Archive for Pitching

More Evidence for the Three-Man Rotation

Effects of varying recovery periods on muscle enzymes, soreness, and performance in baseball pitchers, by Potteiger, Blessing, and Wilson, Journal of Athletic Training, 1992; 27(1): 27–31.

From the Abstract

Results indicate that muscle damage, as evidenced by CK release, occurs in response to baseball pitching. However CK values, muscle soreness, and pitch velocity are not significantly affected by changes in the amount of recovery time typically scheduled between games.

The authors look at a sample of pitchers and how they recover after pitching different lengths of time. The results show a few things. First, the pattern of recovery indicates most healing occurs soon after pitching, and that further recovery occurs at a diminishing rate. After three days of rest, the measures of skeletal muscle damage were back to baseline values. Second, performance on two days of rest is only slightly worse than, and not statistically distinguishable from, performance on four days of rest. This is good news for the Phillies and Roy Oswalt. The results are also consistent with my analysis (with Sean Forman) of major-league pitchers.

You can get the gist of the results from the graphs in the pages below. The study is short, interesting, and it’s not even new. There a lot of studies in the fields of sports medicine, exercise physiology, and sports science that look at popular sabermetric questions. If you have a sabermetric question, it won’t hurt to do a PubMed search on the topic.

In Defense of the Three-Man Rotation

I used to be a fan of the four-man rotation in the post-season, but I have changed my mind. One of the key events that altered my opinion was last year when Joe Girardi successfully rode the three-man playoff rotation of C.C. Sabathia, A.J. Burnett, and Andy Pettitte all the way to a World Series title. At the time, I was skeptical that this was the right move, but I was impressed at how well it worked, which is why I am surprised that the Yankees are going with a four-man rotation in the ALCS.

Sometimes bad decisions turn out just fine, so I wasn’t completely convinced that the Yankees did the right thing in 2009. I was soon persuaded that the three-man rotation was the way to go in the post-season after a conducting a study with Sean Forman on the impact of pitches thrown and rest days on performance. In our analysis of games from 1988 — 2009, estimates showed that days of rest had very little impact on performance. On average, every rest day lowered a pitcher’s ERA by about 0.015; however, the estimate was not statistically different from there being no effect. It seems that most of the recovery benefits that pitchers receive occur in the three days of rest between starts. And though we found the impact of pitches thrown was small, one day of rest was worth throwing about two fewer pitches less than average in the previous game. If you want to get improved performance from managing pitcher workloads, fewer pitches is better than more rest. And the broader lesson is that small deviations in pitches thrown and rest days don’t seem to have much effect.

In the case of Sabathia and Hughes, they should be good to go in Games 4 and 5. In Game 1, Sabathia threw 93 pitches, for the season he averaged 105 pitches per start. Twelve pitches fewer than average translates to an improved ERA by 0.08 runs. And in his previous five and ten starts (where we found stronger effects than the previous game) his average pitches thrown was right on his season average.

In Game 2, Hughes threw 88 pitches, for the season he averaged 102 pitches per start. Like Sabathia, he pitched about the same number of pitches in his last five and ten starts, which included two one-inning relief stints on regular starters rest. According to our estimates, the reduction in pitches thrown lowers his expected ERA by approximately 0.10.

While I don’t expect Sabathia or Hughes necessarily to benefit from having a lighter load in Game 1, I believe each pitcher should pitch about like he has all season if they were to go on short rest. Now maybe the strain of the post-season and the quality of opponent puts a little extra strain on each pitch, but the loads these pitchers are bearing hasn’t been exceptionally high.

Of course, there may be factors affecting the Yankees decision that aren’t public, but if things don’t go well for the Yankees tonight, I won’t be surprised to see Girardi hand the ball to Sabathia in Game 4. Even if the Yankees do win, I think Girardi would be wise to move Sabathia up. The Yankee rotation has struggled as a whole lately, but I don’t think more rest offers much help. I think a tired trio of Sabathia, Hughes, and Pettitte is preferable to allowing Burnett to make a start.

