Win Probability, Leverage Index and Win Probability Added
How win probability, leverage index and win probability added are built from historical game states, how to read them, and what they can and cannot say about a player or a decision.
A home run in the first inning of a 10-0 game and a home run in the bottom of the ninth of a tie game count the same in a home-run column, and no sensible fan treats them the same. Win probability is the family of statistics that tries to put a number on that difference. It starts from a simple idea: at any moment in a game, each team has some chance of winning, and every play moves that chance up or down. Add up the moves that belong to a player and you have a measure of how much he changed the outcome.
Three connected ideas do the work. Win probability, also called win expectancy, is the chance a team wins from a given game state. Leverage index measures how much a situation can swing that chance, so it tells you how much a moment matters before it happens. Win probability added, or WPA, is the actual change in win probability caused by a play, credited to the players involved. This article explains how each is computed, works through examples with clearly marked hypothetical numbers, and describes where these tools are useful and where they mislead.
What win probability is
Win probability is the share of the time a team wins when a game reaches a given state. A state is a set of facts: the inning, whether it is the top or bottom half, the number of outs, which bases are occupied and the score difference. The state of a game that is tied after eight innings with the home team coming to bat has a win probability for the home team that sits close to one half, a little above because the home team bats last. A team that trails by five runs with two outs in the ninth and nobody on has a win probability near zero.
The word probability does not mean the number is a guess. It is built from history. Take every game in a large database where a team was in exactly that state, count how often that team went on to win, and divide. If a home team trailing by a run in the bottom of the eighth with two outs and nobody on won, hypothetically, 150 of 1,000 such games, its win probability in that state is 0.15. The sources that feed this kind of analysis are play-by-play databases that record every plate appearance; Retrosheet is the best-known public one.
Because the table has to be filled for every state, and some states are rare, builders smooth it. Some use a model of run scoring to simulate the rest of the game from a given state, which draws on the same ideas as run expectancy and the 24 base-out states. Others use regression. All of them agree on the shape: the win probability moves slowly early in a game, and steeply late.
The ingredients of a game state
It helps to see why each ingredient matters.
- Score difference. Leading by one run in the ninth inning is far safer than leading by one in the second inning, because the trailing team has fewer chances to score.
- Inning and half. The home team has the last at-bat, so in a tie it holds a small edge. The same state in the top and bottom of an inning differs, because the team at bat changes.
- Outs. More outs left means more chances to score. A tying run on third with none out is worth much more than the same runner with two out.
- Base runners. A runner on third and one out is the classic example of a state where several different ordinary events, such as a fly ball or a groundout, can produce a run.
- The run environment. A state's value depends on how easy it is to score. In a low-scoring era a one-run lead is safer than in a high-scoring one, so good tables are built for a particular period.
Many public tables treat both teams as average. A more refined version starts from pregame odds that reflect the teams' quality and the starting pitchers. The distinction matters for interpretation: a game with a strong favourite starts at, say, 65 percent, and a single hit moves the number from there.
A worked example of win probability added
Win probability added is the change in win probability from before a play to after it. Suppose, as a hypothetical, that the home team trails by one run in the bottom of the ninth with two outs and a runner on first, and its win probability is 0.20. The batter hits a double that scores the tying run and puts the winning run on second. Say the new state has a win probability of 0.60 for the home team. The play moved the home team's chance by +0.40. The batter is credited with +0.40 WPA, and the pitcher is charged with −0.40.
Now suppose the next batter singles and scores the winning run, ending the game. The win probability goes from 0.60 to 1.00, a move of +0.40, and that batter also receives +0.40. Together the two hits took the home team from 0.20 to 1.00, a total of +0.80, and the pitcher absorbed the same amount as a negative.
Several properties follow from this construction. Every play's gain for one side is a loss of equal size for the other, so the sum of all WPA in a game is zero across both teams. Across a whole game, the winning team's players together are credited with the difference between its final win probability of 1.00 and its starting figure, so a team that began at 50 percent gets a total of +0.50 split among its hitters, pitchers and baserunners, and the losing team gets −0.50. A season's WPA for a player is the sum of those moves. A hitter with a WPA of 5.0 has, in the sense of the model, added five wins' worth of probability above what an average outcome would have given.
The usual convention credits batter-pitcher events to those two players, and credits baserunning events to the runner, so the model does not hand any credit to fielders on ordinary plays. A diving catch that saves a run shows up only through the hitter's lower result, not as a credit to the fielder, which is a limit of the stat. For a view that does measure defence, see WAR explained.
Leverage index: measuring how much a moment matters
WPA tells you what happened. Leverage index tells you how much was at stake. It was developed by the analyst Tom Tango and described in detail in the 2007 book The Book: Playing the Percentages in Baseball, which he wrote with two co-authors. The definition is a ratio. For a given game state, you look at all the things that can happen next, such as a strikeout, a walk, a single or a home run, and you weigh the size of the win probability swing each would cause by how often it happens. That gives the expected size of the swing from the next plate appearance. Divide it by the same quantity averaged over all plate appearances in all games, and you have the leverage index.
The scale is set so the average situation has a leverage index of 1.0. A situation with a leverage index of 2.0 moves the game twice as much as the average plate appearance; one with 0.5 moves it half as much. Several details vary between implementations, including how the swing is measured, so check the definition any site uses before comparing numbers from two sources.
