THE BOOK--Playing The Percentages In Baseball

Over at BBTF, you wrote:

“Clutch is the difference between WPA and WPA/LI.”

Has anyone used this measure of clutch to see if clutch hitting exists? For example, you mentioned AROD and David Ortiz having certain values for this in certain years. Does it seem like there is any persistence from year to year in WPA - WPA/LI? Or are players’ clutch ratings here random from year to year?

David at Fangraphs ran a correlation.  It was something like r or r-squared = .01 or something.

Thanks. I appreciate it.

Teeny tiny correction… FanGraphs now measures clutch (hitting at least, not sure how they deal with clutch pitching) as WPA/pLI - WPA/LI. It makes virtually no difference, but worth pointing out nonetheless.

People, including myself, misunderstand WPA/LI all the time.  That is because it has the term WPA in it and they think that it is pretty much like WPA in that it rewards “clutchness” or at least takes the timing of an event into consideration.

What they don’t realize is that the denominator, LI, “cancels out” the clutchness or timing aspect of the numerator, if I may bastardize the meaning of the stat a little.

Very few people realize that it is just a customized (for the base/out/inning score situation) linear weights.

Even I am not sure exactly what it does.  (It’s just not a particularly intuitive stat.) Is that right, Tango?

I didn’t RTFA, only the intro on Primer, but ANYONE who thinks that a stat, any stat, is THE stat for awarding an MVP, well, they are just not too smart of a person.

Not to get into it again, but some people think that increasing a team’s chances of winning, regardless of what happens, constitutes “value,” in terms of an MVP discussion, and some people don’t - they think that no value was created unless a team actually wins.

Both points of view are reasonable.  As are 100 other permutations.  Some people think RBI and runs are important because if you do something to advance your team’s chances of winning, but it leads no runs, then you didn’t create any value.  Again, a reasonable perspective.

The irony, if that is the right word, of the argument that some stat should determine the MVP is that if that is true, why would we need a vote?

It would just be the [insert stat] award.  We have plenty of those…

I read the entire thread on Primer. Tango, you have the patience of a Saint.  That was actually a pretty tame thread though…

"Even I am not sure exactly what it does.  (It’s just not a particularly intuitive stat.) Is that right, Tango? “

You understand it well.  And yes, if it’s tough on MGL, I pretty much only have 1% of the audience buying what I’m selling.

One day, I’ll show the wOBA equation for each game state.

One of the things that people have trouble comprehending is that it uses the inning/score to scale each event relative to the others.  Some people think that because of that, the values for the events fluctuate wildly, as they do with WPA.

What I love about the stat is evinced by the walk off walk/HR example (they have the same value).  If the batter and the pitcher are both aware of that, which of course they are, then the batter should not be “trying” to hit a HR any more than he is trying to walk. And the pitcher of course should be just trying to get an out.  So presumably in that situation the batter is going to increase his walks relative to his HR and the pitcher will do the opposite.  We should not give a batter any more credit for hitting a HR in that situation than we should a walk.  Same for the pitcher.  And that credit (or debit) that we are giving the pitcher and batter is not a matter of luck, or at least it shouldn’t be, as we suspect it is with WPA or some other clutch oriented stat.  We assume, and rightfully so, that with the bases loaded and 2 outs in the 9th inning of a tie game, if a batter gets a lot of walks that he is indeed trying to do that, and he should get credit for that effort.  If he hits a HR, it is not like he is trying desperately to hit that HR, so he doesn’t get as much credit as he normally would, at least relative to the other events, and rightfully so.  Basically, if a batter (or pitcher) is not willing or able to change his approach to adjust to the game situation, then he shouldn’t get the credit that he might think he deserves.  Again, with the bases loaded 9th inning example, if a hitter who normally hits a lot of HR and does not walk a lot is not willing to change his approach in that situation, he is going to get “nicked” by WAP/LI, as well he should.

I think I got that right…

Perfect.

