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November 15, 2013 Baseball ProGUESTusPitch Types and the Times Through the Order PenaltyMost of our writers didn't enter the world sporting an @baseballprospectus.com address; with a few exceptions, they started out somewhere else. In an effort to up your reading pleasure while tipping our caps to some of the most illuminating work being done elsewhere on the internet, we'll be yielding the stage once a week to the best and brightest baseball writers, researchers, and thinkers from outside of the BP umbrella. If you'd like to nominate a guest contributor (including yourself), please drop us a line.
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 offspeed 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 20022012, and includes Baseball Info Solutions’ pitchtype information from FanGraphs. The results are illuminating.
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 allinone 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 betterthannormal 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 lowfrequency fastball group has only a sixpoint (.20 RA9) advantage. Keep in mind that some of that firsttimethroughtheorder 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.
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. Onepitch pitchers lose 36 points by the third time through the order, while fourpitch pitchers lose only 24 points. The fourth time through the order is exactly the opposite. Against onepitch 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 offspeed pitches later in the game. (A PITCHf/x analysis would shed some more light on this issue.) Against the fourpitch 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:
Again, we see by far the largest secondtime penalty for the onepitch pitchers (27 points—column seven), and a gradually decreasing penalty for two, three, and fourpitch pitchers (16, 13, and 11). Interestingly, they all have around the same penalty the third time and later, other than the onepitch pitchers, who essentially retain their quality or even get a bit better, although this is driven by their large fourthtime advantage, as you saw in the previous table. It is not clear that you should take your onepitch starters out early and leave in those who have multiple pitches in their arsenal. In fact, the opposite may be the case. While the onepitch pitchers would do well if they faced the order only one time (as would the twopitch starters, actually), once you allow them to stay in the game for the second goaround, you might as well keep them in there as long as they are not fatigued, at least as compared to the multiplepitch starters. Starters with more than one pitch appear to get 1015 points worse each time through the order even though they don't have the large penalty between the first and second time, as the onepitch 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 threepitch 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.
As you can see, the three and fourpitch starters are better overall by three or four points of wOBA (.11 RA9). The first time through the order, however, the onepitch starters are better by five points or so (.15 RA9). The second time around, the onepitch 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 onepitch pitchers. The pitchers in the second group throw three or more pitches at least 20 percent of the time each. These are truly threepitch pitchers. Let's see the contrast.
It certainly looks like the 42 onepitch pitchers (47 is the number of pitcherseasons) 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 goaround, they are 25 points (.85 RA9) worse than the first time facing the order! The threepitch pitchers suffer only a small (eightpoint) 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 illsuited 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 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 onepitch 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 threepitch 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:
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 secondtime penalty (compared to the first) is worse than when we include the swingmen and emergency starters. Although these pitchers overall are as good as multiplepitch 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 You might think that the onepitch 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 secondtofirst 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 aboveaverage starters for that season.
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 Interestingly, the very good multiplepitch 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 Finally, in case you are interested, here are the numbers for all of the onepitch knuckleballers whom I have been omitting in some of the tables thus far:
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 sixpoint 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:
Now, here is the same chart, from the same database, but using the “delta method.” Note the difference in the last column.
Despite the fact that it is colder in the late innings of night games, we see a solid 11point 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 secondtime result is one point higher than the pitchers’ overall results based on their perseason stats—for all starters in the database combined. 17 comments have been left for this article. (Click to hide comments) BP Comment Quick Links mdangelfan (60465) Torii Hunter?? I'm guessing you were trying to link to Tommy. Nov 15, 2013 06:37 AM newsense (5112) One possible explanation for a lesser penalty for fourth time through for onepitch pitchers may be an advantage from loss of velocity. The trick in hitting them is likely timing (rather than, say, picking up rotation) and a loss in velocity from fatigue on the fourth time through may throw that off. Nov 15, 2013 08:21 AM MGL (2121) That is possible but it seems farfetched to me. If that were the case, we would see pitchers purposely throwing less hard as the game goes on, and being more successful in doing so. I don't think we see that. Nov 15, 2013 11:46 AM therealn0d (51857) Have you considered that by the fourth time through the lineup it is maybe no longer the same lineup? Pinch hitters, defensive replacements...those guys are first timers. Not to mention the nature of the score and the pitch count. Is the starter still in there because his pitch count is low and the game is easily in hand and he's being given the opportunity to get the CG/PG/NoNo? Have the hitters just given up more or less because it's a blowout and their best team is no longer playing (garbage time)? Nov 16, 2013 10:09 AM MGL (2121) I only include batters who were in the lineup when the game started (I also don't include 9th innings or later  those are usually the blowouts with starters still in the game). Nov 16, 2013 11:04 AM therealn0d (51857) well, that was my first reply to this thread, so I'm not certain it's fair for you to wonder why I'm searching for reasons against your results. Maybe you aren't directly adressing "me." Nov 16, 2013 13:22 PM newsense (5112) MGL, can you verify that pitchers such as Kevin Brown and Bartolo Colon actually have shown a times through the order penalty rather than assuming that the group average applies to them? Nov 15, 2013 08:25 AM MGL (2121) Lots of pitchers in each group will show all kinds of different TTOP patterns, just by chance alone. It would be almost impossible for all of the pitchers in the onepitch group to all have the same types of penalties. We are dealing with relatively small samples for each pitcher. In a small sample anything can happen. So Brown and Colon may or may not show the same types of penalty patterns that the group as a whole shows. They likely do, which is the case for any individual pitcher or pitchers in the group, but they easily could not. Nov 15, 2013 11:32 AM Kinanik (37604) This is really cool, thanks. Nov 15, 2013 13:15 PM MGL (2121) Sure, the 80%, 10%, 15% cutoffs are pretty arbitrary. I usually try to find a balance between creating "opposing" (like onepitch pitchers compared to multiplepitch pitchers) categories that are meaningful yet contain large samples of data. I can't always do that of course. Nov 15, 2013 17:11 PM drawbb (3190) What I don't understand about the article is why virtually none of the "Second Minus First" and "Third Minus Second" columns actually match the numbers listed in their antecedent columns. Dec 16, 2013 09:50 AM Not a subscriber? Sign up today!

"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." It is tempting to read this as "I don't like what the data are telling me, so I'll manipulate the data until the message becomes more palatable." While I appreciate the effort you've made here, this bothers me.
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 fourthtimethrough anomaly via data manipulation is weak.
First of all, I don't think I'm "brushing it off." I briefly discussed possible reasons for the fourth time "rebounds" that some groups of pitchers seem to have. I also suggested that an analysis of PITCHf/x data could shed some more light on it.
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 onepitch 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?
You don't find a "solid 10 point penalty for all starters," unless you handwave it away; that's the whole point. For the power pitchers (or at least the ones who throw predominantly fastballs, who I presume are power pitchers by and large), it's the other way around, as your first table irrefutably shows. Making that table vanish, rather than trying to understand its message, is what I object to.
I am afraid we are talking past one another, so we might want to start all over again.
Let's start with this:
"You don't find a "solid 10 point penalty for all starters," unless you handwave 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 goaround, 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 1013 point penalty.
I noted that and said:
"Interestingly, the “fastball” group reverts back to betterthannormal 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 "onepitch" 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 onepitch 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 offspeed 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 overstate 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 ONEPITCH 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 multiplepitch 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.