THE BOOK--Playing The Percentages In Baseball

Maybe I’ll break it down by day and night games to see if that affects the last bucket, as presumably in night games, it gets colder as they game goes on and in day games, it gets warmer or at least stays about the same.  Or maybe I’ll look at indoor games only.

I think the “1st time” for wOBA could possibly be lower than you show it to be. If a pitcher is getting bombed (high wOBA), he’s not likely to make it through the lineup 3 times. I’m not sure if I’m thinking about this correctly, so feel free to tell me I’m completely wrong.

MGL - Is everything related to PAs (except the noted 2B and 3B per 2B+3B)?  Because SF, DP, WP and PB are going to vary by whether there are men on base and the number of PAs with men on base may vary with times through the order.

I am surprised that WP and PB show an inverse relationship.  This may indicate a scorer’s bias.

I think there is definitely a selection bias due to the survivorship of pitchers who are pitching well.  I think this accounts for what Dan is mentioning in post 2 and what you are seeing in the 4th time through the order.  To go through the order a fourth time a pitcher must both be pitching well and the game score must still be close or the pitcher has a no-hitter or shut out going.  I don’t think a starting pitcher gets left in for a fourth time through too many times in 10-2 blowouts.

Mgl, your results echo mine in The Book (1999-2002), where it was something like .340/.348/.356 the first 3 times thru the order, and the 4th time went down to the 2nd.

***

Dan: we are adjusting for the quality of batter/pitchers.

***

As for the reason it goes down the 4th time, I can only see that the pitchers the 4th time through were “on” that day, and so, it was not a random performance.

It could also be that they threw less pitches, so they were a bit fresher.

It is very interesting of course.

I don’t understand how there can be more PA for the 2nd time through order than the 1st. Are those typos or your real result? If the latter, how are you handling plate appearances after double switches in the NL? Could you be counting the first appearances of a batter who entered in the middle of the game but not as a pinch hitter?

And is an adjustment for overall batter/pitcher quality enough without accounting for platoon biases? It’s not overall quality which will keep the batter or pitcher in the game in late innings nowadays, it is quality in the context of their platoon matchup. I’d assume the pitcher is more likely to be removed with the disadvantage.

I think I had a few bugs, which accounted for the first time thru the order being less frequent than the second time.  As far as double switches and the like, I am supposed to be excluding all batters who were not in the lineup when the game started.

As I originally said, there may be some selection bias issues based on how pitchers are pitching and the run environment for that day.

As I also stated, I controlled for the overall quality (more or less) of the pitcher, so if there is selection bias, it is based on pitchers having “good” and “bad” days, which Tango found is not a significant or prevalent effect.

Yes, Peter, the GIDP, WP, and PB are per PA, so yes, if the number of men on base varies each time through the order, that will affect those numbers.  Is there any reason to think that these (number of men on base, etc.) would vary much as a function of times through the order?

I don’t know why the WP goes up so much as the times through the order increases.  Could be that pitchers are throwing more off speed pitches as the game goes on.  Could be scorer bias, for some reason.  If you combine the WP and PB, which is a better indication of “bad pitches” the numbers are more consistent, and the pattern is an increase in total “bad pitches” with a large jump in the last bucket.

I am re-running the numbers, as I did have some small bugs as far as which PA’s were included in each bucket.

Here is a corrected run, for day games only, which should remove the issue of the weather getting colder as the game goes on:

Frequency of occurrence:

1st time: .356
2nd time: .339
3rd time: .263
4th+ time: .042

So that bug (where 2nd time was more frequent than 1st time) is corrected at least.

