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Mitchel Lichtman, or MGL, has been doing sabermetric research and writing for almost 25 years. He is one of the authors of The Book: Playing the Percentages in Baseball. He has consulted for several major-league teams over the years and has occasionally made a fool of himself on radio and TV. He holds a B.A. from Cornell University and a J.D. from the University of Nevada. You can check him out on Twitter at @MitchelLichtman or on his blog at www.mglbaseball.org.
Last week, in this article, I discussed a starting pitcher’s “times through the order penalty” (TTOP)—the tendency for the pitcher’s performance to suffer with each trip through the lineup. In the comments section, several readers wondered whether pitchers who throw primarily one type of pitch might have a particularly large penalty as opposed to pitchers who throw a greater variety of pitches. The speculation was that it would be harder or take longer for a batter to acclimate himself to a pitcher who has a lot of different pitches in his arsenal. In addition, since most starters tend to throw more fastballs the first time through the order, pitchers who follow that up with a higher frequency of off-speed pitches might have an advantage over those who continue to throw mostly fastballs, in terms of the TTOP. Let’s see if that is true.
First I split all the starters into three groups: one, over 75 percent fastballs, two, under 50 percent fastballs, and three, all the rest. The data is from 2002-2012, and includes Baseball Info Solutions’ pitch-type information from FanGraphs. The results are illuminating.
FB% |
N (Pitcher Seasons) |
Overall |
First Time |
Second Time |
Third Time |
Fourth Time |
Second Minus First |
Third Minus Second |
Fourth Minus Third |
> 75% |
159 |
.357 |
.341 |
.363 |
.376 |
.348 |
.027 |
.020 |
-.013 |
< 50% |
359 |
.352 |
.346 |
.349 |
.360 |
.361 |
.003 |
.015 |
.010 |
All others |
2632 |
.359 |
.346 |
.361 |
.370 |
.371 |
.015 |
.015 |
.013 |
Pitchers who throw mostly fastballs lose 47 points in wOBA against (columns eight plus nine) by the third time through the order. (For those who are just joining us, wOBA is an all-in-one offensive rate statistic in the same vein as TAv, but on the OBP scale instead of the BA scale.) Those with a much lower fastball frequency lose only 18 points. Interestingly, the “fastball” group reverts back to better-than-normal levels the fourth time (I don't know why that is, but I'll return to that issue later), but the latter group continues to suffer a penalty as do all the others. Keep in mind that the fourth time numbers represent very small samples for the first two groups, since starters don't often make it past the third time through the order.
The takeaway here is that a starter's pitch repertoire is extremely important in terms of how long he should be left in the game and whether he should start or relieve (we already knew the latter, right?). If we look at columns three and four, we can get some idea as to the difference between a pitcher as a starter and as a reliever, at least as far as times through the order is concerned (there are other considerations, such as velocity—e.g., when a pitcher is a short reliever, he can usually throw harder). The mostly fastball group is 16 points (around .5 runs per nine innings) more effective the first time through the order than overall, while the low-frequency fastball group has only a six-point (.20 RA9) advantage. Keep in mind that some of that first-time-through-the-order advantage for all groups is due to the "first inning" effect (see my original article).
Next I split the pitchers into four groups based on the number of unique pitches they threw at least 10 percent of the time. The categories of pitches (from the FG database) were fastballs, sliders, cutters, curveballs, changeups, splitters, and knuckleballs.