Now, we need to provide the evidence.

Here’s where I get lost re: WPA/LI.  MGL says:
“the denominator, LI, “cancels out” the clutchness or timing aspect of the numerator,” but then says “it is just a customized (for the base/out/inning score situation) linear weights.” What does it mean to cancel out the timing impact, and yet still consider base, outs, inning and score? 

Tango also says that “WPA/LI is the game-state-specific wOBA.” I’m not sure what “game state” means in this context. 

I get the RE24 metric (I think).  It “knows” the base/out situation, but not inning/score (and of course is denominated in runs). 

And wOBA or linear weights of course doesn’t know anything.

What does WPA/LI know that wOBA doesn’t? 

(Let’s leave aside the bottom of 9th bases loaded scenario.  I understand why walk is as good as HR. But RE also mostly takes care of that by valuing BB, 1B, 2B, and 3B the same.  Only a HR is arguably overvalued by RE.)

WPA/LI is to inning/score/base/out what RE24/boLI is to base/out. 

RE24 is denominated in runs (but it doesn’t even have to be actually… I could call it WE24).  WPA is denominated in wins, which I could call it WE9072, if there were 24 base/out states, 18 half-innings, and 21 possible scores (-10 to +10 run difference).

Let me focus on this question:  What does WPA/LI know that wOBA/wRC doesn’t?  Is the only difference in the bottom of the 9th, or are there other situations in which WPA/LI would assign a non-generic value to an offensive event?  And if it’s the latter, could you give an example? 

I’m having trouble seeing how the “game state” (whatever that means) changes the value of a hit once you remove leverage, except in bottom of 9th.

Guy, look at this article:
http://www.tangotiger.net/wpali.html

Go down to TABLE 8, of which I’ll provide a snippet:

Look at how the relative value of the HR jumps at 2 outs, which those of the other positive events go down.  OVERALL, the average weighted value is exactly 1.00 at each base/out state.

The game state is inning/score/base/out.  So, for example, bottom 4th, down by 2, bases empty 2 outs.  I would create a line along the lines of the above. 

I do NOT know how much it differs from a top of 7th, up by 3, also with bases empty 2 outs.

Personally, I don’t see why you find the values in table 8 to be better than those in table 2, or really useful at all.  Why is a base-empty HR with 2 outs twice as valuable as a bases-empty HR with zero outs?  Or, stranger still, twice as valuable as a 2-out HR with runners on 2nd and 3rd??

In any case, I think you need to find a way to boil down WPA/LI to one or two sentences that explain conceptually—not technically—what it does.  I really appreciate all the effort you’ve made here and at BTF to explain it, but I don’t think you’ve yet got that. 

Examples:
If you want player’s impact on team’s chance of winning, you use WPA.

If you want to consider base/out but not score/inning, you use RE24.

If you want to consider players in context-neutral way, you use wOBA.

ANd if you want BLANK, you use WPA/LI.  You need to fill in the blank in 40 words or less, with no formulas.

Your answers focus on the idea that each PA=1.  But why is that important?  If you just want to have level playing field, so players with more hi-LI opportunities aren’t overvalued, you’d just divide WPA by the player’s LI.  But that’s not what WPA/LI does. 

WPA/LI clearly isn’t a context neutral stat.  And yet I don’t think it’s clear to many people exactly what part of the context it does take into account.  Which makes it a hard sell.....

Guy, you’ll have to re-read the article.  In no way can you compare the “value” of the HR in one line to the other.  This is the part that you should focus on:

Let’s look at the last line in the chart again (bases loaded, 2 outs). The “run” value of the HR now shows only 1.15 runs. This seems like an absurdly low number. However, what this shows is the run impact of the HR, given the base/out state, with the leverage aspect deflated. If you take the run value (1.15) and multiply it by the LI (2.8) you get 3.27 runs. What this really means is that this one PA counts as 2.8 PA. And “each” of these “2.8” PA is worth 1.15 runs. So, the batter did generate 3.27 runs, but this was largely built on being placed in such a high-leverage situation. In essence, his one HR generated 3.27 runs in “2.8” PA. If we want to count this PA as a single PA, the impact of this HR is 1.15 runs per unleveraged PA.

