THE BOOK--Playing The Percentages In Baseball

I don’t see any way around the conclusion that quality of pitcher matters more to Jack Cust than it does to most other players.

Pitchers vary quite a bit in their ability to strike people out and allow walks and homers.  But they don’t vary too much in their ability to prevent singles.  It would seem to follow that guys like Deer, Cust, Branyan will be much more dependent on quality of pitcher than guys like Gwynn, Suzuki, Polanco.

I don’t think it’s even something you need to look at empirically.  If you try to set up a simulation or otherwise calculate the probability of homer, double, single, strikeout, etc in a particular batter/pitcher matchup, there seems to be no way around this conclusion.

Whenever I see someone say “I don’t think it’s even something you need to look at empirically”, I cringe.

I understand your line of thought, DFL, but I tend to doubt that your claim will hold.

It seems to me, DFL, that you’re making a big assumption in your theory.  You’re assuming that Cust would get more extra walks and strikeouts from pitchers who give up the most walks and strikeouts to everybody.  What if the reason Cust, and hitters like him, get a lot of walks and strikeouts is that they get extra walks and strikeouts from pitchers who don’t usually allow them?  Or who’s to say that all the hitters who get a lot of walks and strikeouts get them from the same type of pitchers?

How else could you determine which theory is correct than to test them empirically?

I took a very quick look at this for Cust’s strikeouts, and it looks like the guys who got the extra strikeouts against him were the low-K group of pitchers.  That’s nowhere near a comprehensive analysis, but at first blush, the empirical evidence weighs against the theory you proposed.

I think the intuition is easier when you take the other extreme ... imagine an extreme version of Tony Gwynn, where we have a guy who only hits singles and never walks, strikes out or hits homers.  In this case, no matter who the pitcher is, there’s no room for variation in P(Walk), P(Strikeout) or P(Homer).

If this guy is going to get different results against different pitchers, it will be because he has different rates of hitting singles against different pitchers.  But pitchers are pretty much all the same in terms of rate of singles per ball in play, so this seems unlikely.

It seems intuitive to me that the guy at this extreme will do just as well no matter who the pitcher is.  It also seems intuitive to me that the further you get from this guy (i.e. more walks, homers, strikeouts), the more you will become dependent on the quality of pitcher.

I agree that intuition alone isn’t proof.  But I think that in this case, the intuition alone is strong enough that I’d be willing to wager money on it.  I’d guess that Ryan Howard, Jack Cust, and so forth will get a bigger gain in OPS+ this year when facing bad pitchers than guys like Ichiro, Howie Kendrick, etc.

Isn’t it possible that when Gwynn and Ichiro are at bat, and the pitchers know that the pitcher’s K,BB,HR skill isn’t as important that they will change their pitching approach such that overall they are still of the same quality?  That is, Pedro is still PEDRO because he can manage to improve his BABIP skill, at the expense of getting a worse K/BB ratio?

I think this is a great thing to research.  And, to the extent that I did research it in The Book (p.90-94), my guess would be that we shouldn’t expect the profile of the batter to be affected disproportionately by the quality of the pitcher.  But, like I said, it’d be great to research it.

I think DFL is right, but I have to think about it (and maybe do some empirical research) some more.

Tango, I guess it’s possible, but it seems unlikely to me.  Since overall BABIP rates don’t vary too much, if the Pedros of the world have lower BABIP rates against the Gwynns of the world, that would mean they must have higher than usual BABIP rates against the Custs of the world to offset it.  I’m not able to rule that out, but I find the simpler explanation more compelling. ("Simpler explanation” being that pitchers just don’t have much variation in BABIP ability)

MGL, I’m curious how your simulation handles this.  In my own simulation, I remember testing this out by comparing a high-BA, low secondary team with a “take and rake” team.  This was about 5 years ago, and I think I used the Angels and Red Sox.

I chose Angel/Red Sox starting pitchers to make them roughly equivalent overall, and the probabilities it ended up with were something like this ...