# Pitches in Repertoire (> 10%) |
N (Pitcher Seasons) |
Overall |
First Time |
Second Time |
Third Time |
Fourth Time |
Second Minus First |
Third Minus Second |
Fourth Minus Third |
1 |
41 |
.359 |
.344 |
.370 |
.375 |
.303 |
.027 |
.009 |
-.061 |
2 |
1000 |
.358 |
.343 |
.359 |
.371 |
.366 |
.016 |
.018 |
.007 |
3 |
1712 |
.361 |
.349 |
.362 |
.371 |
.372 |
.013 |
.015 |
.014 |
4 |
378 |
.351 |
.340 |
.351 |
.360 |
.368 |
.011 |
.013 |
.019 |
This is even more interesting. It appears that the fewer pitches a starter has in his repertoire, the more quickly batters become familiar with him, as we might expect. One-pitch pitchers lose 36 points by the third time through the order, while four-pitch pitchers lose only 24 points. The fourth time through the order is exactly the opposite. Against one-pitch pitchers, pitchers gain 61 points (small sample size warning—639 PA). Again, I have no idea why. Maybe fastball pitchers are able to ramp it up in the later innings, or maybe they start throwing more off-speed pitches later in the game. (A PITCHf/x analysis would shed some more light on this issue.) Against the four-pitch pitchers, batters gain 19 points the fourth time around compared to the third. If we weight and combine the third and fourth times in order to increase our sample sizes, we get this:
# Pitches in Repertoire (> 10%) |
N (Pitcher Seasons) |
Overall |
First Time |
Second Time |
Third and Fourth Times |
Second Minus First |
Third+ Minus Second |
1 |
41 |
.359 |
.344 |
.370 |
.364 |
.027 |
-.001 |
2 |
1000 |
.358 |
.343 |
.359 |
.370 |
.016 |
.017 |
3 |
1712 |
.361 |
.349 |
.362 |
.371 |
.013 |
.015 |
4 |
378 |
.351 |
.340 |
.351 |
.361 |
.011 |
.015 |
Again, we see by far the largest second-time penalty for the one-pitch pitchers (27 points—column seven), and a gradually decreasing penalty for two, three, and four-pitch pitchers (16, 13, and 11). Interestingly, they all have around the same penalty the third time and later, other than the one-pitch pitchers, who essentially retain their quality or even get a bit better, although this is driven by their large fourth-time advantage, as you saw in the previous table.
It is not clear that you should take your one-pitch starters out early and leave in those who have multiple pitches in their arsenal. In fact, the opposite may be the case. While the one-pitch pitchers would do well if they faced the order only one time (as would the two-pitch starters, actually), once you allow them to stay in the game for the second go-around, you might as well keep them in there as long as they are not fatigued, at least as compared to the multiple-pitch starters. Starters with more than one pitch appear to get 10-15 points worse each time through the order even though they don't have the large penalty between the first and second time, as the one-pitch pitchers do. Remember, for the last two tables, a pitch is considered part of a starter's repertoire if he throws it at least 10 percent of the time.
I'll now split the pitchers into four groups again based on how many pitches they throw. But this time, the cutoff for a "pitch" will be 15 percent rather than 10 percent. The number of pitchers who throw four pitches at least 15 percent of the time each are too few for the their numbers to be meaningful, so I'll throw them in with the three-pitch pitchers. I'll also combine the third and fourth times through the order again so that we don’t have those nasty small samples in the “fourth time” data.
# Pitches in Repertoire (> 15%) |
N (Pitcher Seasons) |
Overall |
First Time |
Second Time |
Third and Fourth Times |
Second Minus First |
Third+ Minus Second |
1 |
447 |
.358 |
.342 |
.362 |
.364 |
.027 |
-.001 |
2 |
1954 |
.359 |
.346 |
.361 |
.370 |
.016 |
.017 |
3+ |
742 |
.355 |
.347 |
.352 |
.371 |
.013 |
.015 |
As you can see, the three- and four-pitch starters are better overall by three or four points of wOBA (.11 RA9). The first time through the order, however, the one-pitch starters are better by five points or so (.15 RA9). The second time around, the one-pitch pitchers fare the worst, but by the third and fourth times through the order, they are once again the best (by six or seven points, or .22 RA9). It is difficult to say what the optimal use of these starters would look like. At the very least, these numbers should give a manager/team more information in terms of estimating a starter's penalty at various points in the game, based on his pitch repertoire.
I'll try one more thing: two groups. The first group consists of pitchers who throw at least 80 percent of one type of pitch, excluding knuckleballs. These are truly one-pitch pitchers. The pitchers in the second group throw three or more pitches at least 20 percent of the time each. These are truly three-pitch pitchers. Let's see the contrast.