***

“If you want to consider base/out AND score/inning, but you want to count each PA as 1, you use WPA/LI.”

Guy, maybe I can help, although I am just reiterating what Tango has already said - somewhere.

(One of) The confusing thing(s) is that using WPA and then dividing by LI is a roundabout way of getting to what the stat means.  And actually, it is only an approximation of what it means, because I think LI is approximated.

Anyway, WPA/LI is exactly the same thing as linear weights.  Exactly.  Of course it is divided by 10 to get lwts wins, but that is trivial.  If you multiply WPA/LI, you get regular old-fashioned lwts.

But…

Rather than using the “overall” (averaged against all game states) lwts values of the various events, you use custom ones for every PA.  “Custom” means adjusted for the inning/outs/bases/score.

For example, with 2 outs and no one on base, we all know intuitively that an extra base hit is very valuable, as compared to a single or walk.  So if you were to compute the lwts value of all the events with no one on base and 2 outs, you would find that the lwts value of the extra base hit is very high compared to the single or walk.  Etc.

Keep in mind that the custom aspect also includes the inning and score, so that, for example, with your team down 2 runs in the last inning with 2 outs and the bases empty, the extra base hit and the single and walk have almost the same custom lwts value.

And because lwts values are always scaled so that they are relative to one another and they have to sum to zero, you don’t have a giant spread in custom lwts values like you do with WPA when the leverage can be 3 or 4 or .1 or .2.  The most you are going to have in general general is a little movement up or down (from the average lwts values) and the absolute most extreme values you are going to get is occasionally when the score is a blowout at the end of the game or the bases loaded, 2 outs, bottom of the 9th example.

The focus should be on TABLE 8.  You have to be intimately familiar with it, how you got there, and what it means.  There is no point in bypassing that table and trying to understand WPA/LI.  If you don’t get TABLE 8, stop.  And stay there until you get it.

In TABLE 8, we see the wOBA value for a walk is as low as 0.45 (men on 2B, 3B, 2 outs) and as high as 0.93 (bases loaded, 0 outs).

Remember 2 things:
1. The average value of a positive event is ALWAYS 1.00000.
2. The average value of a positive event divided by PA is ALWAYS the league OBP (let’s say .333).

So, when you see a value of 0.45 for a walk, it makes perfect sense.  It’s very close to being a neutral event (.333).  You can see why Pujols would get walked here, especially if HIS wOBA is .460 to begin with.

Therefore, when you see the wOBA value with the bases loaded, 0 outs of 0.93 for a walk and 0.95 for a single, this means that the pitcher and batter both know that either event is virtually interchangeable.  The scale is always that “1” is an average positive event, so you can see how much of a killer a walk is.

So, before we talk about WPA/LI, let’s talk TABLE 8.

OK, I think I’m clear on what you’re doing.  The values in table 8 are constructed to tell us the correct RELATIVE value of all positive events for that game state.  With bases empty and two outs, a HR is 4x as valuable as a 1B, but with no outs and runners on 2nd and 3rd, the ratio is just 1.5:1.

At the same time, you want all plate appearances to have equal value, regardless of the actual leverage.  No PA counts more than any other in terms of the average value of positive events.

You’re trying to measure how well a hitter took advantage of his opportunities, controlling for the array of opportunities he happened to have.
Have I got it?

Perfect.

What I like about WPA/LI (assuming I understand it correctly!) is that it provides an opportunity context for WPA. 

One thing I never really liked about WPA being used for evaluating player performances is that there is no reason to believe that two batters were performing in situations of equal leverage.  If one guy is batting in a bunch of two-out, bases-loaded situations in close games and another always comes up with the bases empty in blowouts, and they had equal performances, the former guy would likely have a better WPA than the second guy (well, better if he was good, worse if he was bad).

