What is Leverage Index? Definition, Formula, and Example
Leverage Index (LI) quantifies the importance of any plate appearance by measuring how much the game's win probability could swing on its outcome relative to an average situation, where 1.0 is league-average leverage.
What is Leverage Index in Baseball?
Leverage Index (LI) is a numerical measure of how much the outcome of a single plate appearance can shift a team's probability of winning the game. An average plate appearance has an LI of 1.0. A situation with an LI of 3.0 means the at-bat's result — hit, strikeout, home run — will swing win probability three times as much as a typical PA. The metric was developed and popularized by sabermetrician Tom Tango and is the standard tool for quantifying game-state pressure on pitchers and batters alike.
How Leverage Index Is Calculated
LI is derived from pre-calculated win probability tables that account for three variables: the inning, the score differential, and the base-out state (which bases are occupied and how many outs). For every combination of those three variables, the tables record the standard deviation of possible win probability outcomes. LI normalizes that standard deviation against the all-situations average:
LI = (SD of WP outcomes in this situation) ÷ (SD of WP outcomes averaged across all situations)
Because win probability swings are largest in close games in the late innings with runners on base, LI spikes exactly then. A tie game, bases loaded, two outs, bottom of the ninth can produce LI readings of 5.0 to 7.0. A team trailing by seven runs in the fifth inning will show LIs below 0.3 because nearly every possible outcome has roughly the same effect on win probability — near zero.
Two derived versions appear frequently in reliever statistics:
- gmLI (game-entry Leverage Index): the average LI at the moment a reliever enters a game, measuring how intelligently a manager deploys that pitcher across a season.
- pLI (plate-appearance average LI): the average LI across all plate appearances faced by a pitcher over a period, accounting for mid-inning changes in game state.
Worked Example
In 2023, Josh Hader posted a gmLI of 2.21 as the Padres' closer, meaning that on average when Hader entered a game, the win probability swing potential was more than double that of an average PA. By contrast, a long reliever brought in to eat innings in a 7–1 blowout might show a gmLI of 0.4 for that appearance. The tie-game, runners-on-base situations Hader routinely inherited can spike to LI 4.0 or higher — any single pitch matters enormously. His WPA accumulation that season directly reflected those high-LI entry points: even modest results in extreme situations generate more WPA than dominant performances in meaningless ones.
Why Leverage Index Matters
Bullpen deployment: A manager who consistently uses his best reliever in the highest-LI situations maximizes that arm's marginal value. Leverage Index is the analytical foundation of the "closer by committee" debate — the question is always whether the team's best reliever is achieving a high gmLI or being wasted in low-LI save opportunities.
WPA context: Win Probability Added accumulates proportionally to LI. A strikeout in a 3–0 game in the third inning adds almost nothing to WPA; the same strikeout with the bases loaded in the ninth adds substantially more. LI is why closers accumulate more WPA than setup men with identical underlying stuff — it is context, not performance.
Contract valuation: Elite relievers who pitch consistently in high-LI spots command premium free-agent dollars. Front offices compare gmLI alongside FIP and K-BB% to determine whether a reliever's performance justifies the leverage he's given — and whether that leverage assignment was managerial wisdom or luck of scheduling.
In Legends Deck, Leverage Index informs how reliever cards are rated relative to game context. A closer card deployed in a simulation's late, close game enters a high-LI environment where its pitch quality attributes produce larger win-probability swings than the same card used in a lopsided game. Players who built their statistical records in high-LI environments receive appropriate context weighting in card construction.
Limitations and Misconceptions
LI measures context, not performance. A pitcher with a 4.50 ERA who consistently enters high-LI situations earns a high gmLI despite actively hurting his team. Conversely, a dominant middle reliever deployed only in low-LI spots will show a low pLI even if his raw stuff exceeds the team's closer. High LI and high value are not the same thing.
LI also uses historical win probability tables built on average lineups, not live odds adjusting for the specific batters, defensive alignments, or park factors in a given game. A situation with LI 2.5 facing Shohei Ohtani is categorically different from the same LI facing the opposing pitcher — the tables cannot capture that.