Leverage Index

How important is this plate appearance, relative to an average one?

What is Leverage / Leverage Index?

Leverage Index was created by Tom Tango to measure how much the win probability could swing on the next play, given the current game state (inning, score, outs, baserunners). A value of:

• 1.0 = “neutral” situation (average plate appearance)
• > 1.0 = high leverage (big potential swing in win probability)
• < 1.0 = low leverage (blowouts, early innings with no one on, etc.)¹

When people talk about “leverage” for a pitcher (especially relievers), they usually mean:

• Average Leverage Index (aLI) - the average LI of all plate appearances they faced.
• gmLI / inLI - game-entering or entry leverage when they first appear²

How is Leverage Index calculated?

High-level formula:

1. Take current Win Expectancy (WE₀) for the batting team given:

   • inning
   • score differential
   • outs
   • base state

2. Enumerate the possible outcomes of the plate appearance:

   • out, walk, single, double, HR, etc.

3. For each outcome i:

   • Compute WEᵢ = win expectancy after that outcome
   • Let ΔWEᵢ = |WEᵢ − WE₀| (absolute change in win probability)
   • Weight it by the probability pᵢ of that outcome

4. Compute the expected absolute swing in WE for this PA:

5. Compute the average swing over all plate appearances in your dataset:

6. The Leverage Index (LI) of this state is:

This is exactly how FanGraphs and others describe it: expected WE swing for this state, divided by the league-wide average swing²

Footnotes

1. https://www.mlb.com/glossary/advanced-stats/leverage-index “Leverage Index (LI)” ↩

2. https://library.fangraphs.com/misc/li/ “LI - Sabermetrics Library - FanGraphs” ↩ ↩²