But in comparing WPA to LI, we neutralize those effects, and we’re seeing how a player does relative to his opportunities.  Conceptually, that seems more just to me.

But WPA/LI doesn’t really do that, Rally--it doesn’t really measure contribution to the “game state”, at least not in the same way WPA does, because LI carries the information about the game state and you’re taking that out.

I think the best way to get at the issue you’re raising is to group appearances by LI, such as Sean does at BRef, and compare production rates within those groups.

Don’t besmirch Rally by comparing him to me!

I have a request for Tango or David Appelman.

Basically the question is, what does WPA/LI look like in situations where the LI is very low? Here is what I would do if I had access to the data.

1. Take all PA this season with LI less than 0.1. Divide into two groups: put all the PA in which the batting team was way behind into the first group, and put all the PA in which the batting team was way ahead into the second group.

2. Just looking at the first group, calculate the average WPA/LI of each batting event (single, double, walk, out, etc). Also calculate the average RE24 of each batting event.

3. Do the same thing for the second group of PA.

Here is my rough guess of how the numbers are going to turn out for the first group.

RE24
out: -0.30
1B: +0.46
2B: +0.76
3B: +1.06
HR: +1.40
BB: +0.30

WPA/LI
out: -0.03
1B: +0.06
2B: +0.06
3B: +0.06
HR: +0.06
BB: +0.06

For RE24 I just took standard linear weights. For WPA/LI I am guessing that when the batting team is way behind, they are almost in “walk is as good as a home run” territory. But this is just a stab in the dark. I would love to see what the actual numbers are.

You might also try cutoff points other than LI = 0.1. I should say upfront that if the numbers come out close to my guess, I will take it as support for using RE24/"run leverage index” instead of WPA/LI. I could elaborate but it would be pointless without knowing the result of the calculation.

Don’t besmirch Rally by comparing him to me!

Oops!  Rally may never talk to me again.

dcj, you can play with the WPA Inquirer to get an answer.

http://www.hardballtimes.com/thtstats/other/wpa_inquirer.php

Actually, adding WPA/LI to the results might not be a bad thing to do.

OK, I understand WPA/LI.  But I’m still not sold. 

This is Tango’s summary: “If you want to consider base/out AND score/inning, but you want to count each PA as 1, you use WPA/LI.” That describes your process, but doesn’t really tell us substantively what part of a hitter’s context is or is not being considered.  It’s like if I said “I want to tax people based on their income, but tax everyone equally.” What would that mean? 

WPA/LI puts a premium on making sure that each positive event is properly valued relative to the other events in each situation.  So a HR is hugely valuable with 2 outs bases empty, because all other events have low run values.  A HR with runners on 2nd and 3rd no outs, however, has relatively less value because a double does the job nearly as well. In a sense, the HR is “wasted” in that game state.  WPA/LI tries to reward hitters for selecting the right tool at the right time. 

BUT:  is that a helpful way to think about baseball?  In a game like bridge I can see how this approach makes sense: we might say a player “wasted” a king in winning a K-7-5-4 trick; he could have used it another time to better effect.  But hitters don’t have a stack of 1B, 2B, HR in their equipment bag, and then decide when to play them.  In fact, a bases-empty 2-out HR is not hugely valuable, and certainly not twice as valuable as the 2nd/3rd no out HR.

(You say there is “no way” I should compare values down the columns.  But if you want ratios that work within each game state, and count each game state equally, you will inevitably end up with values for a given offensive event that don’t make a lot of sense. Why shouldn’t we consider that in evaluating WPA/LI?)

