Monday, November 27, 2023
Deconstructing Leveraged Index
About twenty years ago, I introduced Leveraged Index to our little baseball community in a three-part series, which you can read about at the old The Hardball Times (since subsumed by Fangraphs).
The concept was straightforward enough: determine for each game state (inning, score, runners on base, outs) how much impact that situation had to winning or losing the game. Directionally, it made perfect sense: close and late had a higher leverage than blowouts. Of course, sabermetrics is not about directionality, but magnitude. We all know that there's a platoon advantage by handedness, but HOW MUCH is that advantage? We all know that it's easier for a pitcher to throw one inning in relief rather than six innings as a starter, but what is the DEGREE to which it's easier? We all know that Coors is hitter friendly but what is the magnitude of that effect?
And so, as part of that series I also released the Leveraged Index chart.
A few years later, in a long-forgotten article, I also discussed the Leveraged impact focused only on the base-out state. Bases empty? That's low leverage. Bases loaded? That's high leverage. We all know that. With the bases empty, a walk has limited impact. With the bases loaded, it guarantees a run.
Here is the Leveraged Index by Base-Out state (click to embiggen).
Baseball Reference uses a form of this chart on their site, in order to deleverage RE24 (run expectancy by the 24 base-out states), as RE24/boLI. Baseball Reference has so much data oozing out of its site, I would bet that most folks are not aware of this fantastic page.
In 2023, the pitchers to look at are Blake Snell and Spencer Strider. As we know, the performance of Snell with runners on base was much better than his performance with bases empty, while Strider was his opposite. If you treat both scenarios the same, you would think that Snell and Strider had equivalent pitching seasons. But, if you give more weight to facing batters with runners on base, when those situations has more leverage, then Snell easily outpitched Strider.
So, if you allow the leverage to drive your opinion, then RE24 is what you want, and we can see that Snell was almost 30 runs better than Strider. Which of course tracks with their ERA: Snell gave up 45 ER on 180 IP, while Strider gave up 80 ER (or 35 more) in 186 IP. Add 2 ER and 6 IP to Snell, and you have identical IP and 33 fewer ER for Snell. RE24 gets you to a similar place.
But if you deleverage those high-leverage base-out scenarios, Snell is only 4 runs better than Strider. Which of course tracks with their similar wOBA. See, what happens is that each bases loaded situation counts as 2.5X to 2.9X as much as a regular scenario, while bases empty count as 0.4X to 0.9X, depending how many outs. Is a bases empty, 2 out (leverage index of 0.39) strikeout worth exactly the same as a bases loaded, 2 out (leverage index 2.85) strikeout? Or, is the bases loaded one worth 2.85/.39 = 7.3X as much as the bases empty one? In terms of the run impact, it's 7.3X, no question. In terms of a strikeout is a strikeout is a strikeout, they are identical.
How do you see it? Is a 10 yard pass inside the opponent's 10 yard line worth the same as a 10 yard pass at your own 20? You tell me. Is a 20 foot pass through the slot to an open player for an easy goal worth the same as a 20 foot pass from the goalie to his defender? You tell me. You get to decide whether a pass is a pass is a pass. Or whether the context matters. You get to decide whether all strikeouts are the same or whether the context matters.
Now, as much as all the above is fun to think about, I'm here to finish the job in terms of Deconstructing Leveraged Index. I just presented the Base-Out Leveraged Index. Now I'm going to present the other half, something I've never done: the Inning-Score Leveraged Index. Here it is (click to embiggen).
A half-inning of "16" means the bottom of the 8th. All the black lines are the top of the inning. Here we can see that leverage is maximized when the batting team is down by 1 run. This is of course not a surprise, directionally. But as I said, sabermetrics is about the magnitude, not the direction. We can confirm direction, but the value is in establishing the magnitude. And that's what we have here.
And we can also see something plainly obvious: a tie-game and the batting team down by 2 are worth roughly the same, while batting team ahead by 1 or down by 3 are worth roughly the same. So, if you are going to deploy a good reliever, and your choice is a tie game or the batting team down by 3, it is a very easy call: tie game. To suggest otherwise is to miss the impact, the leverage of the game. Sometimes sabermetrics is about reminding you of directionality.
Similar to whether you want the full effect of the situation via RE24, or deleveraged via RE24/boLI, you also get to decide whether you want the full effect of the inning-score as well. Do you want to treat the batting team down by 1 in the 9th inning (leverage index of 4.0) identical to the batting team down by 1 in the 1st inning (leverage index of 1.0)? You tell me. WPA and WPA/LI are both available, which you can also see at Fangraphs.
Obviously, Mariano Rivera would not enter a game unless the leverage was high enough. When you have one of the greatest pitchers of all time, and you can deploy him when his performance can matter the most, when you can leverage his talent, then naturally, you care about the leverage of the inning-score. Do you put Ozzie Smith at SS or 1B? You leverage his talent when he can make the most impact. Ozzie can make .05 more plays than a random fielder at SS or at 1B, but he will see alot more of those impactful plays at SS than at 1B. Do you put Kevin Kiermaier in CF or LF? It's all about leveraging opportunities.
There is no easy answer, no straightforward solution to evaluating the performance of players. There are only dozens of good questions, and so, potentially dozens of solutions to offer.
On a side note: you might think you can just multiply the boLI (base-out) by the isLI (inning-score), but it doesn't work exactly like that. It works sometimes, and doesn't work other times, notably when you care the most (ninth inning, close game). Multiplying two probability distributions only works when they are independent, and in this case, they are decidedly not independent.
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