There are conventions for labelling the numbers. One widely used scheme treats a leverage index below about 0.85 as low, from 0.85 to 2.0 as medium and above 2.0 as high, though the exact cutoffs are a matter of presentation, not law. High-leverage moments cluster late in close games with runners in scoring position. A bases-loaded situation in the ninth inning of a tie game is among the highest-leverage states in the sport, and its leverage index is several times the average. A seventh-inning plate appearance in a 9-1 game is close to zero.
| Situation (hypothetical description) | Leverage | Why |
|---|---|---|
| First inning, nobody on, nobody out | Around or a little below average | Many innings remain and the swing is small |
| Tie game, bottom of the ninth, runner on third, one out | Very high | One run ends the game |
| Down 8 runs in the eighth | Near zero | The result is almost settled |
| Tie game, seventh, bases empty, two outs | Around average | Close score but few ways to score |
The figures in this table are descriptions of direction, not measured values. The point is to show how leverage rises with closeness, lateness and runners in scoring position.
From leverage to usage: relievers and managers
Leverage index became useful quickly in the study of bullpens. Relievers enter in different situations, so a pitcher's average leverage index on entering the game, often shown as gmLI, shows how a manager uses him. A closer typically has a high gmLI, because he is saved for the close games in the ninth, and a long reliever typically has a low one, because he enters games that are already out of hand. Plotted across a season, those numbers describe the pecking order in a bullpen better than the save statistic does.
The save has always had a weakness that leverage exposes. A save is credited in a defined situation, such as a lead of three or fewer runs in the ninth, even though a three-run lead with the bases empty is not tense. Meanwhile a reliever who enters in the seventh with the bases loaded and a one-run lead and gets out of it has done something much harder, and the save statistic ignores it. Leverage index, with WPA, captures both. WHIP, which counts baserunners per inning pitched, is a useful companion because it describes how a pitcher does regardless of the situation.
Managers can use the same ideas in the dugout. The question of when to use the best reliever, when to pinch hit and when to intentionally walk a batter are all questions about win probability. A manager who saves his closer for a save situation in the ninth inning, even when the highest-leverage moment occurred in the seventh, is trading a large swing for a conventional one. How teams act on this is not tracked in this article, and it is fair to say that different clubs weigh it differently.
Context-neutral versions and clutch
WPA has an obvious problem as a measure of skill. A hitter cannot choose when he comes to bat, so a player who happens to bat more often with runners on and the score close will pile up WPA that a better hitter on a weaker lineup does not. The fix is to divide the context out. A common version, called WPA/LI, divides each play's WPA by the leverage index of the situation, which leaves a number that tells you what the player did in units of wins as if every situation had average stakes. It is a measure of what he did, not of when he did it.
The difference between a player's raw WPA and this context-neutral version is the basis of a clutch statistic. A player with a positive clutch score produced more win probability in high-leverage moments than his overall performance would predict. The honest reading is cautious. Studies by baseball analysts over the years have generally found that clutch performance is hard to separate from luck and that it does not persist strongly from one year to the next. A player's clutch score for a season is a description of the past, not a forecast. If a player was clutch in 2019, that tells you little about 2020.
This reasoning is why most front offices and projection systems rely on context-neutral measures when they decide how good a hitter is. WAR, for example, counts a hitter's events at their average run value regardless of when they happened, though some versions adjust relievers for the leverage of their innings. WPA is the right tool for a different question: who did the most to win the games that actually happened?
What the numbers can and cannot tell you
Win probability stats are best used for storytelling and for decisions, not for ranking talent. They answer questions such as what the biggest play of a game was, how a comeback unfolded, or which relievers pitched in the most important moments. A graph of win probability through a game shows the shape of it at a glance, with each swing labelled by the play that caused it. If you read a box score with how to read a baseball box score in hand, a win-probability graph adds the sense of drama a line score cannot give.
The limits are as important as the uses. First, win probability depends on the model: two sources can show different values for the same state because they use different data, eras or smoothing. Second, WPA depends on the context a player was placed in, as described above. Third, the model credits events, not causes: a pitcher who allowed a double that a fielder could have caught is charged with the whole swing. Fourth, the numbers do not know about the strength of the teams unless the model adds it, and the strength of a pitching matchup changes what is likely to happen next. Fifth, small samples are noisy, and a single big play can dominate a season's total.
A final caution concerns the rules. The state table depends on the rules of the game. Since the 2020 season the extra-innings rules have placed a runner on second base at the start of each extra inning in the regular season, and the rule was made permanent later, so win-probability tables built for earlier extra innings do not apply. The 2023 rule changes, covered in the pitch-clock era, also changed how the game is played. As of the 2025 season, check MLB's official rules for the current extra-innings format, and prefer tables built from recent data when you analyse recent games.
Common questions
Is win probability the same as the betting odds? No. Odds are prices set by a market and include a margin for the bookmaker. Win probability is an estimate drawn from historical outcomes. They can be related, but they are not the same number. Betting carries risk, and it is for adults of legal age where it is legal; the US helpline is 1-800-GAMBLER.
Why do some sites show different win probabilities for the same moment? Because the underlying tables differ. Some use a long period and some a recent one, some start both teams at 50 percent and some use pregame odds, and some smooth the data differently.
Does a leverage index above 1 mean the situation is good or bad? Neither. It means the situation is more important than average. A high-leverage moment can go either way, and leverage describes the size of the swing, not its direction.
Can WPA be negative for a good player? Yes. A hitter who strikes out in a high-leverage situation earns a negative WPA for that play even if he is excellent overall. Over a full season the big positives and negatives mostly offset in the context-neutral view.
Why not use WPA as the main way to judge players? Because players do not control when they come to bat. Pythagorean expectation is a related example of a tool that smooths luck out of a team's record, and WAR does something similar for individuals.
Where does park matter? Park effects change run scoring, which changes the value of every state. Park factors explained describes how that is handled in other statistics.
Where to go next
To see the building block underneath all of this, read run expectancy and the 24 base-out states, then WAR explained for the context-neutral view of value. The stats and analytics topic page collects current coverage, and the leaders page shows who tops the traditional lists.