Angels vs star pitcher = 45% chance of winning
Red Sox vs star pitcher = 44% chance of winning
Angels vs terrible pitcher = 60% chance of winning
Red Sox vs terrible pitcher = 60.5% chance of winning

I don’t recall the exact numbers, but on a relative basis, that’s about what it found.  The simulation, using log5-type methods of calculating probabilities, found that the Angels gained a little more than 1% relative to the Red Sox when a great pitcher was used instead of a terrible one.  I’m guessing your simulation would say the same thing, and I’ll further guess that the simulations are “correct” in doing so ... I think “take and rake” players really will benefit more from going against bad pitchers.

A similar prediction would be that Cust-type players have bigger platoon splits than Gwynn-type players.  If quality of pitcher doesn’t change BABIP rate very much, then handedness probably shouldn’t either.

"I don’t think it’s even something you need to look at empirically. “
-- DFL

I think if you concede that it would be worth looking at empirically, we really don’t have an issue here.  One can make reasonable arguments either way, and what DFL is saying is probably right (and was my first guess as well, but I think empirical evidence would still be required to seal the deal.  I was 80/20 toward what DFL way saying at first, and now I’m at 70/30.

I’m sufficiently convinced that I believe it without looking at the empirical evidence ... that would probably have been a better way of wording it, and what I should have said.  I didn’t mean to suggest that the sabermetric community should start accepting things without looking at the data.

I took a closer look at this question.  Not as in-depth as one could go, probably, but I’m curious to get some feedback before I go any deeper.

I went to the 2008 batting Marcels and selected the top five and bottom five players in percentage of three true outcomes (BB, SO, HR): Cust, Howard, Dunn, Branyan, Thome, and Pierre, Polanco, Eckstein, Lo Duca, Betancourt.

Next I divided the pitchers into thirds based on their 2008 Marcels ERA within their league.

Then I looked at how each of the ten players above performed against each third of pitchers during the 2007 season.

Lo-TTO vs. Top = .287 wOBA
Lo-TTO vs. Med = .323 wOBA
Lo-TTO vs. Bad = .368 wOBA
Hi-TTO vs. Top = .375 wOBA
Hi-TTO vs. Med = .398 wOBA
Hi-TTO vs. Bad = .433 wOBA

It looks like the low-power contact hitters feast off the bad pitchers more than the high-power patient hitters.

These low-TTO hitters drew walks equally (poorly) off of everyone, but they got a lot more singles and a lot more extra-base hits off of bad pitchers.

These high-TTO hitters drew more walks off of good pitchers than off of bad pitchers.  They hit singles at about the same rate off of everyone.  They got a lot more extra-base hits off of bad pitches.

Here are the BABIP numbers:
Lo-TTO vs. Top = .285 BABIP
Lo-TTO vs. Med = .309 BABIP
Lo-TTO vs. Bad = .352 BABIP
Hi-TTO vs. Top = .311 BABIP
Hi-TTO vs. Med = .319 BABIP
Hi-TTO vs. Bad = .345 BABIP

One variation I thought about looking at was pairing low-TTO and high-TTO hitters that are similar in wOBA since high-TTO hitters tend to be much better hitters than low-TTO hitters.

Any other suggestions or comments?

Mike,

Can you show the variation in K rates? I would guess that the top pitchers are much more able to strike out high-contact hitters.

I think it’s not much surprise that the hi-TTO get a lot of walks against better pitchers. When I was looking at historical platoon splits one of the first things that jumped out is that LHB draw more walks off of LHP than RHP. They also strike out more, of course, and have lower BABIP and HR/batted ball, but I think in general hitters attempt to be more selective against better pitchers.

I think looking at WPA/LI in this comparison would be pretty cool, since that would really be the knock against TTO players - i.e., they can’t come through with a hit against better pitchers when a walk has a lower impact. I doubt that’s as true as the anti-TTO theorists make it out to be.

Whoops, I should clarify that bit about LHB. BB/(PA-K) is higher against LHP, not BB/PA which is lower because there are many more K.

And also, LHB vs. LHP is not isomorphic to hitting against better pitchers. LHP walk more batters than RHP, and the platoon split for BB is about the same for both RHP and LHP. Better pitchers do not, as a rule, yield more walks, although many of the pitchers who are better pitchers throw more BB than they would if they were not pitching for K’s. But I would think that in the aggregate the better pitchers are trying to strike out the TTO-types, not induce grounders, so more borderline pitches and hence more walks would be expected. Also, the run value of the walk is lower for the better pitchers.