# Pitches in Repertoire |
N (Pitcher Seasons) |
Overall |
First Time |
Second Time |
Third and Fourth Times |
Second Minus First |
Third+ Minus Second |
1 (> 80%) |
47 |
.360 |
.343 |
.367 |
.370 |
.025 |
.009 |
3+ (> 20%) |
104 |
.353 |
.350 |
.357 |
.357 |
.008 |
.009 |
It certainly looks like the 42 one-pitch pitchers (47 is the number of pitcher-seasons) would be much better off as relievers, facing each batter in the lineup only one time. They are not very good overall, and after only one go-around, they are 25 points (.85 RA9) worse than the first time facing the order! The three-pitch pitchers suffer only a small (eight-point) penalty after the first time through the order. Both groups actually suffer the same penalty from the second to the third (and more) time through the order (nine points).
So who are these 42 pitchers who are ill-suited to being starters? Perhaps they are swingmen or emergency starters. Here is the complete list from 2002 to 2012. The numbers after the names are the number of TBF faced as starters and as relievers.
Mike Timlin 20, 352
Kevin Brown 206, 68
Ben Diggins 114, 0
Jarrod Washburn 847, 0
Mike Crudale 9, 199
Grant Balfour 17, 94
Shane Loux 69, 69
Jimmy Anderson 180, 3
Kirk Rueter 620, 0
Jaret Wright 768, 0
Logan Kensing 55, 11
Tanyon Sturtze 57, 277
Chris Young 156, 0
Nate Bump 33, 286
Bartolo Colon 2683, 49
Carlos Silva 876, 10
Aaron Cook 3337, 0
Cal Eldred 12, 141
Rick Bauer 21, 281
Mike Smith 18, 0
Shawn Estes 27, 0
Troy Percival 4, 146
Andrew Miller 306, 0
Luke Hochevar 12, 41
Luke Hudson 13, 0
Dana Eveland 15, 13
Denny Bautista 9, 38
Dennis Sarfate 81, 274
Roberto Hernandez 548, 0
Mike Pelfrey 812, 0
Daniel Cabrera 881, 0
Frankie De La Cruz 15, 37
Mark Mulder 3, 9
Ty Taubenheim 27, 0
Brad Kilby 7, 58
Darren Oliver 17, 264
Justin Masterson 1794, 4
Luis Mendoza 60, 0
Ross Detwiler 627, 51
Cesar Ramos 11, 109
Josh Stinson 17, 21
Ross Detwiler 627, 51
Many of these pitchers barely had a cup of coffee in the majors. Others were emergency starters or swingmen, or changed roles at some point in their careers. Others were simply mediocre or poor starting pitchers, like Kirk Rueter, Jarrod Washburn, Mike Pelfrey, Carlos Silva, and Daniel Cabrera, while others were good or even excellent starters, like Kevin Brown, Mark Mulder, and Bartolo Colon.
I think the lesson is clear. Unless a team has a compelling reason to make a one-pitch pitcher a starter (perhaps he is an extreme sinkerballer, like Brown, Cook, and Masterson), he should probably only relieve. If a team is going to use a swingman for an occasional start, or a reliever for an emergency start, they would do well to use a two or three-pitch pitcher or limit him to one time through the order.
If we remove the swingmen and emergency starters as well as those pitchers who faced fewer than 50 batters in a season, we get this:
# Pitches in Repertoire |
N (Pitcher Seasons) |
Overall |
First Time |
Second Time |
Third and Fourth Times |
Second Minus First |
Third+ Minus Second |
1 (> 80%) |
28 |
.353 |
.336 |
.364 |
.365 |
.028 |
.004 |
3+ (> 20%) |
104 |
.353 |
.350 |
.357 |
.357 |
.008 |
.009 |
Even if we look only at regular starters with one primary pitch other than a knuckleball, we still see a huge penalty after the first time facing the order. In fact, the second-time penalty (compared to the first) is worse than when we include the swingmen and emergency starters. Although these pitchers overall are as good as multiple-pitch starters, they still would have been much better off as short relievers.
Here is that updated list of starters once we remove the ones who rarely start. These guys as a whole should probably have been short relievers.
Cook
Miller
Colon
Diggins
Silva
Young
Cabrera
Wright
Washburn
Anderson
Masterson
Brown
Rueter
Kensing
Mendoza
Pelfrey
Hernandez
Detwiler
You might think that the one-pitch starters in the above list who are good or at least had one or two good seasons might not necessarily be good candidates for short relief. You would be wrong. Those pitchers had huge second-to-first penalties and pitched much better the first time through the order than they did overall. Here is the same chart as before, but including only above-average starters for that season.