**

Let’s compare table 8 to straight wOBA values.  The value of the 1B and XBH really don’t change a lot.  The value of the HR and BB change much more.  Why?  Because the LI you calculate for each game state is an average—in fact, each event is differently leveraged in any given game state.  The actual leverage for HRs and BBs varies from this average far more than the real leverage of 1B and XBH, for understandable reasons.  For example, with 0 outs runners on 1st/2nd, the LI is 2.1.  But by event, its:
BB 2.56
1B 2.13
XB 1.94
HR 1.53
The difference between your custom game state values and the generic values is this difference between the individual event leverage and the average leverage.  So the question is, what’s important about these residual weights?  Why do we want this stat that sort of takes acount of context, but sort of doesn’t?

One reason is to address LAWBH’s concern.  But can’t we just do that by dividing by the players’ season LI (a trivial adjustment in most cases)? 

Here’s how I would answer the basic questions about these stats:
Does it reward hitters for doing well late/close?
wOBA: no
RE24: no
WPA:  yes
WPA/LI:  kinda

Does it reward hitters for doing well with RISP?
wOBA: no
RE24: yes
WPA:  yes
WPA/LI:  sorta

Unless there are clearer answers for WPA/LI, I don’t see how you sell it.  Or, honestly, why anyone should be buying.

dcj: it’s easy enough to figure with an illustration.  I’m going to take man on 1B, 1 out, as that has a standard-ish wOBA equation:

.75 for a walk, .83 for a single, 1.32 for an XBH, and 1.99 for a HR, and +.04 for a K (yes, a K is good because it’s better than a DP).

I’ll take a care of home team down by 10 in the bottom of the 4th.  The WE is .009, and the LI is 0.10.

If you get a HR, the WE is now .020.
If you get a triple, the WE is now .018.
If you get a walk, the WE is now .013.

If you get a single, and the runner advances 1 base, the WE is like a walk.  If the runner gets to 3B, the WE is .014.  Let’s say it’s .0135 for a single.

If you get a double to put it at runners on 2B, 3B, the WE is .016.  If he scores the runner, it’s .017.  Let’s say it’s .0165 for the double.

That’s all we need to know.  The walk adds +.040 wins, the single is +.045, the double is +.075, the triple is +.090, and the HR is +.110.

Roughly speaking, the average positive event adds +.054 wins.  All you have to do is divide the above numbers by .054 to get your game-state specific wOBA!

So, the walk is .040/.054 = .74.

.74 BB
.84 1B
1.42 XBH
2.04 HR

As you can see, these numbers are VERY SIMILAR to just looking at the base/out state, and ignoring inning/score.

So, you are wrong in thinking that a HR is like a walk in this situation.

"A HR with runners on 2nd and 3rd no outs, however, has relatively less value because a double does the job nearly as well. In a sense, the HR is “wasted” in that game state.  WPA/LI tries to reward hitters for selecting the right tool at the right time. “

Perfect example.

***

“Unless there are clearer answers for WPA/LI, I don’t see how you sell it.  Or, honestly, why anyone should be buying. “

The illustration in post 27, but taken to a closer game, is what I need to go.  Give me a few minutes.

Let me take the home team is down by 2, it’s the bottom of the 7th, there’s a runner on 3B, and there’s 1 out.

If we ignore the inning/score, and stick to base/out, the wOBA equation (using TABLE 8) is:
-.45 K
+.79 BB
+1.22 1B
+1.48 XBH
+2.25 HR

According to this, the batter has to be aware that the K is a killer.  And he knows the pitcher knows this.  So, the pitcher will try to K him, and the batter will try to avoid being K-ed (maybe he will turn into a hacker, he’ll shorten his swing, whatever).  He also knows that the walk’s value stays relatively constants (goes from the random .72 to this state’s .79), while the others jump in value, specifically the single.  This state is tailor made for an Ichiro/Gwynn type of player.  And, we knew this anyway.  This just quantifies it for us.  It proves it.

The question Guy is asking is: isn’t it enough to know the base/out state?  Does knowing the inning/score change anything?  Is being down by 2 an important thing to know (HR will tie the game)?

I have no idea. Let’s find out.

