for expected contextual factors
p stands for Player won-lost records, which incorporate actual contextual factors such that player won/lost records are tied directly to team wins and losses
Inter stands for Inter-Game and measures the importance of the player’s performance given the immediate context within the game
Intra stands for Intra-Game and measures the importance of the player’s performance relative to other games
1. Context Multipliers
Context multipliers quantify how the total number of context-dependent player games (pGames) relates to an expected number of player games if the player had played in an average context. As part of the normalization processes undertaken to construct Player Wins and Losses, for a given league, league-wide context is set equal to one by construction. For individual players (and individual teams), however, this will likely not be the case. A context greater than one means that a player tended to play in more win-important situations than average, while a context less than 1 means that a player tended to play in less win-important situations than average.
For example, in 2006, Francisco Rodriguez of the Anaheim Angels had a pWon/pLost record of 8.9 wins against 3.2 losses, for a total of 12.1 Context-Dependent Player Decisions.
Stripped of its context, however, Rodriguez’s basic won-lost record was only 4.5 wins against 3.1 losses, for a total of only 7.5 Basic Player Decisions. Hence, Francisco Rodriguez’s context multiplier for 2006 was 1.601 (12.1/7.5), meaning that, on average, Rodriguez’s performance was 60.1% more valuable than would have been expected.
a. Inter-Game Context
Inter-game context measures the importance of the situations in which a player performed within the context of a single game. This is similar to the concept of Leverage.
One difference with Leverage, as calculated by Tom Tango in the linked article, is that Leverage is calculated before the play and is, hence, independent of the result of the play. Inter-game context, however, is calculated retrospectively, so that it is dependent on the results of the plays that go into the calculation. This may introduce a slight positive correlation between inter-game context and Player winning percentage.
A simple calculation of the weighted correlation between inter-game context and basic Player winning percentage suggests a correlation of
0.22
. Much of this correlation, however, is due to the fact that better pitchers are used in higher-context situations. Looking only at non-pitchers, for example, the correlation between winning percentage and inter-game context is only
0.07
. And even here, this correlation may be due in part to the occasional use of better hitters as pinch hitters in higher-context situations.
b. Intra-Game Context
Intra-game context normalizes the number of Player decisions across games. Games with close scores, a lot of lead changes and/or multiple ties will earn more un-normalized Player decisions than less competitive games. For batters, baserunners, and fielders, intra-game context multipliers will be very highly correlated across teammates depending on how many close games a team plays over the course of a particular season.
For example, in 2005, 8
of the bottom 10 non-pitchers in games added by Team Context played for either the Minnesota Twins or the Washington Nationals.
In 2005, the Twins led the major leagues with 23 extra-inning games and played in 57 one-run games, while the Nationals led the major leagues with 61 one-run games.
Because intra-game contexts are more likely to be below one the closer a game is, while inter-game contexts are more likely to be above one the closer a game is, these two measures have a tendency to be fairly strongly negatively correlated. For all players for which I have calculated Player won-lost records (1916 - 2018), inter-game and intra-game context have a weighted correlation of
-0.45.
When intra-game context is taken into account, Leverage, which only considers inter-game context, has a tendency to over-state the value of high-leverage relief pitchers. For example, in 2006, Francisco Rodriguez’s inter-game context was
1.939
(Fangraphs.com calculates Rodriguez’s Leverage per plate appearance at 2.10, Leverage per Inning at 1.90, and expected Leverage at 1.93 in 2006). His intra-game context, however, was
0.826
as 51 of his 69 appearances were in save situations, which tend to occur in games which generate an above-average number of Player decisions. Combining inter- and intra-game context, then, reduces Francisco Rodriguez’s true context for 2006 to
1.601.
c. Expected Context
One can draw certain expectations about a player’s context based on what position he plays. Starting pitchers tend to have much higher intra-game contexts than relief pitchers. Pinch hitters and pinch runners perform in a higher context, on average, than other batters and baserunners. Context-neutralized Player won-lost records are adjusted for the expected context based on these considerations.
2. Wins over Expectation
a. Inter-Game Wins over Expectation
In 2006, hitters put up a batting line of .197/.276/.333 against Francisco Rodriguez. With the bases empty, batters hit .201/.281/.377 against Rodriguez with 5 home runs in 171 plate appearances. While this is an impressive performance by Rodriguez, he did even better with men on base. With runners on base, Rodriguez allowed a batting line of .191/.270/.273 and allowed only one home run in 125 plate appearances. With two outs and runners in scoring position, his performance improved still further: .128/.227/.154 in 44 plate appearances.