Mike’s data is very interesting (granted it’s only 5 hitters).  We expected the low-TTO players, relying mostly on their hitting skills and the opposing fielders (theoretically) would have a much smaller variance of performance.  Their wOBA was 81 points worse against good pitchers than bad.

The high-TTO players, much more dependent on the pitcher they are facing (theoretically speaking) should have a high variance in performance (feasting on the bad pitchers and succumbing to the great pitchers, disproportionately so) had a wOBA that was only 58 points worse against the good pitchers.

The gap in BABIP is more telling, and follows what I was suggesting.  With the low-TTO guys, the pitchers already know they are going to get lots of contact, and therefore will pitch to that.  And the great pitchers were able to get a huge gap in BABIP relative to the bad pitchers: 67 points.

The high-TTO guys, the pitchers have determined that they can’t rely on their fielders, and therefore, need to rely on their non-BIP skills.  The BABIP gap was only 34 points.

Basically, this sample data reflects the reality we expected (we just didn’t know the extent of it).  So, I’d look forward to even more data from more players.

And of course, since this is Mike Fast, I’d LOVE to see the PITCHf/x data on these hitter/pitcherClass pairs.  This will go to show whether pitchers can disproportionately change their approach, in the face of totally new contexts, such that the resulting outcomes we see can be traced back to their pitching approach.

A bit more detail on the data, some of it that Tom Meagher requested:

Lo-TTO vs. Top = 8.3% K/AB
Lo-TTO vs. Med = 5.1% K/AB
Lo-TTO vs. Bad = 5.4% K/AB
Hi-TTO vs. Top = 38.8% K/AB
Hi-TTO vs. Med = 34.3% K/AB
Hi-TTO vs. Bad = 34.3% K/AB

And the (2008 Marcel) stats for the tiers of pitchers:
Tier ERA BB/9 K/9 HR/9
Top 3.81 3.1 7.3 0.88
Med 4.44 3.3 6.5 1.03
Bad 5.05 3.5 6.2 1.15

Tango, do you know of any database where I can query batter vs. pitcher matchup stats, either for 2007, or for multiple years?  That would make it easier to do larger samples.  As it is, I looked up the batter-pitcher splits in Yahoo for each batter and copied and pasted to a spreadsheet.  But that gets painful for more than a handful of players.

Re: 11, that’s basically the way I would look at the question as well.  Obviously, my guess would be that with more data, we would see that trend start to go in the opposite direction.  I have to admit I’m not of much help as far as how to access that data, but I am eager to see the results.

One thing I do notice about the sample data ... there is actually a substantial difference between the “top” and “bad” pitchers in terms of BABIP.  Is this an artifact of the selection process?  I had been thinking that pitchers don’t actually vary too much in BABIP ability.  Maybe the pitchers that were BABIP-unlucky in 2007 get classified as “bad”?  (I’m not sure what a 2008 Marcel ERA is, so not sure if this is the case)

Best way is probably to parse the data out of Retrosheet. What I did was take the 2007 Retrosheet event files, load them into a database, and ran the following query:

SELECT Batter,
Pitcher,
SUM(IF(eventtype = “20”, 1,0)) AS `1B`
, SUM(IF(eventtype = “6”, 1,0)) AS `CS`
, SUM(IF(eventtype = “3”, 1,0)) AS `K`
, SUM(IF(eventtype = “2”, 1,0)) AS `O`
, SUM(IF(eventtype = “14”, 1,0)) AS `BB`
, SUM(IF(eventtype = “18”, 1,0)) AS `E`
, SUM(IF(eventtype = “21”, 1,0)) AS `2B`
, SUM(IF(eventtype = “23”, 1,0)) AS `HR`
, SUM(IF(eventtype = “16”, 1,0)) AS `HBP`
, SUM(IF(eventtype = “19”, 1,0)) AS `FC`
, SUM(IF(eventtype = “4”, 1,0)) AS `SB`
, SUM(IF(eventtype = “13”, 1,0)) AS `FE`
, SUM(IF(eventtype = “15”, 1,0)) AS `IBB`
, SUM(IF(eventtype = “22”, 1,0)) AS `3B`
, SUM(IF(battereventflag = “T”, 1,0)) AS `PA`
, SUM(IF(shflag = “T”, 1,0)) AS `SH`
, SUM(IF(sfflag = “T”, 1,0)) AS `SF`
, SUM(IF(doubleplayflag = “T”, 1,0)) AS `DP`
, SUM(IF(battedballtype = “F”, 1,0)) AS `FB`
, SUM(IF(battedballtype = “G”, 1,0)) AS `GB`
, SUM(IF(battedballtype = “L”, 1,0)) AS `LD`
, SUM(IF(battedballtype = “P”, 1,0)) AS `PO`
FROM events
GROUP BY Batter, Pitcher;