Why Are Modern Pitchers So Fragile?

Another request.

Why are modern pitchers so fragile? They pitch fewer innings per game, start fewer games, and have more days rest between starts. In addition they have much better training and medicine to cope with the stresses of pitching.
I have heard it repeated that there will no longer be 300 game winning pitchers. What happened to the Nolan Ryans and the Bob Gibsons?

Unfortunately, I don’t have very good data to examine exactly how total pitches thrown have changed going too far back in time. But, given the pattern going back to the late-1980s, I think it’s safe to assume that the extreme loads of pitchers are declining, even though the average pitching load has remained constant at about 99 pitches per game.
Maximum pitches thrown per game

Using some simpler measure of workloads, innings pitched, the pattern is interesting. The figure below shows the change in total innings pitched in a season over time for the maximum number of innings pitched, and by 95th and 75th percentiles, and the median (minimum 10 games started).


Though there has been a general decline in pitcher workloads over time, there was a bump in the late-1960s and early-1970s, when pitching loads increased over what they where in the 1960s. Since 1962, when the leagues both started playing 162 games a season, there have been 65 pitcher-seasons with 300 or more innings pitched. The last one occurred in 1980 when Steve Carlton threw 304 innings. Below are a table of the number of 300-inning performances by seasons and a list of those performances by pitchers.

Year	Count
1962	1
1963	3
1964	1
1965	2
1966	4
1967	1
1968	4
1969	9
1970	4
1971	4
1972	4
1973	7
1974	8
1975	4
1976	2
1977	4
1978	1
1979	1
1980	1
Total	65
Pitcher		Year	IP
Vida Blue	1971	312
Bert Blyleven	1973	325
Jim Bunning	1967	302.33
Jim Bunning	1966	314
Steve Carlton	1980	304
Steve Carlton	1972	346.33
Jim Colborn	1973	314.33
Larry Dierker	1969	305.33
Don Drysdale	1965	308.33
Don Drysdale	1962	314.33
Don Drysdale	1963	315.33
Don Drysdale	1964	321.33
Bob Gibson	1968	304.67
Bob Gibson	1969	314
Dave Goltz	1977	303
Bill Hands	1969	300
Catfish Hunter	1974	318.33
Catfish Hunter	1975	328
Fergie Jenkins	1968	308
Fergie Jenkins	1969	311.33
Fergie Jenkins	1970	313
Fergie Jenkins	1971	325
Fergie Jenkins	1974	328.33
Randy Jones	1976	315.33
Jim Kaat	1975	303.67
Jim Kaat	1966	304.67
Sandy Koufax	1963	311
Sandy Koufax	1966	323
Sandy Koufax	1965	335.67
Mickey Lolich	1974	308
Mickey Lolich	1973	308.67
Mickey Lolich	1972	327.33
Mickey Lolich	1971	376
Juan Marichal	1966	307.33
Juan Marichal	1963	321.33
Juan Marichal	1968	326
Sam McDowell	1970	305
Denny McLain	1969	325
Denny McLain	1968	336
Andy Messersmith1975	321.67
Phil Niekro	1974	302.33
Phil Niekro	1977	330.33
Phil Niekro	1978	334.33
Phil Niekro	1979	342
Claude Osteen	1969	321
Jim Palmer	1970	305
Jim Palmer	1976	315
Jim Palmer	1977	319
Jim Palmer	1975	323
Gaylord Perry	1974	322.33
Gaylord Perry	1969	325.33
Gaylord Perry	1970	328.67
Gaylord Perry	1972	342.67
Gaylord Perry	1973	344
Steve Rogers	1977	301.67
Nolan Ryan	1973	326
Nolan Ryan	1974	332.67
Bill Singer	1969	315.67
Bill Singer	1973	315.67
Mel Stottlemyre	303	1969
Luis Tiant	311.33	1974
Wilbur Wood	320.33	1974
Wilbur Wood	334	1971
Wilbur Wood	359.33	1973
Wilbur Wood	376.67	1972

