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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.