# Pitches in Repertoire |
N (Pitcher Seasons) |
Overall |
First Time |
Second Time |
Third and Fourth Times |
Second Minus First |
Third+ Minus Second |
1 (> 80%) |
11 |
.328 |
.307 |
.332 |
.332 |
.039 |
-.013 |
3+ (> 20%) |
35 |
.321 |
.318 |
.323 |
.323 |
.004 |
.003 |
Here is a list of those pitchers from row one above who pitched very well overall, but were lights out the first time facing the lineup (and still very good for the remainder of the game). Remember that these pitchers were above average in the season or seasons that they went into this bucket—they were not necessarily good or great pitchers throughout their careers or even in any other season.
Kevin Brown
Jarrod Washburn
Jaret Wright
Chris Young
Bartolo Colon
Carlos Silva
Justin Masterson
Ross Detwiler
Interestingly, the very good multiple-pitch pitchers (row two above) had very small penalties each time through the order. These are the starters whom teams should not mind going deep into games on a consistent basis. Here is a list of those starters:
Andy Sonnanstine
Brett Myers
Carl Pavano
CC Sabathia
Chad Billingsley
Chris Carpenter
Cole Hamels
Dan Haren
Freddy Garcia
Hisashi Iwakuma
James Shields
Jose Contreras
Josh Beckett
Justin Duchscherer
Kason Gabbard
Kenny Rogers
Mark Buehrle
Matt Clement
Roy Halladay
Ramon Hernandez
Tommy Hunter
Finally, in case you are interested, here are the numbers for all of the one-pitch knuckleballers whom I have been omitting in some of the tables thus far:
Primary Pitch |
N |
First Time |
Second Time |
Third+ Time |
Second Minus First |
Third+ Minus Second |
Knuckleball |
20 |
.321 |
.354 |
.345 |
.034 |
-.006 |
Where are all the knuckle ball relievers? Although we don't have tremendous sample sizes here (3024 second time TBF), it looks like knuckleballers are brilliant the first time through the order. But once a batter has seen a knuckleballer one time, he does pretty well against him thereafter (although we do see a six-point rebound the third and later times through the order).
More research, especially using PITCHf/x data, is probably needed. However, I think that teams can use the information above to make more informed decisions about what roles pitchers should occupy and when to take out a starter during a game.
Note: In the original article, I discussed the “curious case” of the fourth time through the order penalty. Basically, it shows up only in indoor games. The way that I calculated all of the TTOP was not 100 percent correct, although it was probably good enough for government work. What I did, and what other researchers have done, is this: I separately computed the wOBA against for each time through the order independently and adjusted for the quality (in wOBA for that season) of the batter and pitcher pools in each TTO group. That is not the best way to do it, although it usually yields results that are just fine. The proper way is to compute the TTOP penalties for each pitcher and then compute the weighted average for each segment (second minus first, third minus second, and fourth or later minus third). Using this method, it is no longer necessary to adjust for the pitcher pools. Again, both ways should yield almost the same results, but not always.
In this case, that solved the mystery of the “fourth time penalty.” It no longer vanishes for all games combined when I calculate the TTOP using the rigorous “delta method.” Here is the first chart in the original article:
TTO |
Pitcher quality |
Batter quality |
Adj. wOBA Observed |
“Penalty” |
1 |
.346 |
.340 |
.340 |
— |
2 |
.345 |
.340 |
.350 |
.010 |
3 |
.343 |
.343 |
.359 |
.009 |
4+ |
.339 |
.346 |
.359 |
.000 |
Now, here is the same chart, from the same database, but using the “delta method.” Note the difference in the last column.
TTO |
Pitcher quality |
Batter quality |
Adj. wOBA Observed |
“Penalty” |
1 |
.346 |
.340 |
.340 |
— |
2 |
.345 |
.340 |
.350 |
.012 |
3 |
.343 |
.343 |
.359 |
.013 |
4+ |
.339 |
.346 |
.359 |
.011 |
Despite the fact that it is colder in the late innings of night games, we see a solid 11-point penalty from the third to the fourth times through the order. We also see slightly larger penalties for the second and third times. Although it is not evident from the above chart, using the “delta method” for computing the penalties (that’s the method I used throughout this article), the second-time result is one point higher than the pitchers’ overall results based on their per-season stats—for all starters in the database combined.
