THE BOOK--Playing The Percentages In Baseball

Yep, if you do it on an individual event level he has a leverage adjusted WPA of .69 opposed to .42.  This is something I’ll fix when I implement the park run environment.

I think Clutch is currently calculated with OPS Wins/LI.  It doesn’t make a huge difference, but it does make some difference.

A few questions:

“Or, you can look at it the other way: he’s normally +.02 this year, which if you multiply by 10.9 means that we expected him to add +.22 wins based on his seasonal data.”

I agree that this is the right way to do it. However, 10.9 is something of a weighted average: a HR has 6x its normal impact, maybe a single has 15x its normal impact, etc. Wouldn’t it make more sense to plug A-Rod’s actual season line into the situation, rather than just multiplying +.02 * 10.9? What I mean is,

24 PA total
14/24 outs * -.28 wins (omitting ROE)
2/24 BB * +.38 wins (estimated)
1/24 1B * +.6 wins (really estimated)
3/24 2B * +.72 wins
0/24 3B * +.72 wins
4/24 HR * +.72 wins

Total sum is +.10 wins. That’s how much we should have expected A-Rod to provide, given his season line so far. (Only one single in 24 PA!) So the clutch amount would be +.62 wins.

Of course this is really not a big deal. The only reason it’s so far off is that it’s early in the season and A-Rod only has one single.

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Second question: how does LI deal with a situation like bottom of the 9th, tie game, 1 out, man on 2nd? The IBB has to be extremely common in that case. Assuming that a walk barely changes the win expectancy, it would be unfair to punish an A-Rod for walking rather than adding his customary +.02 wins * 3.2 LI. On the other hand it might be a bad idea to throw out IBB entirely. Bonds derived a lot of his value from IBB in 02-04.

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Third question, for dkappelman if you’re still around: How is OPS Wins calculated?

OPS wins is .025 * PA * (1.7*OBP+SLG -1)

Wow, even among the Sabermetrics community, even when A-Rod does something clutch, he still doesn’t get credit for a clutch hit!

Let’s review the ARod play, and see what it tells us:
http://www.fangraphs.com/plays.aspx?date=2007-04-07&team=Yankees&dh=0&season=2007

1. The win probability before the play was .28
2. The run expectancy before the play was .81
3. The win gain of the play was +.72 wins
4. The run gain of the play was +3.31 runs
5. The leverage index of the game state (inning, score, base, out) was 10.9
6. The leverage index of the base/out state was 2.7
7. The average player would have gained 0 runs and 0 wins
8. The average star hitter (+.01 wins per random PA) would have gained +.109 wins in that situation.
9. The average run value of that play (in a random situation) was +1.40 runs.
10. The average win value of that play (in a random situation) was +0.13 wins.

Now, we want to know: how much clutch to assign the play.

Typically, we treat clutch as “wins above what his performance line would suggest, if his performance occurred randomly”.

The problem here is that we’d have to constantly recompute ARod’s performance line after every game, for every situation.  Say that ARod now gets into a hitting funk, so that he hits like Adam Everett normally has.  Now, his “wins above performance” for that big play would change.

So as to not constantly do this, we accept our first shortcut: the expected win probability of ARod would be 10.9 times his seasonal random wins per PA.  Right now, it might be +.02 random wins per PA, but by the end of the season, it’ll be sa +.01 random wins per PA.  If we multiply that by 10.9, we get +.11 wins that we would have expected ARod to deliver on that play.  He in fact added +.72 wins, or a gain of +.61 wins more than we would have expected from our star hitter.

That +.61 wins is something real to the Yankees, but something that ARod was lucky to get.  Not that he was lucky that he hit the HR, but that he was lucky that he gets to count that HR 10.9 times more than another PA.

That PA was worth +.72 wins, which if we divide by 10.9, gives us +.07 wins.  What that +.07 wins is the impact of ARod’s HR (which would have been the same as a 2B, or 3B) for that particular situation, and the extra +.65 wins is the bonus he got for its impact.

If we do sum of WPA/LI for each PA, what we are getting is a situational-hitting measure.  This *does* consider that a 2B, 3B, HR are equals in the ARod case, but doesn’t have the magnifying impact.  So, if someone says that Darin Erstad gets a groundball out to move runners over in tight games, this measure will give it to us.  It properly values each event, based on the change in the win probability, without giving its magnifying effects.

If we do sum of LWTS/10.x (where 10.x is the runs per win converter), what we are getting is a measure that doesn’t distinguish between the Erstad outs.  A GB out is a GB out.