Foul Out

1st time:  .999
2nd time: .968
3rd time: 1.049
4th+ time .950

Single

1st time:  .975
2nd time: 1.006
3rd time: 1.019
4th+ time 1.045

Dbl+Trpl

1st time:  .956
2nd time: 1.009
3rd time: 1.038
4th+ time 1.065

Dbl/(Dbl+Trpl)

1st time:  1.006
2nd time: 1.006
3rd time: .985
4th+ time 1.001

Trpl/(Dbl+Trpl)

1st time:  .942
2nd time: .935
3rd time: 1.150
4th+ time 1.011

HR

1st time: .940
2nd time: .987
3rd time: 1.081
4th+ time 1.132

BB (No IBB)

1st time:  .996
2nd time: 1.000
3rd time: .995
4th+ time 1.069

HP

1st time:  1.055
2nd time: .937
3rd time: .983
4th+ time 1.154

BB + HP

1st time:  1.003
2nd time: .993
3rd time: .994
4th+ time 1.078

SO

1st time:  1.107
2nd time: .982
3rd time: .899
4th+ time .846

ROE

1st time:  .965
2nd time: 1.009
3rd time: 1.020
4th+ time 1.109

SF

1st time:  .956
2nd time: 1.060
3rd time: .986
4th+ time .970

GDP

1st time:  .943
2nd time: 1.053
3rd time: 1.008
4th+ time 1.008

IFS (infield single)

1st time: .968
2nd time: .981
3rd time: 1.035
4th+ time 1.176

Bunt Single

1st time:  1.029
2nd time: 1.005
3rd time: 1.064
4th+ time .538

WP

1st time:  .818
2nd time: .972
3rd time: 1.180
4th+ time 1.713

PB

1st time:  1.287
2nd time: .730
3rd time: 1.031
4th+ time .535

WP+PB

1st time:  .888
2nd time: .936
3rd time: 1.158
4th+ time 1.536

wOBA

1st time:  .333
2nd time: .343
3rd time: .352
4th+ time .367

If we adjust the wOBA for WP+PB, we actually get:

wOBA

1st time:  .332
2nd time: .343
3rd time: .353
4th+ time .371

So yes, it appears that the night games are what cause the 4th time through the order to revert back.

It is interesting that batters do so well the 4th+ time through the order.  As several people have mentioned, you would expect that pool to be dominated by pitchers who are having “good days.” It makes you wonder about the constant criticism about taking starters out early.  I have always said that one of the biggest mistakes that manages make is leaving in pitchers who are not excellent overall pitchers when they are having so-called “good days.” From this data, it appears that that is a terrible strategy.

I am going to do another run on night games only, excluding the indoor stadiums (I think MIN and TB only).  We should see a marked reversion in the last bucket, presumably due to the weather.

BTW, this data (along with data from night games) gives us a nice proxy for the effect of temperature on each of the categories. Up until now, the only research I have seen on that do not control for things like the batter and pitcher pool, etc.

Joe, a pitcher is of course more likely to be removed at the point in which he faces an opp side batter, but I don’t see how that will have any effect on these results.  No PA’s after the starting pitcher is removed are included in the data.  Plus any bias for or against the starting pitcher when he is in the game is already accounted for when I adjust for his overall, season-long stats.  I suppose if a pitcher is still in the game for the 3rd or 4th times, he is ever so slightly more likely to have faced same-side batters, but I don’t think that is going to have any more than a tiny, tiny effect on the data.

I can’t remember who did the study now, but does anyone know how long the offensive spike at the beginning of the year lasts? Was it until about the end of April?

What do you mean by “offensive spike”?  I don’t have the data in front of me, but I think that offense (rpg) is a little higher in April than you would expect given the temperature, but it is still lower than in the upcoming months.  And whatever it is, I doubt that it “ends” at any particular point in time.  Any change in offense during the year, due to weather, personnel changes, or pitchers needing time to get into shape, is going to be gradual…

Brent, here is the AL+NL OPS (regular season) for each month for 06-08 combined:

April/March: .744
May: .748
June: .760
July: .771
August: .767
Sept/Oct: .764

I don’t see any “spike at the beginning of the year” and if there are any trends associated with weather or any other factors, again, I assume that they are gradual.  Most of what you see in the above numbers are weather related of course.  As I said, I think there is slightly greater offense at the beginning and end of the seasons, even after adjusting for the weather, having something to do with personnel, or pitchers not being in top form at the beginning of the season.

