The Leverage Index

I had some thoughts about this, wanted to share and have feedback.

The leverage index is basically "(a) measure of how important a particular situation is in a baseball game depending on the inning, score, outs, and number of players on base" (quote Fangraphs). Intuitively, it's very simple, if your reliever gets in a game tied-up with two men on-base, you have a high-leverage situation. If you reliever mops-up a 8th inning in a game you are trailaing by 5 runs, you have a low-leverage situation. I'll refer you to the fangraphs.com site for more information.

I won't get into the maths (I'm not sure I understand it myself), but there is some sort of weight that sabermetricians have created, it's called the leverage index. If a closer has saved your team 10 runs in situations with a high leverage index, it has more impact to winning than if a mop-up has saved your team 10 runs in situations with a low leverage index. They created this index so that 1 is the leverage value when you start a game. Above 1, you are in a high critical situation, and below 1, chances are the probability to win or lose the game is lower.

As you probably know, in a course of 162 games, saving 10 runs is worth roughly 1 win. But in the above example, you can't deduce that each reliever contributed to 1 win each because each saved 10 runs. Instead, my understanding of the leverage index is that, if the closer above saved 10 runs with a leverage index of 2.0, he gave your team 2 extra win. The mop-up above who saved 10 runs with a leverage index of 0.5 gave your team 0.5 extra win. In other words, there is half the chance that this mop-up gave your team a chance to come back and win---and there is half the chance this didn't happen.

The reason I write all this is because I want trying to figure a way to apply potential leverage index for the relievers we select in SOM.

Here is what I did: I took all relievers from the 2014 seasons with more than 30 innings. I created six categories:

The closer (any reliever with more than 30 saves)
The 1set set-up man (any reliever with more than 20 holds)
The 3rd string (any reliever with a combined save/holds between 10 and 20)
The mop-up guy: any reliever with more than 55 innings and less than 10 combined holds/saves
The specialist: a select group I chose and who had generally more games than innings---all with less than 55 innings.
The 0.5M guy (aka the extra reliever we have to take but we don't really need): any reliever with less than 55 innings not in the above categories

(While doing this exercice, I had to create another category: the set-up man who won the closer job (ex. Romo), but I'll leave this aside for a moment).

I average the leverage index that you can get on the fangraphs site for all relievers who fit the above categories. Here are the results:

Closer: Leverage index of 1.90
set-up: Leverage index of 1.44
3rd string: Leverage index of 1.18
Mop-up: Leverage index of 0.82
Specialist : Leverage index of 1.02
The rest: Leverage index of 0.74

What I'm wondering is whether I can use these numbers for strat. Does a closer who has roughly the same use than in MLB (80 games, 80 innings, 40 saves) might be attributed a leverage index of 1.90? Does a set-up guy who, in Strat, will often cumulate 120-140 innings, should be attributed a leverage index of 1.44? Or maybe a leverage index somewhere between 1.44 and 1.18? What about a reliever who is both closer and set-up? (For the record the category "set-up guy who won the closer job" had a leverage index of 1.60).

And does this mean that a closer worth 4M who pitches in high leverage situations contribute like a 6M reliever who never closes?

What I'm wondering is whether I can use these numbers for strat. Does a closer who has roughly the same use than in MLB (80 games, 80 innings, 40 saves) might be attributed a leverage index of 1.90? Does a set-up guy who, in Strat, will often cumulate 120-140 innings, should be attributed a leverage index of 1.44? Or maybe a leverage index somewhere between 1.44 and 1.18? What about a reliever who is both closer and set-up? (For the record the category "set-up guy who won the closer job" had a leverage index of 1.60).

Well, you've already anticipated a key problem. Most managers in SOM, including myself, use our closers much more, and in many more situations, than most MLB teams who stick to the 9th-inning closer role do. Many managers use their closers from the 6th or 7th innings on and in many different roles. So, I would imagine that would mess up your rating system a bit in evaluating closers.

So, it could still be workable, but would just need some further tinkering.

Marc, the day I am made GM of a Major League team I want to hire you (don't hold your breath)... Unfortunately I agree with Strether that the formula needs some work for SOM usage.I do not use my relievers at all like Major League teams.

Hal AI is horrible in leverage situations (for me anyway), and not just with pitchers.

When I have a small lead in the 7th, or 8th--bases loaded one or two outs, and a weak hitter up, HAL never pinch hits--The AI is satisfied with a one or two run lead, never trying to get more. The AI literally seems to try to lose from ahead in many games, and is successful way to often.

AS for pitching here is a game where HAL pulled my secondary closer after pitching to one batter to put my LH specialist in (who has no closer rating). Of course a batter reached and immediately F0. All my other relievers were used, and my front line closer was tired. An absolutely idiotic move that probably cost me the game.

http://onlinegames.strat-o-matic.com/ga ... /426942/23

How the AI can make moves this bad frustrates me to no end--a PC league too.

The "leverage" in any situation I have come across depends on how you're using your personnel. You can win by maximizing strong SPs to get the bulk of the innings and hand off mop ups and match ups to a low budget reliever corps. You can also win by having a high dollar R2 reliever set to super-relieve.

When you take the game engine and all that into consideration, I think the policy of paying more for the quantity of innings pitched rather than the quality seems to give you the most margin for error.

An strong R2, a closer, a mop up, and a ROOGY/LOOGY setup seems to get the job done with most conventional rotations.

Thx guys for thė comments. The issues raised is what I want to clarify. When A manager uses his closer as early as the middle innings and cumulate 150 innings, How does it impact the leverage index? I would guess that it's roughly 50 innings as a closer, 50 innings as a set-up man, 50 innings as a 3rd string, for an average leverage index of 1,50, perhaps even less.

I wonder if the degree of leverage also depends on the SP who are being replaced?

In the 2012 card set, I had a team with a pedestrian starting rotation backed up by Raul Valdes and Aroldis Chapman. Using both as super-relievers in the 2 seasons of that card set, Valdes was second to Chapman for CYA in the first season and won the CYA in the second season.

I have no doubt it was only because of them that each team won 100 or more games!

I'm just glad Marc(luckyman) is back and posting deep and interesting material on the boards!!

Very good point, tcochran. It might very well be that the leverage index is influenced by some type of pitcher---i would take a guess that 4-5m starters with low power higher on-base are probably those inducing the higher critical situations for their bullpen.

I know for a fact that the type of stadiums influence greatly (leverage is higher in low-ball stadiums, is lower in Coors-type stadiums---but you need more innings from the bullpen in Coors-type stadiums).

Thx splinter.