If we do sum of LWTS24 / LI24 / 10.x (where LWTS24 is Linear Weights by the 24 base/out state, or BRAA on Fangraphs, and LI24 is the Leverage Index for that base/out state), this does handle some of the Erstad outs (extra impact for moving runners over), but doesn’t have the magnifying effect.  ARod’s HR, for example, is +3.31 runs / 2.7 / 10.x = +.12 wins.  As you can see, a HR isn’t as valuable with the bases loaded as in other situations, relative to other things that can happen.  A walk for example would be +1.00 runs / 2.7 = 0.37 runs, which is about 10% higher than in a random situation.

So, LWTS24/LI24/10.x and WPA/LI are very similar.  The second one has more “situational information” to more properly value the effect of say, a walk with bases loaded and down by 1 run.  But, in both cases, the run and win value of the walk is given its due.

Getting back to ARod.  If we do WPA/LI minus LWTS/10.x, we get his situational impact for that PA, relative to his overall performance.  If this was his first PA of the year, he’d actually end up with a negative clutch, since a HR is expected to add +.13 wins x LI, which in this case would be +1.40 wins.  Hardly possible and hardly makes sense for what we want. 
What we can do is simply not do the subtraction.  Simply report WPA/LI as his situational win impact without the magnifying impact (i.e., treats each PA the same), report his LWTS/10.x as his context-free performance.

It would be tempting, though dangerous, to subtract the two, since we get a situation where in ARod’s case, we get a negative clutch number.

Earlier I said “we accept our first shortcut”.  It is that shortcut that causes the problem.  By expecting that a random ARod HR should deliver +1.40/10.x * 10.9 (+1.4 wins), or +3.31/2.7/10.x * 10.9 (+1.3 wins).  If we were to only look at his overall stat line, or his stat line by the 24 base/out states, that’s how much wins we should expect his HR to deliver, if the LI is 10.9.  We are saved because, given enough PA, the quirk washes away.

Since it’ll be crazy work to NOT accept the shortcut (who wants to do all that work for something so benign), we either accept the quirk, or we don’t compute Clutch at all.

To the extent that you want to accept the quirk, then you would either do:
a. sum WPA/LI minus LWTS/10.x
b. sum WPA minus LWTS*LI/10.x

The first treats each PA “equally”, while the second keeps the magnifying effect.

If you were to do sum WPA minus WPA/LI, what are you calculating?  You are capturing the magnifying effect of the PA, while accepting the ARod HR as a given.  That is, his +.07 wins now becomes his baseline.  Rather than using his seasonal performance to get the +.01 wins or +.02 wins that would have been expected, had his seasonal performance occurred in that situation, you are treating his performance as the universe.

Is this wrong?  I guess it all depends on what it is that you are after.  The one salvation is that you don’t get “the quirk” any more.  Whether ARod got a 2B, 3B or HR in that situation, it is treated exactly the same, and is “clutch”, if you calculate it this way, will always give you the exact same result, regardless of what he does in the rest of the year.

It would be interesting to see how things change in 2006.  Are Ortiz, Pujols, Jeter still on top, and is ARod still on the bottom?

I posted this here:
http://dcbb.blogspot.com/2007/04/lack-of-dominance-in-chart-form.html

I agree that the purpose of the chart is to convey your feelings.  On that, it’s perfect.  It reflects what you see, and there are NO SURPRISES.  (Or virtually none… the few surprises would be mild ones, and a bit interesting, especially with stolen bases, etc.)

But, the larger purpose is that now that we’ve been able to quantify those feelings, we can add them up.

No more are we going to be able to forget about ARod’s slam.  It will no longer be a footnote.  Rather, it will be a looming shadow, one that will always be present, because we were able to quantify our feelings. 

WPA said “I love you”, and no one’s going to take it back.  It will be there from now until eternity.

***

I’m not sure it needs to be revolutionary, and neither is say Leverage Index.

Yes, it simply translates whatever adjective-du-jour is in play into a chart and numbers. Isn’t that good? This would cut out 90% of the drivel we hear and read.

ARod’s WPA was +.78, while the LI was 10.9. That’s it. Take the 1 million words discussed on this subject, and leave it to that one line. People want to be part of the story, and they don’t need to be. The WPA/LI does that in two numbers.

All I want to hear is what ARod himself has to say about how he felt and how he approached the PA (and I want to hear from the pitcher). I don’t care what ESPN mouthpieces think.

After reading through #5 for a few times, I think it finally makes sense to me.