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A better approach, in my opinion, is to accept the data and message, and try to understand better what they're telling us. There seems to be a simple explanation available: guys only make it to the fourth time through the order if they're pitching well, or at least successfully, in which case the wOBA for the whole game is going to be suppressed compared to the overall average wOBA they allow. Here's an easy test for that one: if you look only at games where pitchers did reach the fourth time through the lineup, how does wOBA vary as a function of times through? There were comments on the previous article that hinted at the importance of this question as well, but no followup. That in turn leads to the more interesting question: is a pitcher more likely to make it to the fourth time through if he throws multiple types of pitch?
Lots of fertile ground for exploration here, and thanks for doing all this, but simply brushing off the fourth-time-through anomaly via data manipulation is weak.
I am not sure of what you mean by this:
"There seems to be a simple explanation available: guys only make it to the fourth time through the order if they're pitching well, or at least successfully, in which case the wOBA for the whole game is going to be suppressed compared to the overall average wOBA."
You appear to be suggesting some kind of a selection bias, but I don't think there is one. You are correct that when a pitcher is allowed to face the order for the 4th time, he likely (and on the average) has pitched a very good game, but that will not affect anything unless:
1) He is pitching well because he is "on" that day and the "onness" tends to carry over into that fourth time performance. That "carry over effect" has been mostly debunked by research by me and others. So that should NOT be much of a factor.
2) If he is pitching well and thus allowed to face the lineup for the fourth time, and the "pitching well" is at least partly due to the umpire, weather, and park, then, yes, the 4th time wOBA is likely to be depressed a little and I am not controlling for that.
Remember that I have already shown that for all pitchers combined, the 4th time penalty is 10 points. See the last part of the article. So there does NOT appear to be any selection bias. Then I found that some types of pitchers, mostly the one-pitch pitchers, not only don't see a penalty the fourth time through the order, but they pitch even better. You are claiming that there is a "simple explanation " for that. Not only do I not understand what you are saying, but if there is an explanation for that involving some kind of selection bias, why do we find a solid 10 point penalty for all starters?
Let's start with this:
"You don't find a "solid 10 point penalty for all starters," unless you hand-wave it away; that's the whole point."
Yes, if you read the last part of the article which was an addendum to the original article, when I use the delta method to determine TTO penalties for all starters from 2002 to 2012, the fourth time minus the third time difference was 10 points in wOBA. The delta method is the correct way to determine average penalties. It is basically the average of all starters' penalties, weighted by the number of batters they face the fourth time through the order. So, if starter A had a wOBA of .350 the fourth time and .340 the third time, he had a 10 point difference. If he faced 100 batters the fourth time, that would be the "weight" for that pitcher when calculating the average of all pitchers. If pitcher B had only a 5 point difference and his fourth time TBF were 10 batters, then the weighted average of "all" pitchers would be ((10 times 100) + (5 times 10)) / (100+10), or 9.55. That would the weighted average of all starters' (in this case, two starters) fourth minus third penalty.
That is what I did for all starters. That should have been part of the original article. It has nothing to do with the second article. OK, we got that out of the way.
In this article, I broke down starters into several different groups. In the first go-around, I had 3 groups, mostly fastballs, not many fastballs, and all the rest. I found that the mostly fastball group had a 13 point ADVANTAGE (not a penalty) the fourth (and later) time through the order. The other two groups had the usual 10-13 point penalty.
I noted that and said:
"Interestingly, the â€œfastballâ€ group reverts back to better-than-normal levels the fourth time (I don't know why that is, but I'll return to that issue later), but the latter group continues to suffer a penalty as do all the others."
I did come back to that later, and speculated on why that might be the case - why the predominantly "one-pitch" starters actually did a lot better the fourth time through the order than the third time and even second time (but not the first). I said this:
"Against one-pitch pitchers, pitchers gain 61 points (small sample size warningâ€”639 PA). Again, I have no idea why. Maybe fastball pitchers are able to ramp it up in the later innings, or maybe they start throwing more off-speed pitches later in the game. (A PITCHf/x analysis would shed some more light on this issue.)"
