THERE IS CLUTCH! (or, The Case of the Lucky Lefties)

I think I used a paired sample t-test. Well maybe not paired, but I think the formula is adjusted when the samples aren’t the same size. I haven’t done statistics courses in a few years, but I had a lot and I think I used the right number. If someone knows, please let me know if this was right.

I had four samples:
—n(LM) & n(RM) of balls in play for lefties and righties with runners on, and n(LE) & n(RE) of balls in play for lefties and righties with bases empty.
—The hits in play in each of these subsamples were x(LM), x(RM), x(LE), and x(RE).

I computed the following statistics:
—p(LM)=x(LM)/n(LM), probability of a hit on a ball in play for lefties with men on base
—p(RM)=x(RM)/n(RM), probability of a hit on a ball in play for righties with men on base
—p(LE)=x(LE)/n(LE), probability of a hit on a ball in play for lefties with bases empty
—p(RE)=x(RE)/n(RE), probability of a hit on a ball in play for righties with bases empty
—p™=(x(LM)+x(RM)) / (n(LM)+n(RM)), probability of a hit on a ball in play for all of the guys in the sample with men on
—p(TE)=(x(LE)+x(RE)) / (n(LE)+n(RE)), probability of a hit on a ball in play for all of the guys in the sample with bases empty

The variance of the outcome of a ball in play with men on was:
—var™=p™)
and with bases empty
—var(TE)=p(TE)(1-p(TE))

So the standard error for the righties should have been
SE®=square root of(var™/n(RM) + var(TE)/n(RE))
and similarly for the lefties to get SE(L)
SE(L)=square root of(var™/n(LM) + var(TE)/n(LE))

Then I got the standard deviation of the difference by taking the square root of (SE(L)2 + SE®2). That’s the .0058 value in the article. Since the difference was .013, seems like the t-stat should be .013/.0058=2.30 which is statistically significant.

Can someone check my work, because I’m not 100% sure but I felt pretty confident I was doing it right at the time?

This is an interesting idea but it would be extraordinary difficult to test the mathematics of this. It would require determining the effect of bunting x% of the time on the fielders positioning and the resulting BABIP. Then you’d need to test the bunting success of these hitters. I think that’s more of a qualitative analysis you’d use to check that stuff.

Thanks for the comments. Here are my thoughts.

1) I’m not sure to what extent league-wide differences would matter in this situation. Both groups are pretty similar in terms of distribution across era and across leagues. Is there something systematically biased about those results? If this approach is not credible, it’s because there is something different about the two groups of hitters that is correlated with BABIP split differences like the ones I have described above, but different than the main difference I am discussing above. I think that league differences would be an example, but I’m not really sure the AL and NL differ in their men on/bases empty splits or that the groups above are composed differently.

2) The number of outs thing is interesting, but I counted sacrifice flies as outs in my BABIP formula to avoid some of the large differences you describe with <2 outs vs 2 outs. I’m also guessing that the hitters above had a pretty even distribution of at-bats with differing number of outs. Again, you do hit on another cause for variance in outcomes, but I’m not quite sure that the hitters differ with respect to their at-bats in those situations so that probably doesn’t affect the value of the t-statistic above.

3) Yes, I don’t mean “intestinal fortitude” clutch. I was being facetious. The idea was that the hitters had a naturally tendency to succeed in higher lever situations. For instance, Ryan Howard’s skill level might dictate that he could be expected to hit .265/.365/.565 next year but he may actually hit something like .255/.355/.555 with bases empty and .285/.385/.585 with runners on bases, thus provided more value than .265/.365/.565 suggests, since if a right handed slugger who also hits .265/.365/.565 might hit .260/.360/.560 with bases empty and .275/.375/.575 with runners on. Thus, the lefty is ‘clutch’ by design rather than the intestinal fortitude.

4) I don’t think non-elite hitters are not a useful sample. The whole idea is that context-neutral performance but lefty sluggers is misguided since they will systematically achieve more in higher leverage situations.

5) Larger samples are more helpful, but I do have 130,000 balls in play in my sample and the t-stat considers sample size. As Crashburn wrote above, it would be useful to check hitters with less than 3000 PA. I’d love a list of hitters who regularly were shifted against for the majority of their careers. That might help.