I ran the 2006 numbers for WPA/LI, and it comes in quite close to OPS Wins for qualified players (.945 r^2).  Clutch with OPS Wins ends up correlating with Clutch with WPA/LI pretty well too (.832 r^2).  Pujols and Zimmerman are still #1 and #2.  Jeter moved from 5th to 6th, Ortiz from 7th to 14th.  A-Rod went from 158 to 149. Manny made the biggest jump of the players I looked at from 149 to 108. Troy Glaus is still dead last.

It seems to me that either method get you basically what you’re looking for with some slight variation.

The advantage of WPA/LI is that things will always add up on a game-by-game basis, whereas with OPSwins, you’re always calculating it at the season-to-date level.  And of course, it properly balances things like IBB and Erstad moving runners over when the game is one the line.

Right.  On FanGraphs I think I’m going to swap out OPSWins in exchange for WPA/LI and just make Clutch WPA - WPA/LI.  It’s a much cleaner solution (to me at least), and I don’t need to worry about the constant in OPS Wins from year to year.  Career clutch will also add up correctly.

David—just for the record you’re a legend (not that it need be said)

David implemented the changes, replacing OPSwins with WPA/LI.

Why is this cool?  What WPA/LI measures is everything that everyone has wanted to measure.  In a situation where the bases are loaded and it’s a tie game in the bottom of the 9th, a walk and a HR are *indentical* in worth.  Everyone knows that.  This is the reality.  WPA/LI gives you that. 

For example, let’s use this:
http://www.tangotiger.net/welist.html
Bottom of 9th, tie game, bases loaded, 2 outs, and the win probability is .662
And if we use this:
http://www.insidethebook.com/li.shtml#18
The Leverage Index (LI) is 6.4

Now, anything positive, from a balk to a HR, will add +.338 wins.  If we divide that by 6.4 (i.e., WPA/LI) we get +.053 wins.

Remember something.  In a random situation, a walk is worth +.03 wins, a single is +.04, a HR is +.13, etc.  But, in this particular situation, the hitter, the pitcher, the fans, and the world knows that each of these events need to be treated equally.  Given that a walk and a HR is the same in this situation, you need to treat it the same.  And, +.053 wins is that number (and, it’s between the +.03 and +.13 that we expected). 

In short, if you take the frequency of each event (10% for walks, 15% for singles, etc) and multiply that by the random win value of each event (+.03 for walk, +.13 for HR, etc), you will get something close to +.053.

On the flip side, an out is -.162 wins (.662 minus .500, since we are now in extra innings), divided by 6.4, or -.025 wins.

See?  In this particular situation, any positive play is +.053 wins and any negative play is -.025 wins.  (If the frequency is 32% positive play and 68% negative play, then +.053x.32 -.025x.68 = zero.)

(I know that it’s not 32% but 35%, but I’m using data from all over the place.  This is just a useful illustration.)

Annnnnnnnnnnnd, WPA/LI also removes the magnifying effect of the leverage.  So, ARod has +.78 for his WPA and +.07 for his WPA/LI (LI in that case was 10.9).  As you can see, he added +.07 wins, without the magnifying effect, which is the win value of a random double.

So, WPA/LI has it all: a distinct win value for whatever game state you are in, and no magnifying effect of the situation (which is outside the control of the batter to begin with).

And last year, Ryan Howard’s WPA/LI (which I will from now on I’ll call his Situational Wins) was +7.2, while Pujols was “only” +6.1.  So, Howard performed better situationally than did Pujols.  That is, he “maximized” his performance, hitting HR when they count for more, and getting walked when that counted for more.

However, Pujols earned more clutch wins, because the times he was above average, the leverage was extremely high, enough that he ended up being +1 win ahead of Howard in the end.

***

If you have a bit of a hard time to grasp this, let me put this in wOBA terms.  wOBA gives an average positive value of exactly 1.  It’s 0.72 for a walk, 0.90 for a single, and 1.95 for a HR, among other things.  The weighted average is 1.  Always.

Now, I also happen to have wOBA for each game state.  In the previous example (bases loaded, tie game, bottom 9th, two outs), the value for a walk, single, HR, etc are all set to 1.00.  You can guess the weighted average of the positive values.  Always 1.

This is what WPA/LI does.  While it doesn’t set the average weighted value to 1, like wOBA, it does set the average weighted value in proportion to the negative weighted value (which is typically around -.025 wins).  Pretty much, the weighted values of the positive events will be around +.050 wins.

That is, do WPA/LI for any game state you want, and do it for all the positive events.  You’ll get back around +.050 wins.