Thus, it seems that teams tried to ramp up pitcher workloads just prior to the modern decline. What happened in the 1960s and 1970s that caused an increase in pitcher workloads? Did teams realize the ramp-up was a mistake, which caused the trend to reverse? This was an era of low offense, and the mound was lowered and the designated hitter added as a response. Was there a shift in pitching philosophy or did something structural cause this shift? I’m open to suggestions. The bump may offer a clue.

Aside from the bump, what has caused the declining trend in workloads? Most obviously, the rise of the five-man rotation gave pitchers fewer games to cover. On top of this, teams began to rely more on relievers within games pitched than in the past, going with fresh pitchers in late innings rather than asking starters to pace themselves. The number of complete games has declined continuously since the late-1970s.

I think the decline in pitching loads is less a response to a toughness of pitchers than it is a change in pitching philosophy. Every year, someone is supposedly going to go to have four-man rotation, but then we never hear any more about it. Whether that is because no manager has the guts to stick to a plan that is easy to criticize when injuries that were bound to happen anyway happen, or because the five-man rotation actually leads to better pitching, I don’t know. I have found that days of rest appear to have little impact on performance, so I don’t believe there is any performance benefit from giving pitchers more rest days in a five-man rotation. I’d love to see a team go with a four-man rotation from start to finish.

As for the increased use of relievers, I believe managers have discovered that 100% mediocre arms can be more effective than paced good arms. Teams can increase their chances of winning by going to the bullpen, exploiting match-ups, and pinch-hitting for pitchers. Furthermore, I’ve found some evidence that fewer pitches per game can improve future performance among starters.

In summary, my best guess is that the decline in pitching loads is part fad (four-man rotations) and part innovation (relievers can be better than paced starters).

UPDATE: In my initial cut and paste of the 300-inning pitchers I accidentally left off six seasons at the bottom of the table. I have added the missing seasons.

What Edwin Jackson’s Pitch Count Hath Wrought

Edwin Jackson threw a bit of a lame no-hitter on Friday. I’m sorry if it offends you when I call such a hallowed feat lame, but eight walks in a game for a major-league pitcher is bad (see Pulling a Homer). But aside from this, one aspect of his performance has gotten a lot of attention: 149 pitches thrown. This is the highest pitch count allowed in a game since 2005 (see my previous post on how pitch counts have changed over the past two decades).

I have been conducting a study of pitch counts with Sean Forman, and we will be presenting our findings at the upcoming SABR convention in Atlanta. But since it’s applicable to Jackson’s situation, I’ll reveal some of the findings. Our study uses past pitching performances to estimate the impact of pitch counts on future performance, controlling for numerous factors, using fractional polynomial regression analysis to capture potential non-linear relationships. The results indicate that the impact of the pitch count in a single game on the following game is real but small; and, the impact is linear, not increasing as some analysts have theorized.

On average, every pitch thrown raises a pitcher’s ERA by 0.007 in the following game. Jackson’s ERA was 5.05 going into Friday’s game averaging 104 pitches per game; thus, based on the historical response of pitchers to pitch counts Jackson’s expected performance in his next start is about 5.37. So, Jackson can be expected to pitch worse, but not that much worse. Really, it’s not that big of a deal as a one-time event. Should Jackson continue to average around 150 pitches a game, the impact will grow, but I doubt that is going to happen. As for the impact on injuries, we didn’t look into it in this study. However, I have previously found little correlation between pitching loads and injury.

My take: if you have a pitcher going for a no-hitter—not matter how bad he’s pitching—the benefit of the excitement and media coverage of letting a pitcher throw more pitches is probably worth the cost. Let’s stop freaking out about pitch counts until we understand their influence a little better.

