Background Losses

Sum of Context-Dependent Player Losses (pLosses) for a Team minus Team Losses; equal to one loss per Team Game played.

Background Wins

Sum of Context-Dependent Player Wins (pWins) for a Team minus Team Wins; equal to one win per Team Game played.

Ballpark Factors

Factors which measure the relative likelihood and/or value of certain events, including run-scoring, across different ballparks within the same league and season. Ballpark factors are typically expressed as indexes, relative to 100, reflecting differences in average runs scored in the ballpark relative to league average. The calculation of Ballpark adjustments used in my work is described here. Ballpark factors calculated by me are presented here.

Base-Out Probability Matrix

Matrix showing the probability of transitioning from a particular starting base-out state to a particular ending base-out state. Calculations of base-out probability matrices are described here.

Base-Out State

Number and location of baserunners and the number of outs at the start of a particular plate appearance. There are 24 possible initial base-out states; 28 possible ending states (the ending state may include 3 outs; the 4 ending base-out states associated with 3 outs vary based on the number of runs that scored on the inning-ending play, 0 - 3).

Baserunning Losses

Losses accumulated by a player as a baserunner.

Baserunning Wins

Wins accumulated by a player as a baserunner.

Batting Losses

Losses accumulated by a player as a batter.

Batting Wins

Wins accumulated by a player as a batter.

Component

Each of the nine steps in the process of calculating Player won-lost records.

Component 1

Basestealing (stolen bases, caught stealing, pickoffs, balks). Component 1 decisions are assessed to baserunners, pitchers, and catchers.

Component 2

Wild pitches and passed balls. Component 2 decisions are assessed to baserunners, pitchers, and catchers.

Component 3

Balls not in play: strikeouts, walks, hit-batsmen. Component 3 decisions are assessed to batters and pitchers.

Component 4

Balls in play, including home runs. Component 4 decisions are assessed to batters and pitchers.

Component 5

Hits vs. Outs on balls in play. Component 5 decisions are assessed to batters, pitchers, and fielders.

Component 6

Singles vs. Doubles vs. Triples on hits in play. Component 6 decisions are assessed to batters, pitchers, and fielders.

Component 7

Double Plays. Component 7 decisions are assessed to batters, baserunners, pitchers, and fielders.

Component 8

Baserunner Outs. Component 8 decisions are assessed to batters, baserunners, and fielders.

Component 9

Baserunner Advancement. Component 9 decisions are assessed to batters, baserunners, and fielders.

Context

Importance of a specific play in terms of determining team victories relative to a play of average importance.

Context-Dependent

Player decisions calculated such that player wins and losses are tied to team wins and losses. The calculation of context-dependent player wins and losses (pWins and pLosses) is explained in detail here.

Context-Neutral

Player's expected record if his performance had happened in a typical context with average teammates. The calculation of context-neutral player wins and losses (eWins and eLosses) is explained in detail here.

Correlation

Relationship between two series, expressed as a number between -1 and +1. A correlation of 1 means that two series move perfectly together - literally, if two series have a correlation of 1 it means that one of them can be expressed as a linear function of the other. A correlation of 0 means that there is no relationship between the two series. A correlation of -1 means that two series move in exactly opposite directions.

DIPS

Defense-Independent Pitching Statistic. DIPS measures expected Earned Run Average as a function of only those events which are not affected by defense: strikeouts, walks, hit batsmen, home runs. DIPS was developed by Voros McCracken based on a theory that major-league pitchers have very little, if any, control over balls in play.

e

Prefix meaning "expected". Statistics with an "e" prefix have been adjusted to reflect expected performance in a typical context with average teammates.

eLosses

Player's expected losses if his performance had happened in a typical context with average teammates. The calculation of eLosses is described here.

Event Probability

Probability of a particular event occuring. For example, the probability of a particular ball in play being a triple, given the hit type (ground ball, fly ball, line drive) and location of the hit. The calculation of event probabilities is described here.

eWins

Player's expected wins if his performance had happened in a typical context with average teammates. The calculation of eWins is described here.

eWOPA

Wins over Positional Average (WOPA) calculated using eWins and eLosses.

eWORL

Wins over Replacement Level (WORL) calculated using eWins and eLosses.

