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May 3, 2007

Schrodinger's Bat

Hummingbirds and Sloths

by Dan Fox

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"Baseball's poetic and lyrical celebrants are fond of pointing out that baseball is the only major team sport without a clock. What these people don't understand is that, until about 1945, baseball did a have clock. It was called the sun."
--Bill James in The New Historical Baseball Abstract

It's seemingly one of the oldest adages in the game--if you're a pitcher you shouldn't waste time between pitches. Work quickly, and your defense will reward you by making more plays by virtue of staying alert and on its toes. You can find that particular piece of advice in nearly every instructional book and video on pitching, although often in the more nuanced form of "keeping a good tempo" on the mound. This wisdom came to mind after the quintessential example of a no-nonsense hurler, White Sox pitcher Mark Buehrle, was on display in the major's most recent no-hitter. Reports of the game universally noted how Buerhle worked "fast and efficiently" in mowing down the Rangers.

After reading those words time and time again, I began to wonder just how true that advice is at the major league level. The result is that this week we'll take a small jaunt into the world of quick workers, slow workers, and the error rates of the defenses that play behind them.

Speed and Lethargy

The first hurdle is to identify just who are the speedy workers, and who are the dawdlers--or to put it in other terms, which ones are the hummingbirds (a species of which, the blue-throated hummingbird, has a heartbeat of 1,260 beats per minute) and which are the sloths (who typically move at a speed of 6 to 12 inches per minute). By quick workers we mean pitchers who spend the least time between pitches (their overall tempo on the mound) and not pitchers who get rid of the ball the fastest (their tempo within their pitching motion), nor do we mean the guys who end up throwing the fewest pitches per inning and thereby have quick innings. It should also be noted that for the purposes of this study we're considering only starting pitchers who started 50 or more games in the major leagues since 1970.

There are no publicly available numbers that track exactly what we're after (that I know of, anyway), for example, a formulation of the average number of seconds between pitches. So, in the absence of it I decided to rely on the wisdom of crowds. Although numerically they probably don't constitute a "crowd," I took an informal survey of the Baseball Prospectus staff, asking the question as to which pitchers are known as fast and slow workers given the parameters laid out above. With their list I combined the results of a quick Google search for where pitchers elicited published comment as quick or deliberate workers on the mound.

The combined list of the ten most popular on either end of the spectrum from those two sources follows:

Hummingbirds: Bronson Arroyo, Mark Buerhle, Bob Gibson, Roy Halladay, Catfish Hunter, Jim Kaat, Jon Lieber, Greg Maddux, Mark Mulder, Curt Schilling

Sloths: Jose Acevedo, Matt Clement, Jose Contreras, Joey Hamilton, Al Leiter, Derek Lowe, Vicente Padilla, Rick Sutcliffe, Steve Trachsel, Barry Zito

In perusing these lists you'll probably note that they appear to do a pretty fair job of capturing the common wisdom. Bob Gibson was known for his impatience with opposing hitters who stepped out of the box, and his wrath was felt by his own catchers and teammates who would want to conference with him on the mound. Steve Trachsel, on the other hand, has said he likes to visualize each pitch before it's thrown and has thus been dubbed the pitching version of "the human rain delay" (as opposed to the original edition, Mike Hargrove). In addition, you would be correct in assuming that the first group of pitchers is superior to the second as seen in their aggregate lines:

           W       L     Pct     IP     ERA    ERA+    K/9    BB/9  IP/UER
H-Bird   1766    1248   .586   26558    3.43   124     6.2     2.3    21.8
Sloth     962     831   .537   15095    4.11   110     6.4     3.5    23.5 

The fast workers certainly had longer careers, made more starts, and pitched more innings. In terms of aggregate winning percentage and ERA+, both groups are above average. Our first clue as to what we'll find below can also be seen in that last column, IP per Unearned Run. The slow workers seem to give up fewer unearned runs, and so we would assume the have the benefit of fewer errors getting committed behind them.

But before we zero on in how the defenses behind these pitchers fared, we can make a small quantitative attempt to determine if our anecdotal lists are reasonable in capturing the tempo of these pitcher's work habits.