(I used MySQL; you might have to alter the query based upon what database you use.)

Any crosstab query I run like that has the downside of being incredibly slow, however. Exported to a CSV file, here are the results:

http://pontifexexmachina.googlepages.com/hitter_pitcher_matchups2007.csv

That is exceptionally large for a CSV file - about 5 mb. I’m pretty sure Excel versions prior to Excel 2007 won’t be able to open it - there’s 72,840 rows in there. I didn’t figure out any rate stats. On the plus side, I included the fly ball/ground ball/line drive data in there as a happy accident.

If you need other years, let me know.

Here is the (Marcels projected) BABIP of the pitcher groups:
Top = .280 BABIP
Med = .288 BABIP
Bad = .299 BABIP

Marcel is Tango’s basic projection system.  I’m using it as a proxy for true talent level.

Wow, that’s great, Colin.  Thanks.  I’ll take a look at that on my computer at work.  My home version of Excel would choke on that.

Right, I would say parse the Retrosheet data.

Otherwise, Baseball-Reference Play Index let’s you query on batter/pitcher matchup. It costs 29$ per year.

Isn’t it pretty well accepted that if you have two AAA hitters of similar value, the one that relies more on the three true outcomes is going to be a worse major leaguer (ignoring long term projections etc)? 

Doesn’t that basically prove that Jack Cust is going to get a disproportionate amount of his value from bad major league pitching?

I’ve taken these things as a given for a few years, including the implied assumption that Cust is going have a bigger platoon split than Jacoby Ellsbury.  PECOTA projects platoon splits now, maybe there is some insight to be gained there.

If something is “well-accepted”, that’s a good reason to at least question it.

It’s not like I’m parroting conventional wisdom, I’m fairly certain I’ve seen more than one empirical translation system say the same thing.

I think if you accept these two assumptions ..

1. Log5 is a good approximation of P(Event) when a batter and pitcher meet each other

2. Pitchers vary a lot more in BB, K and HR rates than they do in BABIP.

... then there’s no way around Cust types being more dependent on pitcher quality than Gwynn types.  (Because you can just work out the math, using log5 and low variance BABIPs and see that it has to be that way).

For my part, I basically assumed that both of these were true, and that’s what was going through my mind when I said we didn’t need to study the issue empirically.  The comments from Mike Fast and Tom Meagher about good hitters walking disproportionately often against good pitchers is making me doubt whether the Log5 assumption really is true.

However, Mike’s data also seems to call into question assumption #2, and I’m pretty skeptical about that.  I doubt the “best third” of pitchers really has a BABIP rate 0.05 lower than the “worst third” of pitchers ... I think that’s either a fluke, or in some way, an artifact of the study (i.e. maybe pitchers with lousy BABIP luck in 2007 are lumped into the “bottom third").

So while I have more doubts than I did before, I’d feel comfortable betting that out of the 10 guys Mike lists, the 5 high-TTO guys will show a bigger OPS discrepancy in 2008 than the low-TTO guys (using the same groups of pitchers).

DFL/#25, good job of identifying the two assumptions underpinning your original theory.  I was going to try to do that, but you’ve captured them very well.

I’m pretty skeptical about assumption #1.  The data doesn’t back it up; neither does my intuition.

Your assumption #2 should be accurate.  I think you’re misunderstanding the BABIP data I presented.  The first set of BABIP data in post #11 was for the two groups of five batters each against the three groups of pitchers (which encompass the whole league).  These particular few batters on the two extremes of the Three True Outcomes have on the order of 0.050 BABIP variation between the three groups of pitchers. 