I prefer the wOBA approach because it’s much simpler to understand.  The value of the walk will be between 0.40 and 1.00 depending on the situation, the HR will be between 1.00 and 2.50 depending on the situation, etc.  The wOBA equation is tailored to each game state, to respond to exactly how much impact that event will have at that moment in time.

And, like I said, no magnifying effect of the leverage.  Situational Wins and Situational wOBA.  Learn it, live it, love it.

I’m a bit confused. After the change, FanGraphs has Rodriguez with 1.03 WPA, 1.16 WPA/LI, and -0.14 Clutch. Does that mean that, even with the game-winning hit in the highest leveraged situation possible, Rodriguez has still been unclutch this year?

I’m kind of partial to what I did in the THT Annual: examine how players did at different levels of LI.  Basically, it’s a split, but just using different ranges of LI instead of base/out situations.  To me, that’s easier to interpret.

"I’m a bit confused. After the change, FanGraphs has Rodriguez with 1.03 WPA, 1.16 WPA/LI, and -0.14 Clutch. Does that mean that, even with the game-winning hit in the highest leveraged situation possible, Rodriguez has still been unclutch this year?”

When I add it up PA-by-PA using the wonderful data on Fangraphs I get 1.03 WPA and 1.09 WPA/LI through the first 7 games (34 PA). The 1.09 versus 1.16 is probably just a rounding error.

Using 99-02 figures from here, his LWTS is +8.63. So he has a lot of the other type of clutch, that is, what Tango is talking about in the first paragraph of #12. Indeed all 6 of his HR have come with at least one man on base, and all but one of them were with 2 out.

When you hit a HR with 2 out and men on base in a low-leverage situation, it really hits your WPA-WPA/LI. Here are his top PA for absolute magnitude of WPA-WPA/LI:

4/7/07, bot 9, 2 out, bases loaded, down 1 run, HR: +.652
4/9/07, top 6, 2 out, man on 1st, up 5 runs, HR: -.178
4/5/07, bot 8, 2 out, bases loaded, down 1 run, out: -.174
4/2/07, bot 8, 2 out, man on 1st, up 2 runs, HR: -.157
All 31 other events (30 PA, 1 SB): -.208

I put up a spreadsheet with info for all 7 games’ worth of events here on Google Docs.

Re: studes point.

I agree.  This is why I’ve asked Fangraphs to show splits like this:
http://www.tangotiger.net/urbina.htm

dcj: great job on the presentation!

I see the “problem”.  A HR in a high-leverage situation gives you a plus on the clutch, but a HR in a low-leverage situation gives you a minus!  An out in a low-leverage situation gives you a plus!

Yikes.  If we look at ARod when the LI was above 1, his clutch is +.367, including the +.652.  But in under 1.00 LI, he’s a -.433!

I’ll have to think about this.

I can justify in my head why a home run in a low leverage situation is anti-clutch, but it’s tough to put into words why an out in a low leverage situation would be clutch.

LWTS (using Wins), and WPA/LI, come out to be pretty similar at the end of the season.  They’re even pretty similar right now in 2007, but A-Rods 1.5 pLI is kind of screwing things up. 

I think the apples to apples comparison would be:

WPA - LWTS (with wins)
WPA - WPA/LI

Doing WPA/LI - LWTS gives completely different results.

Let’s say we have two situations in baseball: high leverage, low leverage.  And they each occur 50% of the time.

And our hero, Alexia, has an OBP/SLG of .450/.650 in high-leverage and .150/.150 in low-leverage.  On average, he’s .300/.400, which happens to be the league average.

Because of his great hitting in high-leverage (+3 wins in a random situation x LI of 1.5 = +4.5 WPA), and his poor hitting in low-leverage (-3 wins in a random situation x LI of 0.5 = -1.5 WPA), he comes out with an overall WPA of +3.0 Since he’s a league average hitter, his WPA is also his clutch (+3.0 minus 0).

What if he hit as well in low-leverage as he does in high-leverage?  +3 x 1.5 + 3 x 0.5 = +6 WPA.  His random wins is +3 + 3 = +6 random wins, so his clutch is now zero.

Now, look what I just did.  I increased his performance in low-leverage situations, and this increased his overall WPA, but it *decreased* his clutch.  An increase in low-leverage production lowers your clutch rating.  And a decrease in low-leverage production increases your clutch rating.

So, if ARod keeps hitting HR in low-leverage situations, this decreases his clutch score, which makes intuitive sense.  But, strange as it may sound, if he’s making outs in low-leverage situations, he increases his clutch score.  (But his WPA will go down).

