1. If we stick with the simpler "walk or hit wins, out sends to extra innings" situation:

- assuming a league average OBP of .333 (my definition, including all events), the expected winning probability is easy enough to calculate (1/3 wins the game, and 2/3 sends to extra innings with a 50% chance to win) as .667.

- the LI is equally easy to calculate (.333 gain in wins happens 1/3 of the time, and .167 wins downward happens 2/3 of the time, for an average absolute movement in some direction of .2222, compared to the random of .0346, or an LI of .2222/.0346 = 6.4)

***

Now, say you have an Ichiro-type, where his OBP, overall, is .400. In this case, when Ichiro is at the plate, the Mariners will have a 70% chance of winning, if he does his Ichiro thing. (40% wins the game, and 60% sends it to extra innings where they have 50% chance of winning.) However, suppose in clutch situations, Ichiro has an OBP of .460. That means, the Mariners will win .730 with Ichiro as a clutch hitter, as opposed with .700 with Ichiro as his usual self. So, he adds +.030 wins with his clutch play, per PA (in this situation), over and above his own great self. This is the method you are describing.

Let's look at the other way. His WPA/LI would be (.730-.667)/6.4= .012. His WPA is .730-.667= .063.

That leaves his WPA minus WPA/LI as +.051 wins.

Is one way better than the other?

***

Let's consider another example. Let's assume that Ichiro hits .400 regardless of situation, in a league that hits .333. In this case, your method would say that Ichiro has no clutch skill at all. The other method would do the following:
WPA/LI = (.700-.667)/6.4= .005. His WPA is .700-.667=.033. This leaves him with WPA minus WPA/LI of +.028 clutch wins.

But also note that in low leverage situations, he'll end up with a minus. For example, if the LI was 0.2, and the then his WPA/LI for some blowout situation would be something like (.110-.109)/.2= .005, and his WPA would be a tiny change (.110-.109=.001), giving him a WPA minus WPA/LI of -.004 wins.

In this simplified example, if you had 87% of the games with an LI of .2, and 13% with an LI of 6.4 (overall LI of 1.0), then Ichiro's clutch would be:
+.028 * 13%
-.004 * 87%
= .000 (rounding error)

As you can see, this method, and your method, both agree that Ichiro, overall, gets a clutch rating of 0.

And, WPA minus WPA/LI is superfast to calculate, and doesn't require prior knowledge of the hitter's overall stats and how that translates for each game state! Cool, right?

***

As for what does WPA/LI represent, it's his win impact, with the game situation unleveraged. For example, a hitter with an OBP of .400, in a league of .333 is worth about +.055 runs per PA, or roughly +.005 wins per PA, in a random situation, compared to the average hitter. In the game-ending situation in question, his WPA was +.033 and the LI was 6.4, making his WPA/LI as +.005 wins. So, what WPA/LI does is two fold:
1. It rebalances the walks, hits, HR relative to the out, based on how each of those events will impact the win probability
2. It deflates the leverage aspect

This metric (WPA/LI) is especially ideal for players like Ichiro, who can rebalance their game to take advantage of the new balance required for a game state (sometimes avoiding a K is necessary, sometimes getting a walk isn't all that important, etc).

2. I am just bothered by the lack of a direct link in the WPA/LI method between the batter and his own performance. The clutch metric at fangraphs will rate good hitters are more clutchy than bad hitters because good hitters will produce positive results more often. That's not really what we're after though, is it? Aren't we after a measure of how the hitter is relative to himself in clutch situations?

3. That's not true. You missed when I said:

As you can see, this method, and your method, both agree that Ichiro, overall, gets a clutch rating of 0.
However, you are right there is no direct link... however, none is needed, as I've shown in that illustration.

4. Doesn't your example above assume that all players get the same balance of clutch PA vs blowout PA though? I'm not quite understanding how the WPA - (WPA/LI) method guarnatees that a hitter who hits the same in all situations will get a clutch rating of zero, and my primary objection would be that this method doesn't directly, statistically, define what you're actually after.

WPA - Unleveraged WPA = the impact of having high leverage, not the batter's skill in high leverage.