The second set of BABIP data in post #19 was for the the three groups of pitchers against all the batters in the league.  Here you can see that the best pitchers have BABIP about 0.019 better than the worst pitchers.

I think that’s either a fluke, or in some way, an artifact of the study (i.e. maybe pitchers with lousy BABIP luck in 2007 are lumped into the “bottom third").

I used the Marcel 2008 projections to group the pitchers in thirds specifically to avoid this problem.  The Marcels regress the BABIP performance of the pitchers heavily back toward the mean in an attempt to estimate the true talent level of BABIP skill.

Here are a couple graphs that show the difference between the actual 2007 BABIP distribution and the 2008 Marcel projections that I used.

http://fastballs.wordpress.com/files/2008/04/babip_vs_era_2007.jpg
http://fastballs.wordpress.com/files/2008/04/babip_vs_era_2008_marcels.jpg

Tango can explain the Marcels better than I can, or if you have questions, go look at his page on the Marcels: http://www.tangotiger.net/marcel/. 

Part of the BABIP projection will still be fielding and park, so the top third by Marcel probably has a better BABIP projection than the true talent of the top third context-neutral. That should have little impact on the above findings, though.

Using the Retrosheet matchup data from Colin, I did a more thorough study that included every non-pitcher plate appearance from 2007. 

I also controlled for the quality of the hitter.  I’m not sure I’m happy with how I did that, but I’m not sure what other way I’d prefer to do it.  Any ideas?

I used the 2008 Marcels as an estimate of true talent level.  I divided the hitters on the basis of the ratio of wOBA to the percentage of plate appearances in one of the three true outcomes (K, BB, HR), hereinafter TTO%.  The top 15% in woBA/TTO%, I called high-TTO hitters.  The middle 60% I called mid-TTO hitters, and the bottom 25% I called low-TTO hitters.  (There’s a reason I didn’t make the percentages symmetrical, and I can go into that if people care, but it’s not really relevant to where I’m going with this point.)

Group wOBA TTO%
High-TTO 0.334 40%
Mid-TTO 0.336 28%
Low-TTO 0.339 20%

I thought that was a fairly good job of removing wOBA as differentiator between the groups, but I’ve done so at the expense of compressing the difference in TTO%.

Nonetheless, on to the results...there is some indication that High-TTO hitters do poorer against good pitchers than do Low-TTO hitters.  I don’t know if the difference is statistically significant.

Matchup wOBA K% HR% BB%
Hi-TTO v. Good-P 0.291 0.330 0.037 0.096
Hi-TTO v. Mid-P 0.333 0.275 0.045 0.107
Hi-TTO v. Bad-P 0.373 0.253 0.053 0.117
Mid-TTO v. Good-P 0.298 0.231 0.023 0.075
Mid-TTO v. Mid-P 0.336 0.182 0.030 0.081
Mid-TTO v. Bad-P 0.375 0.160 0.039 0.091
Lo-TTO v. Good-P 0.301 0.146 0.016 0.057
Lo-TTO v. Mid-P 0.344 0.108 0.023 0.067
Lo-TTO v. Bad-P 0.372 0.096 0.024 0.069

Oops, I should have included the number of PA in each matchup group.  Here is that data.

Matchup PA
Hi-TTO v. Good-P 9122
Hi-TTO v. Mid-P 9149
Hi-TTO v. Bad-P 9096
Mid-TTO v. Good-P 36850
Mid-TTO v. Mid-P 36232
Mid-TTO v. Bad-P 36365
Lo-TTO v. Good-P 15255
Lo-TTO v. Mid-P 15448
Lo-TTO v. Bad-P 15151

10,000 PA means 1 SD = 5 points.

So, there MIGHT be something there.

Maybe it is like clutch hitting ... yeah, it’s there, but the effect is so small to be of limited practical significance for any real analysis.  I guess we can’t really attribute the lack of playoff success of early 2000’s A’s teams to “take and rake” teams being bad matchups for good pitchers.

Mike, a big thanks for running these numbers.  I agree that it’s important to control for quality of hitters; as you say, the high-TTO hitters tend to be better than the low-TTO hitters, which complicates matters.