Update: In response to Jackson’s high pitch count, the Diamondbacks will push back his next start a day or two. How much will this help him recover? No much. On average, each day of rest lowers a pitcher’s ERA by approximately 0.015. Thus, his expected ERA drops from 5.37 to 5.34 (with two days of extra rest). Why rest days matter so little is an interesting question. A few years ago, I saw an presentation on muscle recovery from exercise, and one of the interesting findings was that most of the healing happens within the first few days. Whether this explains the finding or not, I don’t know.

How Have Pitch Counts Changed in the Past 20 Years?

Last week I asked the following question:

From 1988 to 2009, by how many pitches did the median number of pitches thrown in a game by starters change?

The answer: the median number of pitches declined by one, falling from 100 to 99. As the box plot below shows, the median has remained close to constant over the past two decades. The line in the middle of each box marks the median, the edges of the box mark the 25th–75th percentile range, and the whiskers mark the 5th–95th percentile range. If you are wondering how the mean changed, it declined from 97.4 to 96.5.

Median Pitches Thrown

Does this means that despite all the lip service paid to pitch limits teams aren’t paying any more attention to pitch counts than they used to? Not at all. The average may have stayed the same, but the extremes have fallen on the high and low sides. Pitchers aren’t just throwing fewer long outings, they are also pitching fewer short outings. The diagram below graphs the maximum pitches thrown in a game by year, and it shows a significant drop.

Max Pitch Count

So, congratulations to Dan for correctly guessing the decline. Dan wins a copy of Stumbling on Wins by David Berri and Martin Schmidt.

More Testing of the Verducci Effect

After doing my analysis of the Verducci Effect yesterday, I became aware of Jeremy Greenhouse’s analysis on the subject. He uses a different method, but also finds little support for the Verducci Effect. His analysis pointed me to Josh Hermsmeyer’s Free Player Injury Database, which is valuable new resource. The database contains injury information dating back to the 2002 season. Because the Verducci Effect is largely about predicting injuries I wanted to see how player workloads predicted time on the Disabled List (DL). If significantly increasing pitcher workloads raises the incidence of future injuries, then pitchers who meet Verducci’s criteria should be more likely to get injured.

The table below lists the estimates for the impact of the Verducci Effect on DL stints. I estimated several models (including continuous estimates of pitcher workload), but I report only four specifications below because the results are consistent with the unreported estimates. I looked at the number of days on the DL (continuous) and whether or not a player ended up on the DL (discrete) using random-effects estimation models, least-squares for the former and logit for the latter. I also included the number of days on the DL in the preceding seasons in two specifications to control for the natural injury propensity of players.

		DL Days		DL Days		On DL		On DL
Verducci	4.27		-1.89		0.28		0.06
		[0.76]		[0.59]		[0.66]		[0.12]
Mean IP		-0.19		-0.16		-0.006		-0.003
		[9.33]**	[12.75]**	[4.69]**	[2.01]*
DL Days (t-1)			0.64		0.10
				[54.16]**	[14.06]**
Constant	37.67		29.48		-0.50		-1.68
		[14.77]**	[18.60]**	[3.23]**	[8.69]**
Observations	1428		1428		1428		1428
Overall R2	0.04		0.63		--		--
Absolute value of z statistics in brackets				
* significant at 5%; ** significant at 1%

Again, the results do not support the existence of the Verducci Effect. The estimates are small and not statistically significant. A change in workload by more than 30 innings for pitchers under 26 is not associated with more days on or trips to the DL. I would like to reiterate that there needs to be further testing of Verducci Effect, but so far there doesn’t appear to be much empirical support for the hypothesis.

Testing the Verducci Effect

For some reason, the Verducci Effect seems to be getting a lot of attention right now. I recall it being mentioned in the past, but I haven’t paid much attention to it. The effect is named for Sports Illustrated writer Tom Verducci, who came up with the concept but didn’t pick the name. Verducci uses a set of criteria to identify pitchers who are at risk for injury due to a significant increase in workload. He describes the criteria for selection and rationale in an article published this week.