For this task we'll use the average time of game for each of a starter's starts, and comparing that with the average time of game for that year. It turns out that time of game is recorded in Retrosheet game logs going back well before our 1970 cutoff, with pretty complete coverage starting in 1941. When aggregated this data confirms what we all know--namely that average time of game rose dramatically in the early 1980s through the early 1990s, and has since seemed to stabilize, even dropping back to around to 170 minutes (two hours, 50 minutes) in the last four years, as shown in the graph below.

image 1

This decline has largely been attributed to the effort to effectively widen the strike zone, starting in 2001 with Sandy Alderson's mandate for a return to the rulebook definition, and perhaps also through a standardization encouraged by tools like QuesTec. Of course the new rules implemented for 2007 including reducing the maximum time between deliveries with no one on base from 20 to 12 seconds, and requiring a batter to keep one foot in the box during his at-bat, may also lead to a further reduction.

What's not as well remembered is that game times increased dramatically after World War II. In the 1930s and extending through 1945 (for the 7,237 games for which times are recorded) the average length was 125 minutes. Then, in 1946 the average time increased to 146 minutes, and game times remained in that range until the next upward trend began around 1980. This increase right after the war coincides with the greater number of night games, which no longer necessitated that games be complete well before sunset. With that sense of urgency removed, the game began to slow as umpires became more lax in their former mandate to "move the games along" by allowing more frequent timeouts. Peter Morris points out in A Game of Inches, Volume 1 that increased dead time on the field was something that had already been increasing, dating from the second decade of the twentieth century, and that it was a trend that fundamentally changed the nature of the game for both spectators and players:

While the increased length of ball games has spawned many complaints, there has been less attention to the specific issue of timeouts. Yet it is important to recognize that the shift from a game in which time was rarely out and in which the action was virtually continuous to one in which timeouts are frequent has removed one of the features that initially distinguished baseball.

But the changing length of the average game is just one of the problems with trying to identify fast and slow workers using game times. Fortunately, this is also one that can be compensated for by normalizing the game time to the year in question. Beyond that, there's considering the quality of the pitchers themselves (poor pitchers pitch longer games by giving up more baserunners), their offenses, the team's relievers, and the number of pitches thrown (high strikeout pitchers will throw more pitches), which all affect the game's time, and will therefore influence the results. But again, rather than attempt to control for all of these factors, we're using game time to simply get a read on whether our lists seems reasonable.

The following table lists our 20 starters, their number of starts, and their average game length per start along with how it stacks up against the weighted average game length given the years in which they pitched.

Name                 Starts AvgTime  PctofYr
Bronson Arroyo          124     174   101.8%
Mark Buehrle            204     159    93.0%
Bob Gibson              171     133    89.3%
Roy Halladay            191     164    95.3%
Catfish Hunter          321     144    96.6%
Jim Kaat                307     143    95.3%
Jon Lieber              314     165    95.4%
Greg Maddux             658     159    92.4%
Mark Mulder             198     172   100.0%
Curt Schilling          412     169    97.7%
--------------------------------------------
Jose Acevedo             58     173   100.6%
Matt Clement            235     178   102.9%
Jose Contreras          102     174   103.0%
Joey Hamilton           209     169    97.1%
Al Leiter               378     178   102.9%
Derek Lowe              189     169    99.4%
Vicente Padilla         144     172   101.2%
Rick Sutcliffe          373     173   104.8%
Steve Trachsel          380     181   104.6%
Barry Zito              221     173   100.6%

For the most part this table confirms our subjectively generated list. Those deemed quick workers came out at 95% of the average time per game, while those deemed slow workers were at 102%. In widening this metric to look at all starts with 100 or more starts since 1970, Gibson still came out as the fastest worked at 89.3%, followed by Tom Browning at 91.7% and Randy Jones at 92.1%. Maddux (fourth), Buerhle (sixth), Kaat (19th), and Halladay (20th) all make it into the top 20. On the flip side, Al Fitzmorris was at 110.1% and Ben McDonald at 109.2%. The fact that by this measure the list of sloths is dominated by somewhat inferior pitchers testifies to the fact that pitcher quality plays a role in game length.

With our two sets of pitchers at the ready, we can now dig into the defenses that played behind them.