You could bypass needing information about Ichiro as a hitter actually and still b edefining something real if you did:

SUM(WPA)/AVG(pLI) - SUM(WPA/pLI)...that expression, in English would be:

1) Find the player's total WPA
2) Adjust that total so that it reflects a neutral leverage (this is the element missing from the fangraphs method...there's no guarantee that the player hit in average leverage overall)
3) Subtract from his actual (neutral) WPA the unleveraged value of his plate appearances.

That gives you (directly) the number of wins your player added because of better than (his) normal performances in high leverage situations.

The AVG(pLI) tweak may not seem like a big deal, but it makes the thing logically consistent and it does have an impact..especially on teams that play a lot of close games.

Let's say that Ichiro, because he hits lead-off on a team that scores a lot of runs and gets into a lot of close games, gets 60% blowout PA and 40% clutch PA (this is an extreme example I know). Keeping the numbers from your example above, Ichiro would rate as +0.028 * 0.4 - 0.004 * 0.6 = +0.0088 Wins/PA. My method would correct for that by noting that Ichiro's net LI is not 1, but in fact 2.68 (I know this is very extreme...I'm doing this to prove a point). My way will give you zero clutch rating no matter what your LI distribution looks like if you hit the same in all situations.

5. GREAT point. I think it was the missing link.

It should be noted that most players will have an LI around 1.00 for their careers. Ichiro, from 2002 to present is at exactly 1.00. Jeter is at 0.95. Bonds is 1.03. Vlad is 1.02. You'll be hard-pressed to find anyone outside of PH who have a 5-yr LI level much different than 1.00.

That said, your correction should be applied, and will be especially important for relievers.

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Now I wonder what happens if we again re-assess the stability of clutch. Probably not much, as Tango points out... over a long enough period of time, those average leverage ratings will shake themselves out for batters. I know I did a little bit of work on whether clutch was stable for relievers (it wasn't) and they will be more affected. I suppose some poking around the data set never hurt anyone.

7. *does victory dance*

(in high-pitched serene voice) I helped!

No, in all seriousness, I always start when I go to define a metric by trying to figure out what is needed to get the thing to actually tell me what I want to know in real-world terms. It sometimes helps me to step back and read my equation in English and make sure it's actually doing what I want.

Tom is of course correct that for batters, average LI is going to be close to 1 for any length of time...but in single-seasons I've seen batters get 1.1s and 1.15s and when you go to test the stability of Clutchiness, you need to test it from single-season to single-season. This will have measurable impacts on 9th place hitters (who are less likely to hit in clutch situations) and MOTO hitters (more likely). And of course, for relievers, it will be EXTREMELY important.

8. A good example is Prince Fielder this year, with an LI of only 0.91. With Matt's correction, his Clutch rating goes up by 0.50 wins.

9. Yep...which...is a pretty big deal.

Richie Sexson: 0.95
Ichiro: 0.95

Just from the Mariners.

Could make a substantial (and important) difference to single-season numbers and improve the stability of clutch ratings for players who demonstrate real skill in that area.
Last edited by SABR Matt; 09-18-2007 at 04:13 PM.

10. What happens to David Ortiz when you apply the adjustment? FanGraphs has him as one of the least clutch players in baseball this year.

11. He gets worse...goes from -1.38 to -1.50

12. Incidentally, Ichiro's best clutch season (2003) gets WAY better:

1.66 / 0.90 - 0.79 = 1.054...up from 0.87

13. So the formula is WPA/pLI - WPA/LI.

***

Incidentally, does anyone else notice that players who changed teams mid-season have weird clutch ratings using the Fan Graphs formula WPA - WPA/LI?

Mark Teixeira: WPA = 1.90, WPA/LI = 0.55, Clutch = 0.30

Ty Wigginton: WPA = 0.45, WPA/LI = -0.53, Clutch = 0.34

Luis Castillo: WPA = 0.65, WPA/LI = -0.53, Clutch = 0.62

Kenny Lofton: WPA = 0.46, WPA/LI = -0.06, Clutch = 0.45

What is the cause of that?