Not only was Rodriguez’s performance better with runners on base but it was also noticeably better the closer the game. When the Angels were within four runs of their opponent, batters hit .179/.264/.286 against Rodriguez with 3 home runs in 264 plate appearances. When the difference in the score was more than four runs, however, opponents hit .333/.375/.700 against Rodriguez with 3 home runs in 32 plate appearances.
By just about any measure, Francisco Rodriguez’s performance in 2006 was “clutch”. That is, Rodriguez clearly performed better in more win-important situations within games than in less win-important situations. Whether Rodriguez’s performance here is indicative of a real “clutch” skill or not is considered elsewhere. Regardless of whether this is a “skill” or not, however, the timing of Rodriguez’s performance unquestionably contributed to more wins for the Angels in 2006 than a more balanced performance would have. In fact, the inter-game “clutchness” of Frankie Rodriguez’s performance improved his Player won-lost percentage by
7.5% (0.075) or by an additional 0.6 wins
(not including any adjustment for context).
Inter-game wins over expectation are discussed in a bit more detail elsewhere.
b. Intra-Game Wins over Expectation
Francisco Rodriguez appeared in 69 games for the Angels in 2006. The Angels went 59-10 in those games. This was largely a function of Rodriguez’s role as the team’s closer, which meant that he was primarily used in the late innings of games which the Angels were already winning.
In the 59 Angels wins in which Rodriguez pitched, he was 2-0, 47 saves, 2 blown saves, 60-2/3 innings pitched, and a 1.34 earned run average. In the 10 Angels losses in which Rodriguez pitched, he was 0-3 with 2 blown saves, 12-1/3 innings pitched, and a 3.65 ERA.
Regardless of the reason why Rodriguez appeared so often in Angels wins, the facts that (a) he performed so well in so many Angels victories and (b) he performed better in Angels wins than in Angels losses both made Rodriguez’s performance more valuable to the Angels than if his best performances had occurred more often in Angels losses. I calculate that Rodriguez’s intra-game wins over expectation improved his team-dependent Player won-lost percentage by
6.6% or an additional 1.0 wins (again, not adjusting for context). Intra-game wins over expecations, what they mean, and why they are important are all discussed in a separate article.
c. Expected Intra-Game Win Adjustment
In addition to adjusting Context-Dependent wins to tie player wins to team wins, I also adjust Context-Neutral wins to account for the expected impact of Player wins on team wins. The premise of this latter adjustment is that a team of players who are slightly better than 0.500 will, in fact, win far more than half their games, while a team of slightly below-average players will lose most of their games. Expected "team win adjustments" are discussed in detail in a separate article.
3. Teammate Adjustments
Player wins and losses are shared between teammates for certain events. For example, pitchers and catchers share responsibility for stolen bases and wild pitches, while pitchers and fielders share responsibility for balls in play. The method by which these shared responsibilities are calculated is described elsewhere. For pure Player wins and losses that tie out to team wins and losses, all that can be done in terms of dividing responsibility for, say, allowing a stolen base, is to divide the Player losses accrued on the play between the pitcher and catcher. Because of this, the cumulative winning percentage of a team’s pitchers on shared plays will be exactly equal to the winning percentage of a team’s fielders on shared plays. As such, it can be difficult, if not impossible, to judge how much of a particular player’s (or team’s) performance in shared components is due to his (or their) talent and how much is due to their teammates’ talents. Perhaps the best recent example of this phenomenon is Doug Mirabelli.
Context-neutral Player Won-Lost records, on the other hand, control for the quality of one’s teammates. For example, Francisco Rodriguez’s teammates changed his Context-Dependent wins by
-0.01 (-0.11%)
.
Teammate adjustments tend to be fairly small in magnitude. Over the Retrosheet era (1916 - 2018), for example, the spread of teammate adjustments, expressed in wins over the course of a full season ranged from
+0.71 for Reggie Jackson in 1976 to -0.60 for George Case in 1942.
All articles are written so that they pull data directly from the most recent version of the Player won-lost database. Hence, any numbers cited within these articles should automatically incorporate the most recent update to Player won-lost records. In some cases, however, the accompanying text may have been written based on previous versions of Player won-lost records. I apologize if this results in non-sensical text in any cases.