Will Carroll‘s experiment with using comments as something more than just comments was a rousing success, and I’d like to try a version of my own. I don’t do a lot of quantitative work-it’s not that I’m incapable of it, but I find that I often end up with a lot of information, and a difficulty in separating the signal from the noise. So I have a lot of data here, but no real conclusions. What I’m going to do here is just throw it all on the table, and then we can discuss it together in the comment thread and see what will come of it.

This all began with an e-mail from a subscriber named Steve:

The Indians signed RHP Chen-Chang Lee:

He is listed at 5’7″. I remember the bromide, ‘teams have a bias against short right-handed pitchers,’ something the Astros tried to leverage over the years. But ‘short’ meant 5’11” or 6’0″ (Roy Oswalt), not 5’7″ (David Eckstein). Who was the last effective major league pitcher to be that short? I’m not saying this is a silly signing or Lee can’t be successful (he was very good in the Olympics and can apparently throw 94 mph), but I’m honestly curious what other truly short pitchers there have been.

This prompted me to start thinking about pitcher size. I write a lot about ideal pitcher frames, and I complain about short pitchers as much as the next guy, but does it really matter? I’m not convinced of it, but here’s some work I’ve done, without coming to any real conclusions, that I hope will spur some discussion below.

The first thing I did was to call the Indians in order to get more information on Lee, and I was able to reach a team official who informed me that Lee is actually five-foot-eleven. “Look, I’ve stood next to the guy, and he’s taller than me,” said the official, who added, “I don’t think we’d be giving that kind of money to a pitcher who was five-foot-seven.” In addition, Lee is different from most pitchers in the sense that he’s a side-armer. A converted shortstop who did not begin pitching until he was 14 years old, Lee’s fastball sits at 88-92 mph coming from that lower angle, and he also features a solid slider. He’ll likely begin next year in the rotation at High-A Kinston in order to get him innings.

So, let’s shift our focus and switch to the major league starters. Thanks to some great work from out data guru, William Burke, we can examine some pitcher profiles and see what they look like. First we have the performances by height of every starting pitcher this year:

Height GS     IP      ERA
5-10   78    503.0   4.51
5-11  162    998.0   4.47
6-0   444   2653.2   4.16
6-1   673   4276.0   4.23
6-2   888   5677.2   4.41
6-3   784   5069.1   4.32
6-4   578   3620.1   4.83
6-5   454   2724.0   4.69
6-6   176   1265.0   3.99
6-7   169   1085.2   3.93
6-8    16    134.1   4.49
6-9    51    319.2   5.41
6-10   43    251.1   4.23

The average height for a starting pitcher is 6’2¾”, and the mid-point of the values lies just barely over 6’2″; the taller pitchers throw off the average significantly. There are 279 starts made by players five or more inches over the 6’2″ average, but none five inches or more under it. While they’re not the largest groups, note that the only heights with ERAs under four are the cadres comprising those who are 6’4″ and 6’5″-sizes generally associated with the classic power-pitcher’s build.

Build connotes both height and weight, though, so I took this one step further. Using the top 40 starting pitchers this year as measured by VORP, I calculated the BMI (body mass index) for each player. Now BMI is a pretty silly system when you check out how it’s used; by this measurement, Dan Haren and Jamie Moyer are overweight, while Matt Cain is obese. But if we can ignore the labels, it does give us a good sense of the player’s bulkiness.

The average weight of a starting pitcher this year is 213.05 pounds. Combined with our average height, that gives us a BMI of 26.8. From there I developed a matrix using standard deviations from these average heights and BMIs, with an 0.5 standard deviation from the average considered normal, 0.5-1.5 from average significant, and more than 1.5 extreme. Thus, we have:

                -1.5   -0.5          +0.5   +1.5
Height/Weight  Skinny  Thin  Normal  Beefy   Fat   Total
+1.5 Skyscraper   0      0      3      1      1      5
+0.5 Tall         0      1      2      1      0      4
     Normal       0      6      5      5      1     17
-0.5 Short        1      4      5      2      1     13
-1.5 Diminutive   1      0      0      0      0      1
     Total        2     11     15      9      3     40

The next thing I did was to play Olympic diving judge and get rid of the highs and lows-so anyone in the extreme categories is out. Before we do that however, let’s quickly pay homage to the two opposite ends of the spectrum. There is only one Skyscraper/Fat pitcher (CC Sabathia), and only one Diminutive/Skinny pitcher (Tim Lincecum); both are among the best in the game. I’m not sure that tells us anything other than that there are no absolutes. So focusing on the remaining nine categories, we end up with the following.

Tall/Thin: Dan Haren
Tall/Normal: Scott Baker, James Shields
Tall/Beefy: Carlos Zambrano
Normal/Thin: Zack Greinke, Cole Hamels, Cliff Lee, Jon Lester, Mike Mussina, Ervin Santana
Normal/Normal: Aaron Cook, Ryan Dempster, Justin Duchscherer, Kyle Lohse, Joe Saunders
Normal/Beefy: Felix Hernandez, Paul Maholm, Ricky Nolasco, Brandon Webb, Todd Wellemeyer
Short/Thin: Shaun Marcum, Jaime Moyer, Roy Oswalt, Jake Peavy
Short/Normal: John Danks, Jeremy Guthrie, Scott Kazmir, Daisuke Matsuzaka, Edinson Volquez
Short/Beefy: Johan Santana, Ben Sheets

Looking at these lists, and combining them mentally by height and BMI, and you start to see some trends here. Which group is the best? Which group would you think is more likely to give you 225 innings? Which group has the best health record? There are some interesting answers here. Normal/Thin is the most impressive list overall, but looking at the beefy list gives me far more confidence in regards to durability.

Now back to the original e-mail, which asks about five-foot-seven pitchers (even though we now know that Lee is merely short, as opposed to off-the-charts small). With no pitcher under five-foot-ten starting a game this year, William Burke compiled the top pitchers’ seasons by those under that height in the modern-modern era (since 1969), and the list is dominated by two names:

Year Height GS    IP      ERA   VORP   Pitcher
1977   68   34   221.1   3.38   38.3   Fred Norman
1997   69   25   182.2   3.74   36.4   Tom Gordon
2004   69    0    89.2   2.21   36.3   Tom Gordon
1993   69   14   155.2   3.58   34.0   Tom Gordon
1974   68   26   186.1   3.09   33.3   Fred Norman
1979   68   31   195.1   3.64   33.2   Fred Norman
1973   68   35   240.1   3.60   32.1   Fred Norman
1973   69    4    91.0   1.68   29.1   Fred Beene
1994   69   24   155.1   4.35   29.0   Tom Gordon
1998   69    0    79.1   2.72   28.3   Tom Gordon
1983   69    0    87.1   2.47   25.7   Salome Barojas
2005   69    0    80.2   2.57   25.3   Tom Gordon
1976   68   24   180.1   3.09   24.3   Fred Norman
1977   69   10   116.2   2.70   24.1   Pablo Torrealba
1989   69   16   163.0   3.64   23.0   Tom Gordon
1975   68   26   188.0   3.69   22.0   Fred Norman
1987   69   22   158.2   4.37   21.8   Guy Hoffman
1973   69    0    89.2   2.41   21.6   Ramon Hernandez
1992   69   17   100.0   3.06   21.1   Brian Barnes
1969   68   33   202.0   3.52   20.9   Tom Phoebus

So where do we go from here with this data, or indeed, is there anywhere to go? Let’s begin a discussion in the comments section about where we are so far.