Everything in this post has issues with significant figures since I’m just basing it on what Mike put up, so proceed with caution, but…

In run values, over 600 PA against each class of pitcher relative to performance on the whole, you get:

Batter,GdPitc,MdPit,BdPit
Hi-TTO,-22.43,-0.52,20.35
Md-TTO,-19.89, 0.00,20.35
Lo-TTO,-19.83, 2.61,17.22

This makes the Hi-TTO group look bad, but that’s really because as a group they’re only hitting .334 vs. .336 and .339.

Their runs/600PA relative to their performance against the mid-level pitchers is:
Batter,GdPitc,BdPit
Hi-TTO,-21.91,20.87
Md-TTO,-19.83,20.35
Lo-TTO,-22.44,14.61

So while the Hi-TTO hitters are more affected by good pitchers than the middle group, the Lo-TTO hitters are more effected by the good pitching. And we know that over 600 PA the Hi-TTO are about a run worse than the Md-TTO and the Lo-TTO are about a run and a half better than the Md-TTO, or 2.5-3 runs better than the Hi-TTO.

So these figures indicate, unless I’ve screwed up too much, that against good pitchers there might be a small penalty for TTO-hitters but that this is not true relative to low TTO hitters, who seem to be the worst against good pitchers. Meanwhile, against bad pitchers, the low-TTO hitters have an obvious penalty.

And looking at the difference between Hi-TTO and Mid-TTO hitters, compare their differences against the medium and bad pitchers: they each gain 1.92 runs per 600 from more walks and 3.96 runs per 600 from fewer K. The Mid-TTO hitters also gain more from HR, 7.51 vs. 6.67, but the Hi-TTO hitters are making up for this on balls in play - 8.31 gained against bad pitchers for them against 6.96 for the Mid-TTO hitters.

So TTO hitters are only meaningfully feasting on bad pitchers *relative to the lo-TTO hitters*, and that’s because the lo-TTO hitters are unable to take advantage of the extra BB, extra HR, and fewer K from bad pitchers. They gain 11.23 runs on balls in play, but only 0.38 from BB, 2.16 from fewer K, and 0.83 from HR. So both the hi and lo groups benefit more than the larger group from balls in play against bad pitchers, but the lo-TTO pitchers lose 10 runs in value from not capitalizing on the shift in TTO (the hi-TTO pitchers lose about .75 runs relative to the mid).

Meanwhile, against good pitchers, the Hi-TTO hitters are, relative to their performance against medium pitchers, losing the same 6.67 runs they gain against bad pitchers. The Mid- and Lo-TTO hitters each lose 5.84 from fewer home runs. They lose more from extra K (-9.90 versus -8.82), and the lo-TTO hitters lose only 6.84 from K. It’s the third true outcome that’s most interesting: good pitchers cost the mid-level hitters only 1.2 runs per 600 PA from issuing fewer BB. The Hi-TTO hitters lose 2.1 runs from BB, but the Lo-TTO players lose almost as much, 1.9. This leaves balls in play; the mid hitters lose 4.02 runs per 600, the TTO hitters are better at only 3.23, and the slappier hitters lose 7.84 runs on balls in play. So the good pitchers neutralize the lo-TTO hitters’ strength more than they exploit the hi-TTO players weakness.

Hmm, one more number I like to look at, BB/(PA-K).

Hitter,GdPi,MdPi,BdPi
Hi-TTO,.143,.148,.157
Md-TTO,.098,.099,.108
Lo-TTO,.067,.075,.076

In other words, when the pitcher cannot manage a strikeout, the middle group is about the same against the top 2/3 of pitchers and the lo-TTO group is about the same against the bottom 2/3. Amount gained from extra walks by Hi-TTO against bad pitchers = amount gained from extra walks by the middle group against bad pitchers = amount lost from fewer walks by Lo-TTO hitters against good pitchers. And the amount lost by Hi-TTO hitters against good pitchers is half that.

So if all of the above is basically accurate, if you have three equal hitters, you prefer the Hi-TTO by a bit against bad-pitchers, the lo-TTO against the mid-level pitchers, and the even profile hitter against good pitchers. And you definitely don’t want the lo-TTO hitter if a bad pitcher is on the mound.

Tom/#34, if you would be interested, I could send you the whole spreadsheet.  Email me at my Gmail account (mikefast).