I then took the same chart and combined the third and fourth times (and later) data. I didn't "hide" the fourth time data. That was presented in the chart before that. They were exactly the same charts, but one had first time, second, time, third time, and fourth time (and later). The other had first, second, and third (and later).
I noted that the fourth time data for some of my groups was a relatively small sample so it might suffer from sample error as opposed to the first, second, and third time data which was much larger and much less prone to sample error.
I certainly do not know how much of the fourth time "reverse penalty" with some of these groups is noise and how much is something about their repertoires that truly enables them to get "better" deep in the game. But I briefly addressed that and offered some speculation as to why that might be the case.
I don't know what else you want me to say or do or NOT say or do.
OK, that is out of the way.
You wrote:
"There seems to be a simple explanation available: guys only make it to the fourth time through the order if they're pitching well, or at least successfully, in which case the wOBA for the whole game is going to be suppressed compared to the overall average wOBA they allow."
I don't know what you mean by that. You will have to explain it again in different terms and be more specific. A "simple explanation" for what?
As I said, it is very true that in games where there is a fourth time through the order, the pitchers would have pitched well and gotten lucky the first three times through the order, but that should not effect the data they way I calculated the "penalties." There is going to be a very slight survivorship bias which I hadn't thought of until now, and I am going to address that in a further comment as soon as I look at the data and figure out how much of a bias there is. That bias should slightly over-state the penalties for all times through the order, but mostly the fourth time penalty. It should be slight though. The reason for the bias is this: All pitchers in a season who got to the fourth time (or had lots of TBF the fourth time) were slightly lucky in that entire season and the ones who did not (or had few TBF against that fourth time) were slightly unlucky.
"Here's an easy test for that one: if you look only at games where pitchers did reach the fourth time through the lineup, how does wOBA vary as a function of times through?"
You will certainly find that the first through third times will be a low wOBA and the fourth time will show a very strong penalty, since the pitchers who were allowed to pitch to the order the fourth time were "selected" to a large degree on the basis of how they pitched prior to that. But - here is the important thing - I did not calculate the penalties like that! For example, I did not calculate the fourth time penalty using only those games where the pitcher made in to the fourth time! Of course I didn't. If I did that, there would be a huge selection bias and it would look like there was a huge fourth time penalty, as I explained above. I used all games for a pitcher.
For example, let's say that a pitcher had 300 first time TBF, 300 second time, 250 third time, and 50 fourth time.
And let's say that the wOBA against was .340, .350, .360, and .370. My fourth time penalty for that starter would simply be .370 - .360, or 10 points. Then, when computing the average for all starters, I would weight that 10 points by 50, as I explained above. So, in computing the "fourth time minus the third time" penalty, I am using all games in which the pitcher faced the order for the third time, not just games where he faced the order for the fourth time. If I did that, the third time wOBA would probably be something like .330 and not .360 (since the manager is letting him continue late in the game). In that case it would look like the penalty was 40 points rather than 10 points. I hope that is clear.
"There were comments on the previous article that hinted at the importance of this question as well, but no followup."
What question? If there was a question or questions that I did not answer or address, I apologize. I do the best I can with my time. I don't even get paid to write these articles. In fact, I have written hundreds of articles, a book, and spent thousands of hours contributing to the sabermetric body of knowledge. I do it because I enjoy it and it is a passion of mine. I make zero money from it.
"That in turn leads to the more interesting question: is a pitcher more likely to make it to the fourth time through if he throws multiple types of pitch?"
I don't know, but I can find out in about 5 minutes. I suspect that the answer is maybe, but either way, yes, or no, it is not by much.
If you paid attention to my article, you will see that the ONE-PITCH pitchers are the ones who should be continuing the fourth time, if anything, since they are the ones who get BETTER the fourth time. The multiple-pitch pitchers continue to have a penalty the fourth time. Look at the first chart. Those are the ones who should be taken out after the second or third times. However, again, for some of the groups that I studied, the number of pitcher seasons is relatively small, and this the number of TBF the fourth time is small for the entire group. Because of the possibility of noise/sample error, we simply can't trust those numbers very much. Even for a sample of 8,000 batters faced (e.g., Group I in the first chart), one standard deviation of wOBA is around 5 points.