The WE is .293 (and the LI is 2.08, so the opposition better have a decent reliever out there).

Ok, a HR clears the bases and ties the game.  The WE is .552, for a gain of +.259 wins.

A walk puts runners on the corners, so the WE is .344, for a gain of +.051 wins.

The K means you are at 2 outs, and the runner on 3B.  WE is .205, or a drop of .088 wins. 

The single gets the run in and puts the runner on 1B for a WE of .382, or a gain of +.089 wins.

The double puts the runner at 2B, the WE is .417, for a gain of +.124 wins.

The triple gives you the extra run, for a gain of +.185

Here’s the table for change in wins:
-.088 K
+.051 BB
+.088 1B
+.130 XBH
+.259 HR

And after following the process I lied out in the article, this is the wOBA values:
-.54 k
0.81 bb
1.17 1b
1.58 xbh
2.83 hr

As you can see, the K is a bit more costly (-.54 wOBA value compared to neutral -.45), and the HR jumps hugely in value.  Now, all of a sudden, it’s not necessarily a Gwynn-type player that helps (it still does), but now a HR hitter who doesn’t K also jumps up in value (say, Vlad).

The most important thing in looking at this, is this: the average value ALWAYS remains at 1.000000.  The batter cares about the relative value of various events, so he can know how he can change his approach, if he can.  And the pitcher also needs to know how damaging everything is.

Basically, WPA/LI gives you the blueprint as to how to approach each PA.

If you want something to blow your mind, imagine that the game state not only includes the inning, score, base, out, but it also includes the count! 

So, imagine you have the above scenario, but the count is 0-2.  Now what does the batter do?  He’s in a huge hole, the K is enormously costly.  How does he change his approach?  Presumably, he has to shorten his swing so much as to just get a single (which itself is valuable).  But the pitcher knows this too!

And the ultimate would be to take the identity of the pitcher, the batter, their repertoires, the fielding talents of the fielders, the speed of the runner (in case of GB), and the park/run environment.

WPA/LI is simply the first progression from the 24 base-state analysis.

If you are not sold, at least tell me you are still in the room.

Thanks to Studes and Tango. #27 and #29 were very helpful. You’ve convinced me that WPA/LI is better as a single stat than RE24/run leverage index.

But, I am still not completely sold. I’ll try to work out an example that explains my worries.

I’ve in the room.  But I’ve got one foot out the door :>). 

I see why the values in table 8 provide an interesting “map” to the relative values of different events in a given game state.  It tells a story, like WPA does in a different way.  But I don’t see how WPA/LI is a superior measure of hitter performance or value.  It tells me how well the hitter “selected” his offensive output within any given PA, but at the cost of less accurate valuations ACROSS his PAs (in my view). 

What might be interesting would be to find a way to show what kind of hitter is best leveraged in different game states.  A simple way is to create a table showing the custom wOBA weight (table 8) divided by the generic wOBA weight.  That would show you which events are most/least highly leveraged in that game state, controlling for the overall leverage. 

And maybe you could estimate how well/poorly different hitters are leveraged in each game state.  For example, show the value of Pujols, Ichiro, and Ryan Howard in any given game state (relative to their respective average values), given those hitters’ diestribution of offensive events.  Are there game states in which Ichiro is nearly as valuable as Pujols?

Guy said:

A simple way is to create a table showing the custom wOBA weight (table 8) divided by the generic wOBA weight.

I already did something like that in post #2 here:
http://www.insidethebook.com/ee/index.php/site/comments/leverage_index_by_base_out_states/#2

Some guy named Guy commented on that in post #3.

Guy also said:

For example, show the value of Pujols, Ichiro, and Ryan Howard in any given game state (relative to their respective average values), given those hitters’ diestribution of offensive events.  Are there game states in which Ichiro is nearly as valuable as Pujols?