14. I'm guessing it's something to do with the database not lining up correctly...like it's only getting one of the teams and not both or something.

15. Let's hear it for Yuniesky Betancourt! Clutch hitter extraordinaire!

16. Man, Chipper Jones has a negative clutch, and it's possible he could win the batting title. Go figure.

17. clutch = SUM(WPA)/AVG(pLI) - SUM(WPA/pLI)

This would mean that
sum(WPA) - sum(WPA)/AVG(pLI)
is equal to the extra wins that the player himself was involved in, purely because he found himself in that position.

That is, if you look at:
sum(WPA) - sum(WPA/pLI)
this represents the extra wins from both being lucky to be in that spot, plus the extra oomph for the clutch performance.

Since this equation:
clutch = SUM(WPA)/AVG(pLI) - SUM(WPA/pLI)
gives the player his clutch skill, without the inflation aspect of LI, then the remaing part, sum(WPA) - sum(WPA/pLI), represents all the extra "real" wins, that the player "earned" (much like the Powerball example).

18. SUM(WPA) - SUM(WPA/pLI) to me is equal to the number of wins the player created because of the situations in which he found himself. I'm not sure how that's useful/helpful though.

19. Right, that number is a combination of two things: his performance for the game state without the leveraged aspect, plus the leveraged wins of which he was lucky to have "earned".

We have three win levels, on a continuum:
SUM(WPA/pLI)
SUM(WPA)/AVG(pLI)
sum(WPA)

The gap between the first and the second is the clutch skill (without the inflationary aspect of leverage... this is purely how well Ichiro, Erstad et al can leverage their skills to the situation at hand).

The gap between the second and third is the random wins that a player is a part of, and only "earned" because he happened to be in the right place at the right time.

The gap between the first and the third includes the gap between the above two, and therefore, is a mish-mash of what it is doing, and we should not reference it, as it confuses the matter.

20. David has made the correction for the players on multple-teams. (Click links in post 40)

He's working on modifying the clutch formula.

21. Cool...nice to have an inside with the guy who runs the site...my ideas have already made an impact.

22. What do you mean, OPS+ doesn't overrate Ichiro? Of course it does!

What it does not do is fully define him.

OPS+ is an incomplete measure of a player - and more like Ichiro and less like Frank Thomas you are, the less complete it becomes.

But Ichiro does benefit from idiosyncratic calculation of OPS, namely the double counting of singles, and the large quantity of singles that don't advance a runner a second base.

Of course, he is great on the bases and in the field. But, in terms of what it measures it helps Ichiro. Using OPS+ as a total measure of a player will certainly underrate Ichiro - but that's an incorrect application of statistic, because it is not a total player rating stat.

The one thing that is in Ichiro's favor is that his OBP is usually pretty high, despite the few walks. So, he's not masking a poor OBP with a good SLG, like, say, Jimmy Rollins. Relatively speaking, Ichiro's strength is the more important portion of the OPS, the on base.

23. That depends what you're using OPS+ to rate. His whole game? Just hitting? All offense? Just the quality of his play or also his quantity (he plays almost every game)?

Of all the players with a 109 OPS+ in 2005 and 2006, I'd rather have Ichiro than almost all of them.

Just because OPS+ "double-counts singles" and has a weird calculation doesn't necessarily mean than all the "mistakes" don't cancel out and make it relatively accurate.

24. OPS+ is roughly OBP*1.25+SLG all divided by the league average of that.

The impact of OBP and SLG to each of the events is detailed here:
http://www.insidethebook.com/ee/inde...lg_make_sense/

That makes the run impact of 1.25*OBP+SLG as the following for each event:
+0.48 1B
+0.83 2B
+1.20 3B
+1.54 HR
-0.27 BB
-0.30 out

The single is fairly valued. The extra base hits, especially the HR, are overvalued, and the BB is undervalued.

A straight OPS still keeps the single fairly valued, the run value of the walk drops down to +.24 runs and the run value of the HR increases to +1.65 runs.

OPS is a horrible stat, relatively speaking. OPS+ is a slight improvement. They "work" as long as you aren't a power hitter with few walks, or a walk machine with no power.

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