## LI

During the course of a game, some situations are more tense and suspenseful than others. For instance, we know that a one-run lead in the bottom of the ninth inning is more suspenseful than a one-run lead in the top of the third inning. Batting with two runners on and two outs in the eighth inning is filled with more pressure than batting in the same situation in the second inning. Leverage Index (LI) is merely an attempt to quantify this pressure so we can determine if a player has been used primarily in high-leverage or low-leverage situations.

There are many different iterations of LI, including the following ones available on the site:

pLI: A player’s average LI for all game events.
phLI: A batter’s average LI in only pinch hit events.
gmLI: A pitcher’s average LI when he enters the game.
inLI: A pitcher’s average LI at the start of each inning.
exLI: A pitcher’s average LI when exiting the game.

Calculation:

Leverage Index certainly isn’t something you would calculate during a game, but you can track it on our live Win Expectancy graphs located in the Scores section of the site during games. The reason you wouldn’t calculate it live is because there are a large number of simple calculations that go into each Leverage Index, which makes tracking it with a table or a graph ideal (the bar graph below the line graph is the LI).

Source: FanGraphs

The mechanics behind Leverage Index, however, are easy enough to follow. If you’re extremely interested, you should read this full explanation from Tom Tango, the creator of this flavor of LI. Leverage Index is essentially a measure of how critical a particular situation is. To calculate it, you are measuring the swing of the possible change in win expectancy.

You take the current base-out state, inning, and score and you find the possible changes in Win Expectancy that could occur during this particular plate appearance. Then you multiple those potential changes by the odds of that potential change occurring, add them up, and divide by the average potential swing in WE to get the Leverage Index.

A simple example will make that much easier to comprehend. Imagine the home team has a WE of 0.60 and then let’s assume that there are only two possible outcomes of this play (Single, Strikeout) just for clarity’s sake. Imagine each occurs 50% of the time on average (Again, just for clarity). Let’s say the WE after a single would be 0.7 and the WE after a strikeout would be 0.4. Let’s also say that the average swing is 0.04.

To get the LI of this fictional situation, you would take (0.1*0.5 +0.2*0.5)/0.04. This would be an LI of 3.75, which is extremely high! This makes a great deal of sense because the potential change in WE during this one at bat is quite large. It could end at 70% or 40% when most only have a spread of about 4%.

If you’re curious, you should read the linked article from Tango because he offers a more thorough explanation. In real life, there are more than two possible outcomes, so you have to average over far more possible scenarios. There are also other ways of arriving at the same answer, but this method is typically the easiest to understand.

An LI of 1 is average. We officially classify anything below 0.85 as low leverage and anything above 2.0 as high leverage.

Why Leverage Index:

Leverage Index is a measure of how “on the line” the game is at that particular moment. The great thing about LI is that it’s extremely intuitive, even if the calculation might not be. You know when the game arrives at a high leverage moment. If we polled people from various baseball backgrounds (statisticians, players, coaches, fans) they would all generally agree on which moments were high leverage. LI is simply a quantification of that intensity based on Win Expectancy.

This allows you to determine how players perform in different situations (high, medium, and low leverage). It allows you to review the way managers use their relief pitchers. It warns you that the game might change very dramatically.

Performance in high or low leverage moments isn’t a repeatable skill, but it’s important for teams to manage according to the situation and there’s plenty of room to admire players who contribute during big moments.

How To Use Leverage Index:

Leverage Index is a snap to use. An LI of 1 is average. Anything above 1 is above average and anything below it is below average. We bin the situations into three groups (Low: 0-0.85, Medium: 0.85-2.0, High: 2.0+), but then can range from essentially 0 to around 10 for the most intense moments.

You can look at the LI of a situation and recognize that this moment could really swing the game in either direction if the number is high. If it’s low, you can acknowledge that no matter what occurs here, the game is unlikely to be fundamentally altered.

When looking at LI for players across multiple games and seasons, you can get a sense of how they were used. For batters, there typically won’t be a huge range of average LI for starters, but pinch hitters who are used in big spots will have high phLI. Relievers who get the big innings will usually have higher LI.

You can also use the “Splits” to see how each player performed in each of these types of situations. Although it is important to remember that performance based on leverage is not a particularly repeatable or predictive skill. A .400 wOBA in high leverage situations one year tells you very little about the player that you couldn’t glean from their overall stat line.

Context:

An average (or neutral) LI is 1. High leverage is 2.0 and above, and low leverage is below 0.85. 10% of all real game situations have a LI greater than 2, while 60% have a LI less than 1. You can use this table of Leverage Indexes to familiarize yourself. Leverage Index is conditional on Win Expectancy and because that changes with the run environment, LI will be a little different from year to year. Average will always be 1 and the cut points are the same, but the specific events and situations will change a bit.

Things to Remember:

● Leverage Index depends on the inning, score, outs, and number of runners on base.

● Leverage Index is a measure of the potential swing in WE relative to average. Average is always 1.0.

● There are a variety of ways to calculate LI and several variants available at FanGraphs, showing things like the average LI when a pitcher enters and the average LI when they exit a game.

● If you go to a player’s “Splits” section his FanGraphs player page, you can find how the player performed in low, medium, and high leverage situations. While some players may have performed well in high-leverage situations compared to their average performance, that does not necessarily mean they will continue to produce that way in the future. “Clutch hitting” is generally the result of small sample sizes and random variation. A player shown to be very clutch one season does not necessarily mean that he will be very clutch in the next.