And, this was done by Sky for Adam Dunn here, on a count (not base/out) level:

http://www.insidethebook.com/ee/index.php/site/comments/hitting_by_count/#14

As I noted, you really want to do this at the inning, score, base, out, count level.

So, I’ve shown one for base/out, and Sky shows one for count.  You really just need to expand that all the way.  Well, “just” is the long part.

Sky’s work in this regard is fantastic.

I in no way think a pure value metric should be adjusted by count. A hitter has waaaaaaaaaaaaay too much control over that.

Colin: I was definitely not talking about “value”, but approach.

But, if you want to talk about “value”, I would do it component-wise.  If, let’s say Dunn is a +30 run hitter, you can say that he’s +10 at 0-0, +5 at 1-0, -3 at 0-2, etc, etc, so that if you add it all up, he’s +30.

This is no different than putting a run value on a pitcher’s pitch.

Okay, I have my example.

To keep things simple I am looking only at runs, not wins. Here are my stat definitions.

BRAA: Context-neutral linear weights, that is, 0.48*1B + 0.78*2B + etc. I am using the ones from THE BOOK Table 7, which assumes a run environment of 4.9 R/G (1999-2002 MLB).

RE24: Linear weights by base-out state. I am grabbing this from Fangraphs. I chose the 2007 AL because that also has 4.9 R/G.

boLI: Leverage index by base-out state, as in Tango’s link in post #32. I am using the figures from TABLE 3 in the WPA/LI article. They should be consistent with the BRAA figures.

The analog of WPA/LI in this situation is RE24/boLI.

--

What makes a hitter “clutch”? There are two components.

1. He performs better across the board in high-leverage situations.

2. He changes his approach depending on what the situation calls for. (E.g., he trades strikeouts and home runs for fly balls with 1 out and a runner on 3rd.)

BRAA takes into account neither (1) or (2). RE24 takes into account both (1) and (2). As I understand it, WPA/LI (or in this situation, RE24/boLI) is supposed to take into account (2) but not (1).

Thus, RE24/boLI - BRAA should be a pure measure of (2), and RE24 - RE24/boLI should be a pure measure of (1).

But, what if a player has “well-shaped” production in high-leverage situations and “ill-shaped” production in low-leverage situations? If we normalize so that each PA has the same weight, we will conclude that his overall situational performance is about average. In fact, though, the high-leverage situations are more important, so he creates more runs for his team than would a player with “average-shaped” production in all situations.

Note that all this is keeping the across-the-board performance level (say, wOBA) constant in both high and low-leverage situations.

I conclude that RE24/boLI - BRAA is not a pure measure of (2). Instead, we should weight each PA by its leverage, so that a few well-shaped contributions in high-leverage situations can cancel out a larger number of ill-shaped contributions in low-leverage situations. In other words, the appropriate measure of (2) is RE24 - boLI*BRAA.

It is a bit easier (for me, at least) to see why boLI*BRAA - BRAA is a pure measure of (1). Indeed, boLI*BRAA is essentially leverage-weighted wOBA.

So, I propose:
To ignore both (1) and (2), use BRAA.
To count both (1) and (2), use RE24.
To count (1) and ignore (2), use boLI*BRAA.
To count (2) and ignore (1), use BRAA + RE24 - boLI*BRAA.

I am suggesting BRAA + RE24 - boLI*BRAA as a replacement for RE24/boLI, and likewise BWAA + WPA - LI*BWAA as a replacement for WPA/LI.

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As an example, I selected 247 PA from Vlad Guerrero’s 2007 season so that:
BRAA = 15.2
RE24 = 20.5
RE24/boLI = 11.5
boLI*BRAA = 15.5

Then RE24/boLI - BRAA = -3.7 while RE24 - boLI*BRAA = 5.0.

Was his situational hitting good or bad during those 247 PA? I made a spreadsheet (Excel file) so that you can decide for yourself.

I’d appreciate feedback on #36. I am to the point of saying that WPA/LI should never be used, but I am open to counterargument.