Take it to the extreme, and make him hit .000/.000 in low-leverage situations.  Now, instead of being -3 random wins in this situation, he’s -6 random wins.  This is the scorecard for this Alexia:

high-leverage:
+3 random wins
1.5 LI
+4.5 WPA

low-leverage
-6 random wins
0.5 LI
-3.0 WPA

total
-3 random wins
1.0 LI
+1.5 WPA

clutch = +4.5 wins

So, he went from a clutch of +3.0 to +4.5 by trading hits for outs in low-leverage situations.

Man, if you thought negative loss shares was a b-tch, try to wrap your head around this.

Why? Seems intuitive to me. The worse a hitter he is overall, the more impressive his play in high-leverage situations. If Pujols hit .300 when the game is on the line, we’re not impressed. If Neifi Perez does…

Imagine someone who hits 4 HR in a blowout.  LI of each of his PA was .5, .2, .1, .001.  In this case, his clutch score would be a huge negative.

Someone else in the same game goes 0-4 with 4 GIDP, with similar LIs.  He’d be a huge clutch player!

And remember, we are not comparing these players to themselves, but simply to the league average player.

Doesn’t seem intutive to me.

I’m thinking WPA - “neutral wins” doesn’t measure what we think it measures.  (Whether “neutral wins” is OPSwins, LWTSwins, WPA/LI, or whatnot… they are all pretty much the same thing.)

Personally I don’t see the issue with the guy who gets 4 HR in a blow out ... he’s just a guy who does well when there is no reason to do well—the guy who get a 4.0 GPA in his mock tests (but then flunks the real thinG). He defines anti-clutch.

The out guy is more problematic, for sure ...

Just thinking aloud here. Does the out really matter that much. Presumeably if the situation is very low LI (0.1) then the possibly change in WPA is also very small, say 0.01. Either way it means a very small positive contribution to clutch.

We could just exclude the out when calculating clutch, but this isn’t logically right.

It seems intuitive to me. The way I understand it, what we’re measuring is how much better a player is in clutch situations.  Now, to throw out some numbers, compare two players. Player 1 has a wOBA of 300 in clutch and non clutch situations, and Player 2 has a wOBA of 250 in non-cluch situations and 300 in clutch situations. I think we’d agree that Player 2 was clutchier, and that is what this measure is showing us.

Wait, I missed this

And remember, we are not comparing these players to themselves, but simply to the league average player.

John/22: WPA will be 0, but WPA/LI will always be around -.025 wins for an out, regardless of situation.  So, when you do:
WPA minus WPA/LI
Then you are doing:
.0001 - (-.025)
So, every out in a super low LI situation *adds* .025 wins of clutch (and this is regardless of how well or poorly you did in high-leverage situation). 

I urge all to read post #18, and look at the great file at the end of post #15.

The WPA minus WPA/LI can be also expressed as:
WPA * k, where k=(1 - 1/LI)

So, we see that k=1 when LI is infinity.  That is you get full credit for the WPA as clutch. 

When LI is = 1, clutch will always be zero!

And when LI approaches zero, k = negative infinity.  However, as LI approaches zero, WPA also approaches zero.  The two infinities pretty much cancel out, and what you are left with is the negative of the random wins (-.025 wins for an out becomes +.025 wins, as LI approaches zero).

This can’t be what we mean with clutch.  When LI approaches zero, it’s really irrelevant what the batter does, so he should earn little clutch or choke points.

If you follow this to its logical conclusion, you end up with clutch = WPA * LI / j, where j is some constant.

Very strange…

TEST - I CAN’T SEEM TO POST MY RESPONSE.

THIS IS A TEST

Tango—for some reason my post refused to work (I am copying/pasting in ...

I’m sending you in an email to your Yahoo account

Tango. Sorry for multiple posts. This is bizarre. (I’m just trying to nudge up the comment leaderboard).

I have published my response here

http://docs.google.com/Doc?id=dhs5qrkx_1drfqqt

POST 1 OF 2 (SORRY, BUT CAN’T POST BOTH TOGETHER)

Here is another attempt to be slightly more lucid on the issue of clutch having thought about it some more. First, we need to revisit our definition of clutch and LI. LI is the ratio of the maximum swing in win probability to the average swing in win probability for the given situation. So, what is clutch? Clutch is making a hit, or doing something that positively contributes to the outcome of the game when it matters. There is also something antithetical to clutch—called choking. This is making an out in the same situation.