And I am not sure why you are searching for reasons why there is NO fourth time penalty. As you can see from the last chart in the article, there is an 11 point fourth time penalty, almost exactly the same as the second and third.
BTW, as someone pointed out on The Book blog, the second time through the order is only a "penalty" relative to the first time. As I have mentioned and you can see in some of the charts, the second time around is about equal to a pitcher's (and batter's) overall performance for the season. So the second time is not really a "penalty" it is just that the first time is an advantage for the pitcher. But, that is really a glass half full or half empty semantic thing...
I find your work reasonable, but I also wonder what may be missing. There may be some confirmation bias? I don't mean to criticize without purpose...I'd love to join in the effort when time permits I have much longer thoughts on this, but i don't think this the space for it.
Now, how much of an individual pitcher's (or sub-group of pitchers, like, say, sinker-ballers) TTOP patterns is random chance and how much is due to something about the pitcher himself is another story. I addressed that to some extent in the first article. Basically, most of the variation we see in a pitcher's own patterns as opposed to whatever group he belongs to, is due to chance as far as we can tell. That is because, again, of the small sample sizes we are dealing with. Even in 4 or 5 seasons, a starter only has maybe 100 TBF in each of the first 3 "times through the order" segment.
The 80% cutoff is pretty strict, though, and I worry about SSS. More categories (80%, 70%-79.9%) would be interesting to see, whether the effect is somewhat continuous.
The big thing seems to be: watch out for Tony Cingrani next year!
That is one reason why I also often use multiple groupings. The problem with using too many groupings is that it is possible to keep changing the cutoffs until you finally get the effect you are looking for or not looking for! And that could have occurred by chance (Type I error).
Just look at the very first row of the first table. We see 341, 363, 376, 348 listed as the wOBA for the first through fourth times through the order, respectively. Yet when looking further right at the Second Minus First and so on columns, none of them match what simple subtraction dictates they should be.
Is this a function of the "subtraction" columns being weighted by plate appearances? If so, that should be made a lot clearer. If it's another reason, though, I'd be glad to hear what that is.
I hope this message off an old article reaches you somehow. I've read The Book and enjoyed most of it, but I have a general question, which touches on the third pitch and many other conclusions in your study and so many other recent studies by others: would these conclusions turned into baseball truisms hold true in an un-juiced era?
I'm well aware that third-time theory rings true for 90 percent of the starting pitchers of the era you analyzed, but has anyone done a study of pitchers from 1950s through 1989?
As someone who played the game at a modest level, I understand what seeing more pitches from a pitcher can do for a hitter. I think some of my work with Dr. Bill Harrison also helps me understand how the eye & brain can be a much greater key to success than the intricacies of an MLB swing.
Still, I wonder how much the 3rd PA theory has to do with the training and mindset of modern pitchers. If you listen to John Smoltz or just watch a lot of baseball with an open mind, you realize that starting pitchers today are behaving much more like relievers than the starting pitchers from 1950-2000. They tend to throw every pitch as hard as they can, and when they get in trouble, their first instinct is to try to throw harder.
When throwing this way, any pitcher (other than the freakishly gifted, who also have the savvy to know they can pitch effectively mixing 90 percent effort with a sprinkle of 100 percent effort pitches) will wear down after facing 15-20 batters.
I don't know where the chicken or egg that created this current environment that has made baseball resemble schoolyard strikeout (with the 3 true outcomes) started, but I don't think pitching is best managed this way, especially when you throw the health of the pitcher into the equation (I believe there are severe arm injuries far more often in the 21st century).
Can anyone point to statistical analysis that supports the third time through the lineup from 20th century play?
Does anyone have other theories on why this theory might be true now, but not so then (use of video and advanced scouting reports? more quality arms in the bullpen? shorter attention spans?)?
I'd love to have an analysis on deadball era baseball on things like bunts, intentional walks, pitching around hitters and stealing bases to know how some strategies are effective at the levels I coach (ages 13-18) where home runs might happen as often once every 50-100 PA rather than current every 25-50 PA.
Thank you,
Ryan