MGL,

In your day games you show that both ROE and IFS increase each time through the order, so I am wondering if you had ever checked UZR to see if it follows the same pattern?  It would be interesting (to me at least) if fielding gets worse later in day games, and perhaps how night games compare. 

If patterns or large effects are seen, it might be an opportunity to attempt to quantify things like sun fields, lights taking effect, overcast days, fatigue, heat fatigue, etc.

Interesting.  Never did look at UZR versus day/night, etc.

My guess is that most of the effects you see in day versus night games are due to the temperature changes as the game goes on.  Temperature probably affects UZR as well as balls in general are hit harder (as well as farther) in warmer temperatures.  There are probably other effects though.  It might be that fielding in general is better in day games as the balls are easier to see.  Or maybe not. Maybe the sun is more of a problem in day games.  Or maybe ground balls are easier to field during the day, but fly balls are harder.  No idea.  Someone could easily look up the error rates in day versus night games on B-R.com.

Interesting stuff though.

OK, here are the corresponding numbers for night games only.  I also excluded all MIN and TB games (indoor) and all TOR games in April and September and ARI games in June-August (many, of not most, are indoor).

First I’ll show wOBA:

wOBA

1st time:  .338
2nd time: .343
3rd time: .352
4th+ time .347

All my wOBA’s are normalized to the average of all PA’s in all the buckets AND it is adjusted to the pool of pitchers and batters for all PA’s as well.  Interestingly, the first time through the order, in night games the wOBA is 5 points higher.  I am not sure why.  Maybe it has to do with eliminating the games I eliminated.  Anyway, here are the other components:

Frequency of occurrence:

1st time: .353
2nd time: .339
3rd time: .266
4th+ time: .042

Foul Out

1st time:  1.023
2nd time: .979
3rd time: 1.039
4th+ time .809

Single

1st time:  1.003
2nd time: .993
3rd time: 1.025
4th+ time .980

Dbl+Trpl

1st time:  .949
2nd time: 1.025
3rd time: 1.046
4th+ time 1.045

Dbl/(Dbl+Trpl)

1st time:  1.006
2nd time: 1.002
3rd time: .993
4th+ time .981

Trpl/(Dbl+Trpl)

1st time:  .931
2nd time: .981
3rd time: 1.070
4th+ time 1.162

HR

1st time: .943
2nd time: 1.006
3rd time: 1.074
4th+ time 1.069

BB (No IBB)

1st time:  1.034
2nd time: .995
3rd time: .972
4th+ time 1.025

HP

1st time:  .999
2nd time: .990
3rd time: 1.048
4th+ time .881

BB + HP

1st time:  1.030
2nd time: .994
3rd time: .980
4th+ time 1.009

SO

1st time:  1.089
2nd time: .979
3rd time: .928
4th+ time .969

ROE

1st time:  1.001
2nd time: 1.015
3rd time: 1.001
4th+ time .959

SF

1st time:  .960
2nd time: 1.070
3rd time: .976
4th+ time 1.012

GDP

1st time:  .973
2nd time: 1.026
3rd time: 1.001
4th+ time 1.128

IFS (infield single)

1st time: .947
2nd time: 1.014
3rd time: 1.060
4th+ time 1.045

Bunt Single

1st time:  1.035
2nd time: 1.017
3rd time: .988
4th+ time .823

WP

1st time:  .948
2nd time: 1.004
3rd time: 1.044
4th+ time 1.197

PB

1st time:  .967
2nd time: 1.047
3rd time: .913
4th+ time 1.456

WP+PB

1st time:  .950
2nd time: 1.009
3rd time: 1.019
4th+ time 1.225

That raised the effective wOBA by 1.5 points in the 4th bucket, BTW.

Fantastic insight about day v night!

For 2005-2008:

I used BAbip as a proxy for range, and ROEbip=ROE/(AB-HR-SO+SF+SH) for error rate.  Any suggestions for better proxies?

For 2006-2008 (to match the run) for Times Facing Opponent in Game split:

Frequency in PA:

All data from B-R.com, and I am not sure how they handle players in the starting lineup vs substitutes, but given the frequencies it does not look like they differentiate between them.