The denominator of LI is 0.0346—that is the average change in win probability for a typical event. Is a typical event (LI=1) clutch? No. In fact if we say that clutch = WPA - WPA/LI then when the context is exactly average it makes sense that clutch = 0. The formula above accomplishes that (and I love Tango’s reasoning in post #5 & #18). That means that if LI=1 equals no clutch then only for LI>1 can we have a clutch situation. If LI =1.1 we have a very small clutch situation. If LI= 5 then it is a much more important clutch situation. That’s the beauty of LI right? It tells us how clutch a situation is.

What about if LI<1? Well this can’t be clutch. It is inverse clutch, or anti-clutch, or whatever. It isn’t clutch. If the game is 18-0 blowout then the batter and pitcher may be in “batting practice” mode and care less about the outcomes—18-0 or 21-0—who cares? I would argue that a player who hits a lot of HR in this situation is showing some sort of anti-clutch tendencies ie, to hit when the pressure is off. Likewise, guys who easily give up outs could be doing so because the outs matter much less. Indeed I think it was Earl Weaver (I can’t be sure though) who said that sometimes he’d sit on a pitch even if he knew he could hit it out of the yard because he hoped the pitcher would throw it at a more important point in the game.

PART 2 (NOW OF 3)

Anyway, I digress. The point is that this is an entirely different concept to clutch. The difficulty comes in when we add clutch and anti-clutch to get net clutch (which is essentially the fangraphs implementation). I think this is wrong. We need to differentiate between clutch situations (LI>1) and anti-clutch situations (LI<1).

PART 3 OF 3 (SORRY)

If fact you could argue there are four different groups: (1) Clutch (LI>1, WPA +ve) (2) Choke (LI>1, WPA -ve) (3) Anti-clutch (LI<1, WPA +ve) (4) Anti-choke (LI<1, WPA -ve). Take all these four, work out WPA - WPA/LI and you have everything you need to know about clutch hitting.

If you want clutch to mean the difference between actual WPA and the WPA the player would have gotten under average leverage, then you have the formula right, and you’ll have to live with rewarding players for making outs at the “right” time.  (That’s one of the reasons I’m not a huge WPA fan.)

But another approach is to think of all PAs as having some degree of clutchness, rather than just LI>1.  After all, performing well in a typical situation DOES have value, just not as much as in higher LI situations.  So then 0 clutch = 0 LI. 

The simplest formula would be something like WPA * LI/11.8, which maxes out at around 90% of WPA (like the current formula).  But that gives you much too low a clutch score for LIs of 3, 4, 5.  So you probably need something with an exponent.  WPA * LI^2/(LI+1)^2 may be close to what you want.  You’d get this:
LI Multiplier
.5 .11
1 .25
2 .44
3 .56
..
7 .76

Someone here can figure out how to make the curve steeper if you want to do that.

I was thinking Guy/33, but I thought: what does that tell us?  I’m not sure that it returns a number in a useful unit.

That’s why my post/16 (Urbina) would be the best choice.  And studes’ article in THT annual shows us how to bring WPA to life by focusing on actual plays and results.

If you want clutch to mean the difference between actual WPA and the WPA the player would have gotten under average leverage, then you have the formula right, and you’ll have to live with rewarding players for making outs at the “right” time.

This is the key point. It is how you define clutch. It is also a subjective argument. The definition of clutch as the above is one possible option, as is the definition that clutch hitting can only exist where there is an above averge LI (LI>1).

Out of interest the dictionary definition (in my dictionary) is: an extremely important or crucial moment of a game.

At the end of the day I agree with Tango/34. The presentation that Studes did in THT 2007 was a perfect example of what to do with WPA/LI/clutch.

Tango/34:  Perhaps it would it be useful to standardize the definition of high/med/low leverage (each representing approximately 1/3 of PAs).  Then you could develop clutch metrics that took the ratio of a player’s performance in high-lvg PA/IP to his overall performance.  You could scale it to 100 like ERA+ or OPS+. 

Taking your Urbina example, he had an avg OPS-against of .628 and was .666 in high-LI situations, for a Clutch+ of 94.  Probably better to use ERA or WPA/LI instead of OPS against, but you get the idea.....

Guy—you still have a problem as to how to define clutch. Is it all three? Just high leverage? LI>1? Or are we just going to look at low, med, high Li situations and infer clutch from that.

In here:
http://www.tangotiger.net/files/clutchdata.txt

I noted the following

Leverage situations
0: <= 0.345 LI
1: <= 0.659 LI
2: <= 0.971 LI
3: <= 1.453 LI
4: > 1.453 LI

Each leverage situation has roughly 20% of all PAs (after PA exclusions, but prior to batter exclusions). 

So, roughly speaking, you get about 20% of the PA when the LI is 1.4 or higher, and you get about 45% of the PA when the LI is 0.7 or lower.