More than a decade ago, with the help of then-Oakland pitching coach Rick Peterson, I began tracking one element of overuse which seemed entirely avoidable: working young pitchers too much too soon. Pitchers not yet fully conditioned and physically matured were at risk if clubs asked them to pitch far more innings than they did the previous season — like asking a 10K runner to crank out a marathon. The task wasn’t impossible, but the after-effects were debilitating. I defined an at-risk pitcher as any 25-and-under pitcher who increased his innings log by more than 30 in a year in which he pitched in the big leagues. Each year the breakdown rate of such red-flagged pitchers — either by injury or drop in performance — was staggering.

I figured now would be as good a time as any to put off the other important things I should be doing in order to find out if the Verducci Effect is real. I used a sample of major-league pitchers from 1998–2007 to estimate the impact of ratcheting up pitching loads on performance on innings pitched and era, using both their recent major-league and minor-league workloads to predict performance. In some specifications I included the average between the present and past seasons’ performances (Mean IP or mean ERA) to peg a typical performance level for each pitcher. The Verducci Effect was considered to be in force if a pitcher was under 26 had increased his workload by more than 30 innings in the previous year. I also measured the Verducci Effect continuously using the actual number of innings pitched increased before the preceding season. I only looked at performance in the majors, but minor-league workload totals counted toward the Verducci Effect. I estimated the impact using a random-effects estimation technique that controlled for detected serial correlation. The regression estimates are below, but if you’re not familiar with reading such tables you can skip over them and read my write-up that follows.

	 		IP Change	 IP Change	IP Change	 IP Change
Verducci		19.07		22.17		
			[3.18]**	[3.73]**		
IP Change * Under 26					0.23		0.21
							[3.37]**	[3.15]**
IP Change						-0.25		-0.17
							[10.41]**	[7.22]**
Under 26						14.89	17.04
							[4.46]**	[5.29]**
Mean IP			0.06				0.13	
			[3.96]**			[6.98]**	
Constant		-12.23		-4.83		-21.97		-6.61
			[5.78]**	[4.90]**	[8.83]**	[5.98]**
Observations		2383		2383		2316		2316
Overall R2		0.0122		0.0058		0.0379		0.0257
Absolute value of z statistics in brackets				
* significant at 5%; ** significant at 1%				
			ERA Change	ERA Change	ERA Change	ERA Change
Verducci		-0.09600	-0.10295		
			[0.21]		[0.22]		
IP Change * Under 26					-0.00391	-0.00386
							[0.78]		[0.77]
IP Change						0.00611		0.00609
							[3.71]**	[3.74]**
Under 26						-0.24738	-0.25085
							[0.93]		[0.95]
Mean IP			0.47554				0.00684	
			[13.67]**			[0.17]	
Constant		-1.90261	0.49064		0.36013		0.39538
			[8.05]**	[2.98]**	[1.50]		[2.86]**
Observations		2380		2380		2313		2313
Overall R2	0.0707	0.0000	0.0034	0.0038
Absolute value of z statistics in brackets				
* significant at 5%; ** significant at 1%		

The first row of each table measures the straight-up Verducci effect. If you increased your workload by more than 30 innings in the preceding season and are under the age of 26, then we should expect to see a decline in innings pitched and ERA. However, it turns out that this is not the case. In terms of workload, Verducci Effect pitchers actually increased their innings pitched between 19 to 22 innings. In terms of performance quality, pitcher ERAs declined by an average of 0.1 runs; however, the effect was not statistically significant, which means it’s probably best to say there is no effect.