Yeah, thanks, it’s good stuff I think.  I might write up a full article for THT or Fangraphs.  I think that people have been underestimating the impact of times through the order, partially because the impact was muted by the temperature thing, as most games are night games, and even because of the WP/PB thing - although the WP/PB might simply be a function of the fact that it is late in the game and have nothing to do with the familiarity of the batter/pitcher matchup.

It looks like around 10 points in WOBA per times through the order. That is a lot!

Depends on what you are looking for in ROE rate.  ROE per ground out is the “best,” but if in a certain situation more ground balls are hit, and thus there are more errors, it won’t show up in ROE per ground out of course.  So it depends on whether you want to look at actual ROE per PA (which affects run scoring) or you want to know in what situations the fielders are actually handling balls better or worse, etc.

Doesn’t look like a lot of differences in those B-R numbers, but if you are not controlling for the pool of pitchers in each bucket, the numbers are pretty worthless.  The better pitchers will predominate in the later times through the order buckets, canceling out or muting any effects you get from the familiarity advantage (for the batter).

The day/night breakdown is very interesting.  Great stuff. 

Does the pattern look any different if you look at April/May vs. July/Aug night games?  I would think temperature would be a larger factor in the spring, and less so in the middle of the summer.

what contribution would the effect of temperature changes have on starter/reliever splits?

Just quickly perusing the data, it looks to me like the main effect of subsequent PAs is that the batters simply put the ball in play more often. They strike out less, walk less, get more GIDP, and more IFS.

MGL, can you do an ISOBIP (iso on balls in play) by time through the order. I wonder if the quality of contact is improving or just the amount of it.

Matt

For those with The Book, you can compare MGL’s results to mine at Tables 81, 82.

The wOBA for 1st time through the order was .345, and the 3rd time was .362.

Per 600 PA, there were 101 SO, and 84 SO, respectively.

So, if we remove the SO from the denominator, the wOBA per non-SO PA is:
.345*600/(600-101)
= .415

That’s the wOBA, treating SO as a non-event, for 1st time thru the order.

For third time:
.363 * 600 / (600-84)
= .422

So, per non-SO PA, you see have a bigger impact per PA.  The SO is the biggest effect though, as noted in The Book (but not with the clarity here).

What do the numbers look like when you isolate the pitchers who made it through the batting order four times?  They would be the ones to look at to see if they are actually improving the 4th time through the lineup vs the 1st, 2nd and 3rd times.
vr, Xei

Xei, way too much of a selective sample there!  If a pitcher makes it 4 times through the order, he necessarily got lucky in the early going, so you are going to see a large increase as you go through the order.

In any case, why would a pitcher improve through the order?  Are you wondering whether a manager can see that a pitcher is getting better or at least that he is not getting the usual worse, and that is one reason that he is left in the game?  Interesting…

Will, good point about starter/reliever splits.  Maybe we should rethink the large difference we find, which is usually on the order of 1 to 1.5 runs per 9. It appears that relief pitchers may be benefiting by around 10 points (if I have that right) due to colder temps.  I am assuming that the average relief pitcher comes pitches in the 4th+ bucket, and that the average starter averages the 2nd bucket (1st,2nd and 3rd combined). 10 points in wOBA is around .34 runs per 9.  So maybe we should reduce that starter/reliever split by that amount.  Great point!

A lot of adjusting needs to be done with pitchers and batters for game time temperature, I think. 

Could that be another reason for the pinch hit penalty?

And what about backup catchers who usually play in day games after night games?

Great stuff here, I think!

Matt, I’ll try and rerun the data. I wanted to look at other ways of categorizing the components anyway (like wp and pb with runners on base only or ROE, IFS, and GDP per ground ball).  I also wanted to see if the G/F ratios change, which I suspect they might.

Guy, is there any reason to think that the temp change from beginning to end of game is different in April or May than in August or September?  Is that what you mean?