The chart I use here:
http://www.insidethebook.com/li.shtml

Is based on the “low-leverage” being 0.75 and worse, the “medium-leverage” being 0.75 to 1.5, and “high-leverage” being at least 1.5.  (I also marked the “very high-leverage” as 3.0 and higher).  As you can see, I basically doubled the leverage for each category.

***

If we want to come up with more rigid leverage points, perhaps the push that David needs to add the leverage splits on Fangraphs, I’d suggest the following:

1 - make sure that the “medium leverage” will end up with an overall weight of 1.00, with around one-third of the PA.

2 - try to make the split between low and medium leverage somewhat meaningful.  I put the line so that “top of 9th, up by 3” to just be in the “medium leverage” category.

3 - Once you get that, the medium/high boundary line will kinda work itself out.  But as a sanity check, remember that the ace reliever will pitch about one-sixth of his team’s relief innings.  So, it’d be nice if the percentage of “high leverage” relief PA is also around one-sixth.

So, the 0.75/1.50 lines do the job.

And further added the 3.00 split let’s you have a manageable number of PA to look at, as studes did in his article.

John/37:  I was suggesting that you think of “clutch” PAs as the high-LI category, whether defined as >1.3 or >1.5 or whatever (but I think >1 sets the bar too low).  And a player’s clutch rating would be the ratio of his performance in clutch PAs to his overall performance.  You could certainly devise a rating that penalized a player more for doing well in low-LI situations (for example, ratio of high-LI to low-LI performance), but I agree with you that it’s mainly the performance in high-LI situations we should care about.

I like the idea of looking at how different players perform at different leverage but it feels arbitrary—and I’m not sure if really helps with the definition of clutch.

I know I keep beating the same drum on the beauty of the old formula (WPA - WPA/LI) was that it presented a clutch continuum. You could argue that your bucketing method does as well—but it is much less clean. LI=1 is clearly an inflexion point and this should be used as the boundary to define what is clutch (ranging from a very little clutch, LI = 1.01 to highest clutch possible, LI=10.9) and what the opposite of clutch.

Guy

Sorry I posted before reading your reply. That sounds fair. I think where we (sort of) disagree is on the cut-off. The definition of 1.3 or 1.5 seems arbitrary. Anyway as LI gets closer to 1 clutch tends to 0.

I agree with your thought that a LI of, say, 1.1 or around there isn’t clutch so we should just exclude ....

If you do the math using the formula clutch = WPA-WPA/LI

LI 1.1, WPA 0.3, Clutch = 0.027
LI 2, WPA 0.3, Clutch = 0.15

In other words for a WPA change of 0.3 you need 5x a LI of 2 to equal a LI of 1.1. The low LI situtaions are not weighted that highly, especially if you take into account the fact that the lower the LI the lower the likely WPA change.

John:  The problem is with poor performance. 
LI .3, WPA -0.1, clutch = +0.23(!) That’s what Tango is saying doesn’t make sense.

* *

I don’t know that it matters, but I don’t agree about the “inflection point” idea.  Average leverage is just that, average.  It has no special significance other than that.  I don’t see why we should define clutch as zero at LI=1, and anything below that as “anti-clutch” or whatever.  Every PA matters at least a tiny amount (LI=0 never happens), but some matter much more than others.  So it makes just as much sense to me to think of clutch as a continuum from 0.1 (almost no importance) to 10.7 (maximum importance).

I don’t find making the LI point at 1.5 or whatever as arbitrary anymore than making “close & late” as 7th and later innings, with the lead or tieing right on base, at bat, or on deck.  (In fact, this definition is remarkably similar to my LI charts, though it diverges when you include the outs.) Or, why have a breakdown by RISP?  That’s arbirary too.  As this chart shows:
http://www.tangotiger.net/RE9902event.html
Each of the 24 base/out states has its own peculiarities, and I wouldn’t think RISP is the best grouping of it.

However, in order to bring WPA and LI to life, you need to present it in real terms.  Saying that Pujols +3 wins in clutch, as fantastic as it is, pales in comparison to seeing his actual production line in the high-leverage situations.

The WPA and LI numbers make it easy to grade things, and sort and find, but acceptance of it has to be tied to something more real.

Otherwise, we’re left with: count this ARod HR as 5.3, count that ARod HR as 0.3, etc, add them all up, and ARod has 9.8 leveraged HR.

I think we’re quibbling over the pennies here.

So it makes just as much sense to me to think of clutch as a continuum from 0.1 (almost no importance) to 10.7 (maximum importance).