Getting Defensive

To determine whether quick pitchers effectively reduce the frequency of errors committed by their fielders, or if the slow-working pitchers have the opposite effect, we'll take a look at the batted ball data. Specifically, we can calculate the number of balls that were put in play against each pitcher (not counting home runs) and what percentage of those balls were recorded as errors. Once again, we have a little bit of a historical problem, since errors are and have been on the decline for over a century. This fact is often cited as evidence of an increasing level of play, and just since 1970 the number of errors committed per 100 non-home run balls in play has declined roughly 25%, as shown in the following graph:

image 1

As before, we can correct for this long-term trend. We'll use the actual data for each pitcher's team when the pitcher was not on the mound during that season, and compare that to the rate of errors when they were. If it's the case that fast workers reduce errors and slow workers induce them, then we should see errors rates that are lower than the team rate for fast workers, and higher for slow ones. Our results can be summarized neatly in a table:


Type      PBIP     PE   E/100BIP   TBIP      TE    E/100BIP  Ratio
HBird     61701    891    1.44    436694    6470      1.48    99.1%
Sloth     43313    605    1.40    420656    5970      1.42    97.9%

How to read this table: PBIP represents the number of non-home run balls put into play against each type of pitcher, PE is the number of errors recorded, E/100BIP is the number of errors per 100 balls in play, TBIP is the total number of balls put in play against the rest of the team's pitchers, TE reflects the team errors with the accompanying error rate, and finally Ratio represents the ratio of errors per 100 balls in play behind these pitchers versus their teammates, weighted by year.

So, with that explanation out of the way, a Ratio higher than 100 percent indicates that the group of pitchers experienced more errors behind them than did their teammates. When you boil it down, what you find is that both types of pitchers have fewer errors made behind them than when they are not on the mound, and that our sloths actually enjoy a lower-still ratio of errors. If anything, this indicates that it's the slow pokes who depress error rates on batted balls.

This result flies in the face of the common wisdom, but there are two issues to consider, however. First, it's not surprising that both our fast and slow workers see fewer errors made behind them than when others are on the mound. As previously noted, both sets in our group of twenty are above average, and better pitchers suppress the number of errors made behind them since they don't give up as many hard-hit balls. This is, after all, the basis for the argument to scrap earned run average altogether and instead simply use run average. So while it could be the case that the hummingbirds suppress the errors behind them, this doesn't seem likely give the fact that overall both the fast and slow workers suppress errors at essentially the same rate.

But to confirm our indication that there is little if any difference in the defensive reaction behind the different types of pitchers, we can remove that factor by creating a subset of our 20 pitchers with nearly identical performance statistics. Taking Buerhle, Halladay, and Lieber from the hummingbirds, and Leiter, Contreras, and Trachsel from the sloths, we see that their aggregate statistics are indeed quite similar:


           W       L     Pct      IP     ERA    ERA+     K/9    BB/9  IP/UER
HBird    365     273   0.572    5666    3.99     117     6.0     2.1    18.4
Sloth    344     302   0.533    5336    4.07     113     6.8     3.8    24.2

You'll notice in this table we've added innings pitched per unearned run, which again confirms that the sloths aren't burned as often by errors behind them. Drilling down to the batted ball data:


          PBIP      PE   E/100BIP    TBIP      TE   E/100BIP  Ratio
HBird    16719     243     1.45     127324    1810    1.42    110.6%
Sloth    14571     194     1.33     155190    2158    1.39     92.3%

Once again, the sloths see their defenses commit fewer errors, although with this subset the hummingbirds encountered more errors than their teammates did. This also seems to indicate that quick workers don't suppress errors more than do slow workers.

Which brings us to our second point, the puzzling fact that in both the full and subset cases above our sloths actually had fewer errors made behind them than the hummingbirds. The resolution to this puzzle lies in digging a little deeper into distribution of the vectors of the balls put into play against each type of pitcher. Our full set of fast workers turned out to be more dependent on the ground ball, as almost 4% more non-home run balls in play against them (54 percent to 50 percent) were on the ground. Groundballs are more apt to become errors than flyballs, around 2.4 percent in this sample, as opposed to about a quarter of one percent for the other batted ball types. Therefore, the error rate of the hummingbirds rises accordingly. In fact, the error rate on ground balls for both groups was almost identical, and by correcting for that fact, it turns out that the sloths did in fact experience fielder errors at a slightly higher rate than hummingbirds. However, the difference is on the order of one error per 5,000 balls in play, which is clearly not a significant result.

What are we left with? There's no evidence that quick workers reduce or that slow workers increase the number of errors that are made behind them, by either keeping fielders on their toes or lulling them to sleep. I don't know about you, but at the highest professional level that pretty well conforms to my expectations. Johnny may daydream in Little League, but Derek Jeter doesn't in the big leagues.

Related Content:  Pitchers,  The Who,  Errors,  Time,  Jose Contreras,  Bob Gibson,  Slow Starts

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