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Arms Deal
2004-06-03 00:30
by Mike Carminati

Let arms yield to the toga, let the [victor’s] laurel yield to the [orator’s] tongue.—Marcus Tullius "Dody" Cicero

This past weekend I attended and spoke at the SABR meeting in Philly, and one of the speakers, in the course of comparing the careers of Roberto Clemente and Al Kaline, referenced a derived stat, assists minus errors, that I find interesting. Each Kaline and Clemente had exceeded their errors by at least ten assists in multiple seasons. It got me to thinking about a means to measure an outfielder's arm objectively though my friends and I felt that assists minus errors really didn't measure much of anything.

For the heck of it, I ran the all-time assists minus errors per season for all outfielders. There have been 791 instances of an outfielder's assists exceeding his errors by at least ten. Kaline did it three times; Clemente, five. Here are the ones over 20 all-time:

NameYrAEA Minus E
Chief Wilson191434628
Harry Niles190634628
Jim Fogarty1889421428
Mike Mitchell1907391227
Chuck Klein1930441727
Danny Murphy191134826
Tris Speaker1909351025
Max Carey191632824
Johnny Callison196326224
Stan Spence194429524
Chet Chadbourne1914341024
Gene Moore193632824
Hardy Richardson1881452124
Tommy McCarthy1888442123
Ed Hahn190724222
Fred Snodgrass191131922
Harry Heilmann192431922
Ira Flagstead192331922
Mike Griffin189225421
Patsy Donovan190230921
Ping Bodie1917321121
Sam Thompson189628721
Al Kaline195823221
Casey Stengel191730921
Joe Orsulak199122121
Max Flack191622220
Matty McIntyre190625520
Tommy Griffith192127720
Tilly Walker1914301020
Roy Thomas190527720
Charlie Duffee1889432320
Cy Williams192129920
Joe Jackson1911321220
Hugh Nicol1884482820
Jack Tobin1914311120
Jimmy Sebring190427720

You may notice that, aside from Joe Orsulak, no one on the list is from the last 40 seasons. There are some fairly well-known players on the list, but for the most part this is not a terribly impressive list. By the way, the worst ever in this criterion was Abner Dalrymple in 1879 with a negative 36 (4 assists and 40 errors). No one has registered a negative 20 since 1903 (Cy Seymour).

I thought that I could devise something better, and I think I have.


Now, Fielding Win Shares isn't the best solution since James, when he wrote Win Shares just a couple of years ago, did not have fielding breakdowns by position in the outfield. One of the shortcomings of Win Shares is that it lumps all outfielders together so that all centerfielders appear to have tremendous range and all right fielders appear to possess a great arm.

Fortunately, the number of games for every outfielder has now been broken down by position. Ideally, the putouts, assists, errors, and double plays would be, too, but that is not yet the case. Therefore, I prorated those stats by the games played per position.

Of course, this assumes that a player will play each outfield position the same way and generate the same statistical result. However, I felt that this was preferable to lumping all outfielders together under one category. By the way, if you don't care two whits about my methodology, feel free to skip to the results.

My first slice returned some interesting results, but I was still troubled by the prospect that assists and putouts were being distributed evenly per outfield position for those players who played more than one outfield position (weighted by games played per position of course). But was this a significant problem?

I tallied up the number of seasons for all outfielders prior to 1996 when we have the stats split out by position (i.e., by year, player, and team/stint). There were 9693 such player-seasons in which the outfielder played one position exclusively and 11902 in which he played more than one outfield position, or 55%. Given that over half the players were affected, I felt that it was a significant enough issue to merit more attention.

First, I took a look at my simple formula to prorate the fielding stats per game played per position (e.g., prorated putouts per position equal the total OF putouts times the games played at that position divided by the total number of games played for all outfield positions, as opposed to the total games played in the outfield since the player could have occupied multiple outfield positions in a given game—sounds simple enough, eh?). Here's an example of what the results would be for a player that I made up: The player had 200 total putouts on the year and played 50 games each in left, right, and center. The prorated putouts would be 66.67 for each position—200 divided by 3—since he played the same number of games per position.

If we change his games per outfield position to 20 in right, 100 in center, and 30 in left (but still 150 in total) and keep the putouts at 200, the prorated putouts results are 26.67 in right, 133.33 in center, and 40.00 in left (i.e., 200 times the games played per position divided by the total OF games).

However, in both scenarios above the putouts per game for each position is the same, 1.33. Let's assume that in the given year, the average right fielder had 1.2 putouts per game, the average center fielder had 2.2 putouts per game, and the average left fielder had 1.8—I just made 'em up. The putouts that the player registered in center would then be woefully lower than expected, they would be lower also in left, and they would be higher in right.

You'll also notice that that his 200 putouts are lower than expected for 150 games. One would expect 260 putouts for an average out fielder that year (using an average of the typical left, center, and right fielder's putouts per game, which would be 1.73 here, multiplied by 150 games). Therefore, this could either be a part-time player, that is, a late-inning defensive replacement, or he could have been moved around in the outfield on a regular basis, say, in an Earl Weaver-like outfield rotation. Since we don't have the total innings played by position, there's no way to say. Innings would be a more reliable basis for calculations that games, but until someone (Retrosheet?) calculates the innings pre-1996, we're stuck simply with games to perform our calculations.

OK, back to our example with 50 games per position and 200 putouts, if we weight the putouts per position based on the numbers above, then we would get 46.15 putouts in right, 84.62 in center, and 69.23 in left. Add them up, and you get 200. Now, using 20 games in right, 100 in center, and 30 in left, you get 16.11 putouts in right, 147.65 in center, and 36.24 in right. The PO/G ratios would be 0.81 in right, 1.48 in center, and 1.21 in left, all lower than the average but proportionately lower. The ratios for the first example are 0.92 in right, 1.69 in left, and 1.38 in right, again lower but proportionate by the number of games by position.

If you want the formula that I used to weight the results, it gets a bit complicated. First, calculate the expected number of putouts per game per position by totaling the numbers for those players who played only one outfield position for the year. Now take that number per position and divide it by the average for all three OF positions to get the normalized value. Finally take the normalized value and multiply it by the total number of putouts multiplied by the number of games for the given position divided by the total of the outfield games per position multiplied by the position's normalized putouts per game. I told you it was complicated.

So now we have the prorated fielding stats for all outfielders since the dawn of time. Ok, what does that do for us? Well, now we can use those stats to determine how well a player compares to his era. We can see how many putouts above expected a player is, which is a good indicator of a player's range. Do the same with assists, and you can see who has a superior arm.

The one thing you will see in the results is that it was easier for players to be far superior to their peers in the early days of the game. As baseball followed the tenets of Stephen Jay Gould and its talents converged, the differences in the fielding stats lessened. Therefore, the results will be broken down by era.

To be continued…

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