No, you can’t do it that way.  Knowing that someone faced 28-36 batters means that they pitched pretty well batters 1-27.  It won’t really mean much whether they were great at batters 1-9 or 10-18 or 19-27.  You really have to be careful about starting with an endpoint, and working backwards.  That kind of process is fraught with selection bias.

A relevant article was penned by Voros here:
http://www.baseballthinkfactory.org/files/primate_studies/discussion/mccracken_2001-03-20_0/

I agree, simply fantastic insight on the day/night.

I’ve been meaning to revisit this starter/relief issue with
a) more retro data
b) across the retro eras

To now also include the D/N flag is simply fantastic.  I’m going to look forward to doing that work.

The pinch-hitter thing is also another great point.  MGL: email Andy, and ask him if he can include that switch, and rerun his study.  This would be so very cool.

MGL:  I was thinking that the drop in temperature was likely larger in spring games.  However, maybe that’s not true. 

But I’m having second thoughts about temperature as the main explanation here.  How much does the temperature drop in a stadium over 2 or 2.5 hours—is it really enough to affect wOBA this much?  If it were, then why don’t we see a substantially higher wOBA in day games than night games overall?  I’d think the temperature difference between day and night games is at least as large as the difference between innings 1 and 8 of a night game.

Another way to think about this is that pitcher fatigue is a greater factor in day games because it’s hotter.  By the time they are facing batters for the 4th time, they are running out of steam more than at the same stage of a night game.  So, in night games the pitcher-having-a-good-game factor (which also incorporates the fact that a specific pitcher matches up better against this lineup than the respective wOBAs would predict) can be seen in the 4th PA results, while in day games it’s overtaken by heat-induced fatigue.  Hitters, I think it’s fair to say, will be less impacted by the heat of a summer day game.

One reason you don’t see substantially higher (I think there is some, but I am not sure) scoring in day games is that players are rested in day games following night games.  So the pool of offensive players is definitely a lot worse in day games.  If you want to compare day and night games you have to control for that.

I agree that pitcher fatigue may be a factor in day games.  Let’s juts say that an increase in offensive performance as a function of temperature includes pitcher fatigue.  What do you hypothesis about night games where it is warm the whole evening, like in Texas in the summer?  Do you think that we should see a rise in wOBA in the 4th+ bucket similar to day games?

I think that the average drop in temp from around 7 PM to 9 to 9:30 PM is at least 5 degrees, but I am certainly not sure.

MGL,

Do you have similar figures for hitters?  I am wondering if part of this effect can actually be explained in a different way.  Instead of suggesting, “Hitter A performs better in his third or fourth at-bat against Pitcher A,” perhaps another explanation is that, “Hitter A performs better in his third or fourth at-bat REGARDLESS of the pitcher.”

Might you have these numbers?  I could envision your familiarity bonus being partially explained simply by having a number of at-bats against ANY pitcher during the same game.  Rather than a “familiarity bonus,” it would essentially be a “reverse pinch hitting bonus.”

Well, at some point I guess you can’t tell which it is.  Although I suppose you could compare a batter who has batted 3 or 4 times in the game against the same pitcher with a batter who bats 3 or 4 times and then faces a relief pitcher and then compare a relief pitcher who just comes in the game against a pinch hitter versus a batter who has been in the game and batted 3 or 4 times.  If you throw every combination in the mix, you might be able to tell where the effect comes from.

I doubt, however, that the effect is simply the batter being in the game for a while (although there is probably SOME effect).  If that were the case, we probably would not see such a large difference in pitching between when a pitcher starts and when he relieves.  If batters had such a large advantage in and of itself after 4 or 5 at bats, it would be unlikely that closers would be so effective, I would think…

You’re probably right.  It’s interesting, though, that none of this advantage seems to carry over into subsequent games with the same batter/pitcher matchup.  If these rematches occur two months later in the season, then it’s no surprise.  But pitchers often face the same team two starts in a row - one home, and one on the road.  I’ve never seen any study that looks at these games to see if the advantage carries over to that second matchup.  Does anybody know if this has been considered?  I don’t have a copy of The Book at my desk, so I apologize if it’s covered in the pitcher/hitter matchup section.