6) Using BABIP instead of AVG was precisely because I don’t believe that clutchness exists on much of a significant level in high leverage situations, and that the ability to make contact and the ability to hit homeruns should not be affected. That’s why I checked and found that the homerun rates did not also reflect a similar skill for lefties— in fact, there was a slightly negative “clutchness” in homerun hitting by lefties though not significant I don’t think. It was specifically hitting through the shift that made these guys so valuable.

Haha, I hope Howard’s agent Casey Close doesn’t read TGP. I’d hate to give Ryan Howard the break he needs to make the $4MM extra, and take away the budget for a midseason pitching upgrade or something. Unless he’s hiring entry level Econ PhDs. In that case, read away, Casey! :)

The lefty dominant lineup is probably overblown only in the sense that I think the effects on bullpen selection only affects the Phillies by a run or two per year. Left handed hitters numbers accurately reflect the fact that most pitchers are right-handed already. Ryan Howard’s context-neutral statistics are that he is a .950 OPS hitter because he faces mostly righties, so he is no more or less valuable than a .950 OPS righty who also naturally faces mostly righties. Obviously if 70% of pitchers would lefties, Howard would be worse off and Manny (or whoever you think is a .950 OPS righty) would be better off, but then Manny would have a 1.000 OPS and Howard would have a .900 OPS. Their numbers reflect the distribution of pitchers already.

The point of this exercise was to launch interest in the question as to when context-neutral statistics are not the best thing to evaluate performance. For instance, if I said that Burrell hit .222 with RISP a few years ago, most of us would have said that was a silly way to predict his performance with RISP the following year and that the best approximation for doing so would be his total average. That’s true. But there can still be reasons hitters systematically hit worse in certain situations. I guess my point is partly that David Ortiz’s reputation as super-clutch is actually true but not because of mental willpower. It’s because he pulls everything and that’s more likely to be a hit with runners. Ortiz actually homers less frequently with runners on base. He gets way more hits because he his hardly hit balls to rightfield systematically turn into hits when it’s more important and outs when it’s less important.

Sabermetric orthodoxy would say that the added run value a hitter will provide can be discerned from their AVG/OBP/SLG/SB/CS and adding in maybe some baserunning stats. I’m saying that’s not quite right. You need to consider the fact that some hitters will hit slightly better in higher leverage situations for systematic reasons rather than post hoc intestinal fortitude reasoning. Ryan Howard is probably about $500K more valuable (1 run) than his context-neutral stats would suggest. So is David Ortiz. So is Jason Giambi. Because these hitters will systematically overperform the implied run value of their AVG/OBP/SLG/SB/CS stats, they are more valuable than the right handed equivalent.

You make a good point about the lefty hitters all getting to hit more with runners on first base. Some thoughts on that:
1) I would guess that those situations are higher leverage on average— certainly higher leverage than no one on, but maybe lower leverage than bases loaded or ducks on the pond— first base occupied does somewhat depend on whether a that underweights situations where there’s a runner on 2nd or 3rd or both, or even a slow runner on 2nd allowing the 1B to play off the bag. I still think you’re right though.
2) Also, I wonder if righties also are more likely to ground into double plays because they hit more of their groundballs to infielders with stronger arms.
3) I’m not sure how often non-power hitters pull the ball. Looking through numbers, it seems like non-power hitters frequently hit the ball the other way nearly as often as they pull it. I’d love to get more data on this, but there seems to be no real way to collect this kind of stuff. I have an email out to Sean Forman at Baseball-Reference about getting more of this data. I would absolutely love if anybody knew how to get a hold of it!!

B-R has splits data too, but it’s a matter of tabulating it for hundreds of hitters. I did it for about 20 people to see how long it would take me to finish and realize that I’d need to be copying and pasting for a few days straight to even compile the data. I’ll check out Bill James online but it’s probably still the same issue.

Ortiz was bound to fluctuate around some mean. Cumulatively he hits .041 points better with runners on, which is about the same as Bonds and Giambi. It’s a little on the high side, but I think it’s indicative that there’s a trend there that amounts to about 1 run more valuable than a right-handed Oritz would be over the course of a season.

That’s absolutely amazing about Tabler. I have no idea what to even say about that. Thanks for that link. Hitting .489 in 88 at-bats with the bases-loaded for a .282 hitter is ridiculous. The average hitter hits 29 points better with bases loaded. hitting 207 points differently in 88 at-bats by chance would only happen about 1 out of every 5,000 times. I guess about 1 out of every 5,000 hitters is bound to be this lucky, but it does raise a big question mark as to whether that’s actually the best conclusion.