The last two columns of the tables represent attempts to quantify the Verducci effect as a continuous phenomenon; that is, the more your workload increases the stronger the effect ought to be. To do this I used three variables: the change in workload (measured by innings pitched), an indicator of whether or not the player was under 26, and an interaction term that multiplies the change in workload times the under 26 indicator. The interaction term (listed on the second row of each table) captures any difference in performance from workload by Verducci Effect pitchers. For innings pitched, Verducci Effect pitchers increased the number of innings pitched by about 7 innings for every 30 innings pitched. In addition, being under 26 increased expected innings by 15 innings, while the change in workload tended to lower innings pitched for all pitchers by about 8 innings. Thus, the net result for an under 26 pitcher increasing his workload by 30 innings is an increase of about 7 innings pitched. Note these results are all statistically significant, but this was not the case for ERA.

So, where are we? The results do not bode well for the Verducci Effect. Pitchers who were predicted to decline actually improved. One potential problem with this study is that pitchers who pitched no innings at all in a season were not included; however, I think this bias is slight since this number is small, as even injured pitchers normally get in a few innings every season. Frankly, this is about as quick and dirty as you can get with a test; but, it’s a starting point, and I’d like to see others examine the effect further. While appreciate the intuition behind the Verducci Effect, I don’t see much evidence for it.

Update: More Testing of the Verducci Effect

Tim Hudson’s Hometown Discount

The long-awaited announcement of Tim Hudson‘s new contract with the Braves has finally come. The terms guarantee Hudson $9 million a year over the next three seasons, plus a $1 million buyout of a team option for a fourth year. The fourth-year option also pays out $9 million, so the total value that could be paid out is $36 million over four years. The contract voids a $12 million option for 2010, that the Braves were likely going to buy out for $1 million.

Hudson is an interesting player. He’s ranged from good to dominant. He was really pitching some of his best baseball as a Brave right before his injury. The good news is that he pitched well in his return through 42 innings. With a full offseason to recover, I think there is good reason to believe that he will be back to normal; however, the injury risk may have reduced his value somewhat. I proceed to my valuation with this caveat.

If Hudson pitches as he did in 2007 and 2008 over the course of a full season, then he’ll be worth about $12.5 million per year over the next three seasons. Thus, it appears that Hudson is giving the hometown discount that he promised—smart move by Frank Wren and the Braves. This allows the Braves to trade one of its other starters (who will it be?) and still have pitching stability going into the future.

If you see Hudson out and about in the Atlanta area, be sure to say “thanks”—but, please, don’t pester him. Or, maybe throw a little support to the Hudson Family Foundation. He wants to be in Atlanta, and he has strengthened his club by doing so. It’s nice to have you on board for the long haul, Tim.

Question of the Day

If the Yankees end up losing the World Series because they can’t get good production out of a starter for the final three games, how will this affect the machismo argument regarding pitcher rest?

Even if the Phillies come up short, Charlie Manuel made the right call to give his pitchers four days of rest. It’s an issue of physiology: the body needs time to recover from strenuous activity.

The Duncan Effect

At Inside Pulse Sports Pip of Fungoes asks:

it’s time for a comprehensive study of whether there is a “Duncan Effect” on pitchers, like the one that JC Bradbury did on Leo Mazzone. Until then, no one knows for certain what kind of an impact (if any) Duncan has on pitchers.

Well, because you ask so nicely, I’d be happy to oblige. :-) Actually, it’s easy because I already did the study.

Two years ago, Sports Illustrated asked me to look into the question, and I ran a study similar to the one I did for Leo Mazzone in The Baseball Economist. I looked at how pitchers performed with and without Duncan, controlling for factors such as age, parks, and pitcher quality. I found that Dave Duncan’s pitchers improved their ERAs by about 0.35 runs—yeah, he’s pretty darn good.

If you haven’t seen this before, it’s because the estimate buried on page 60 of the September 27, 2007 issue of SI in a story about Duncan and his sons. I meant to write about it at the time, but I never got around to it.

UPDATE: Pitchers Hit Eighth posts the link to the SI article in the comments. Thanks!