Expected Context

Expected context. Expected product of inter-game and intra-game context based on the position(s) played by a player. The calculation of Expected Context is described here.

Expected Win Adjustment

Expected intra-game win adjustment based on player's individual performance, assuming that the rest of his team consisted of average major-league players. The calculation of Expected Win Adjustment is described here.

Extrapolated Games

Retrosheet has released some seasons for which they only have play-by-play data for some games. For these seasons, Player won-lost records for missing games can be extrapolated from Player won-lost records for the games for which Retrosheet has released play-by-play data. See here for further details.

Fielding Losses

Losses accumulated by a player as a fielder.

Fielding Wins

Wins accumulated by a player as a fielder.

Harmonic Mean

The Harmonic mean of A and B is equal to 2*(A*B) / (A + B). Frequently, in my work, the 2 in the above formula would end up dropping out, so I simply use (A*B) / (A + B).

Hit Type

Type of batted ball for a ball in play: bunt, ground ball, fly ball, or line drive.

Inning Probability Matrix

A matrix indicating the probability of a team winning a game given the specific lead/deficit at the start of a particular inning. The calculation of Inning-Probability Matrices is described here.

Inter-Game

Within a single game. Relative importance of situations within the same game on that game's final outcome.

Inter-Game Context

Inter-game context measures the average importance of the situations in which the player participated within the context of the game. Inter-game contexts are discussed in more detail here.

Inter-Game Win Adjustment

Adjustment to player's winning percentage based on the timing of his performance within games. Inter-game win adjustments are discussed in more detail here.

Intra-Game

Across games. Relative importance of situations within one game as compared to the importance of comparable situations across all games.

Intra-Game Context

Intra-game context normalizes player decisions so that total player decisions are equal across all games. Intra-game contexts are discussed in more detail here.

Intra-Game Win Adjustment

Adjustment to player's winning percentage based on the timing of his performance relative to his team's performance. Intra-game win adjustments are discussed in more detail here.

Leverage

Relative importance of a situation. Conceptually, leverage is the same as inter-game context, as I use the term. Leverage was developed by Tom Tango.

Linear Weights

Run-scoring estimator which is constructed by estimating the number of runs generated by each possible offensive event (single, double, triple, home run, etc.). Summing up this value for each event generated by a player or team then represents an estimate of the total number of runs generated by that particular player/team. Linear Weights were first developed by Pete Palmer for his series of Total Baseball books.

Losses

Player decisions which contribute toward the player's team's probability of losing.

Net Wins

Total Player wins minus Total Player losses associated with a particular play or plays. Net wins for various events are described here. Net wins for various events by season by league derived from my work are presented here.

p

Prefix standing for "Player". Statistics with a "p" prefix are adjusted such that player wins and losses tie to team wins and losses.

Pennant Probability

Probability of a team winning the pennant, given their current record, the current records of their opponents, and the number of games remaining in the season. The relationship between Win Probability and Pennant Probability is discussed here.

Persistence Equation

Equation measuring the extent to which a statistic (typically, a Player's won-lost winning percentage in my work) persists over time. The persistence of a statistic can be viewed as the extent to which something represents a real "skill" as opposed to being the result of simple random chance. Persistence equations are described in more detail here.

Pitching Losses

Losses accumulated by a player as a pitcher. This is not to be confused with the traditional baseball statistic, pitcher losses.

Pitching Wins

Wins accumulated by a player as a pitcher. This is not to be confused with the traditional baseball statistic, pitcher wins.

Playoff Probability

Probability of a team making the playoffs, given their current record, the current records of their opponents, and the number of games remaining in the season.

pLosses

Player losses calculated such that player losses are tied to team wins. For a team, the sum of player losses will be equal to team losses (plus 0.5 pLosses per tie game) plus team games played. The calculation of pLosses is described here.