I think this is where it comes back to definition.I’m just using LI=1 as the baseline of 0 clutch. I would argue if base/out/inning situation is below LI=1 then there is NO way it is clutch. Also the math works to magnify the high LI situation so when LI is slightly over 1 this is swamped.

I agree with what you say that it is an interesting and worthwhile excerise to work out how hitters perform across the full 0.1 to 10.9 LI continuum. Anything below average, I’d argue, cannot be clutch.

I think this is probably an agree to disagree issue.

However, in order to bring WPA and LI to life, you need to present it in real terms.  Saying that Pujols +3 wins in clutch, as fantastic as it is, pales in comparison to seeing his actual production line in the high-leverage situations.

The WPA and LI numbers make it easy to grade things, and sort and find, but acceptance of it has to be tied to something more real.

I agree with that 100%.

Just caught up with the rest of this thread.  I’m going to try and get leverage splits up sooner than later, for those interested.  No definite timeline, but maybe by mid-May.

The numbers are probably illustrative, but we also have to think about words and concepts associated with those words.  I think using the term “anti-clutch” has the potential to be confusing. 

If we accept the dictionary definition from #35, clutch would be performing well in “an extremely important or crucial moment of a game.” I think most people would agree with that definition.

If that’s clutch, then pure “anti-clutch” would be performing well in an extremely unimportant or non-crucial moment of a game.”

By that definition, “anti-clutch” is not necessarily the same thing as being a player who cannot hit in the clutch.  Yet, if you tagged a player with an “anti-clutch” label, 9 out of 10 dentists surveyed would think the player was incapable of hitting in the clutch. I don’t think that’s what anti-clutch in this situation means, and I don’t think it is what the “net” clutch numbers here produce.

A great player who hits well in all situations, including crucial moments of the game AND non-crucial moments of the game would be both clutch and anti-clutch, right?  Where would that put him, numbers-wise?  If I understand the discussion above (without understanding the math), doing well in the non-crucial situations would penalize him and doing well in the crucial situations rewards him.  That would not be in accord with saying he is poor in crucial situations. 

I think the splits idea is a good one because it is “pro-information.” But if clutch will be in any way accessible to a typical fan, anti-clutch will result in confusion.  Most people will only be interested in how well a player hits in crucial situations. The splits will be great for stat heads, but for everyone else, it would simply add yet another data dump to wade through. 

That argues for a demarcation line.  Obviously it is interesting to know what a player will do in a super-crucial situation (something north of 1.5 LI), but I think it would be most accessible to show a player’s WPA for situations that are more crucial than whatever the average situation is.  Maybe there is no average, but I have a hunch that Tango has computed an average LI for all events. 

I’d argue that you should report the sum WPA for all LIs in excess of the average situation.  It would be nice if the number is 1.0, but I suspect it will not be that neat.  That would cover the complete range of clutch situations, from barely clutch to extremely clutch, and omit how a player hits when nothing is on the line.  (You could still subtract the portion attributable solely to the “luck” of getting a PA in the clutch situation).

In that system, “anti-clutch” would indicate “he cannot hit when in crucial situations,” whereas “anti-clutch” currently means he hits well in non-clutch situations.

This is not a “no-split” argument.  It is more of an argument that the splits should be available somewhere for stat heads, but something more intuitive, and accessible (like on Fangraphs), should be the base system for most fans to evaluate how players perform in the clutch. 

I believe anything that involves the current version of the “anti-clutch” concept makes it inaccessible.

By definition, LI = 1.000 is the average situation in terms of crucialness (swing in win probability).

Quick question: Is there anyway to park adjust OPS wins (.025 * (1.8*OBP+SLG-1)) like you would do mOPS (1.8*OBP + SLG) to get something like mOPS+ (lgmOPS*sqrootPF/1.00)/mOPS*100 = mOPS+)? Oh and sqroot is the square root of the run park factor after it’s divided by 1.00.

I like OPS wins as a quick measure like mOPS+ in wins but I was j/w if you could park adjust it like you do mOPS+.  However, is it calculated like WEA (in real-time) in that you wouldn’t need to park adjust?

Thanks

Hey did you get a chance to look over my post?

That “1.8” is more like “1.7” or whatever it is to make the league average of a * OBP + SLG = 1.

As for park adjusting, I’d hate to do it, since the point of this is to make it straightforward.  The more complex you make it, the less ideal it becomes. 

In any case, if you insist, I’d probably do:
a * OBP + SLG - sqrt(PF).

So, “a” is 1.7 or whatever.  sqrt(PF) would be the square root of park factor.