Positional Average

Average winning percentage expected for a player who played the same position(s) as a particular player. The calculation of Positional Averages is described here. Positional Averages by position by season are presented here.

Positional Replacement Level

Replacement Level performance of freely available players who could have been found to play the same position(s) as this player. Set equal to one standard deviation below Positional Average. Positional Replacement Levels by season are presented here.

pWins

Player wins calculated such that player wins are tied to team wins. For a team, the sum of player wins will be equal to team wins (plus 0.5 pWins per tie game) plus team games played. The calculation of pWins is described here.

pWOPA

Wins over Positional Average (WOPA) calculated using pWins and pLosses.

pWORL

Wins over Replacement Level (WORL) calculated using pWins and pLosses.

Replacement Level

Level of play which could be achieved by a player who is "freely-available" to any major-league team. The term, which was first coined by Bill James, comes from the concept that a player who plays at "Replacement Level" or below, can be easily replaced by a cheap minor-leaguer or journeyman major-leaguer.

Run Probability Matrix

A matrix indicating the probability of scoring X runs within an inning given the current base-out state. The calculation of a run probability matrix is described here.

Run-Scoring Environment

Average runs scored per game for a particular set of games. Run-scoring environments can vary by ballpark (Coors v. Petco), because of differences in rules (DH v. pitchers hitting), or because of differences across seasons (1968 v. 2000). Run-scoring environment can also be affected by the level of play (little league v. major-league, etc.), although this latter factor is irrelevant to the work presented on this website which deals exclusively with Major-League Baseball.

Standard Deviation

Statistical measure of the spread of a range or distribution. Standard deviation is equal to the square root of the variance. In a normal distribution, approximately 65% of all values will fall within one standard deviation of the mean, 95% of all values will fall within two standard deviations, and 99% of all values will fall within three standard deviations of the mean.

Teammate Adjustments

Effect of a player's teammates on his won-lost record based on shared responsibilities for certain plays between batters and baserunners and/or between pitchers and fielders. Teammate adjustments are described in more detail here.

Three True Outcomes

Strikeouts, walks (or hit-by-pitch), and home runs. These are the only outcomes of a plate appearance that involve only the pitcher and the batter.

Variance

Statistical measure of the spread of a range or distribution. Variance measures the average squared difference of a set of numbers from their mean.

WAR

Wins above Replacement. Measure of total player value developed by Sean Smith, available at Baseball Reference. An alternate measure also called WAR is also calculated by Fangraphs.

WARP

Wins above Replacement Player. Measure of total player value developed by Baseball Prospectus.

Weighted Correlation

Measure of correlation, weighted by the relative size of the individual observations of the sample being measured. The precise calculation of weighted correlation is described here.

Weighted Standard Deviation

Measure of standard deviation, weighted by the relative size of the individual observations of the sample being measured. The precise calculation of weighted standard deviation is described here.

Weighted Variance

Measure of variance, weighted by the relative size of the individual observations of the sample being measured. The precise calculation of weighted variation is described here.

Win Adjustment

Increase in a team's probability of victory relative to the average increase in win probability of a particular event.

Win Probability Matrix

A matrix indicating the probability of a team winning a game given a the current base-out state, the current lead/deficit, and the current inning. The calculation of Win Probability Matrices is described here.

Win Probability

A concept whereby the probability of a team winning a baseball game is estimated based on the current inning, baserunners, outs, and score differential.

Win Shares

Estimated wins contributed by a player. The players on a team receive 3 Win Shares per team win and 0 Win Shares per team loss. Win Shares were developed by Bill James and described in his 2002 book of the same name.

Wins

Player decisions which contribute toward a player's team's probability of winning.

WOPA

Wins over Positional Average.

WOPA_b

Batting wins relative to expected batting wins accumulated by non-pitchers.

WOPA_p

Pitching wins relative to expected average pitching wins.

WOPA_r

Baserunning wins relative to expected baserunning wins accumulated by non-pitchers.

WORL

Wins over Replacement Level.

WORL_f

Fielding Wins over Positional Replacement Level.

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