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— Where BTF's Members Investigate the Grand Old Game
Tuesday, December 18, 2001
Total Baseball’s Fielding Runs?A Primer
How are Pete Palmer’s fielding runs calculated?
This article is part of a broader series of articles, written for SABR-L [The Society of Baseball Research’s Mailing list] and crossposted to STATLG-L [Baseball (and Lesser Sports) Discussion List ], comparing the results generated by different defensive measurement systems. The players chosen for this comparison were two 1978 shortstops later traded for each other - San Diego’s Ozzie Smith and St. Louis’s Garry Templeton. I was intrigued by the similarities in their overall fielding stats prior to the trade and the separation that developed very quickly after they were swapped for each other. I’ve shortened the article from the original post but left the details of the method intact.
In developing Total Player Rating (TPR), Pete Palmer devised a measurement of fielding skill in terms of runs. Fielding Runs (FR) is added to runs generated from batting skill and baserunning (stealing) skill (and pitching skill for pitchers) to come up with an overall total rating expressed in runs, later converted to wins.
Palmer calculates FR for SS (see Note 1) by first calculating a league average for the position according to the following formula:
AVG(POS,LG) = .20*(PO+2A-E+DP)/(league PO - league K)
where PO, A, E, and DP are the total putouts, assists, errors, and double plays for the league’s shortstops, and league PO - league K represents an estimate of the total number of outs made by the league’s fielders. Palmer multiplies assists by 2 because "more fielding skill is generally required to get one than to record a putout".
Once Palmer has that average for the position and league, he compares what a SS actually did produce to what he estimates an average player would have roduced in the same number of outs:
FR = .20*(PO+2A-E+DP) - ((team PO - team K) * AVG(POS,LG) * %PT)
where PO, A, E, and DP are the putouts, assists, errors, and double plays registered by the shortstop, team PO - team K is the number of outs made by that team’s fielders, and %PT is an estimate of the amount of playing time at the position by this shortstop, based upon the player’s complete fielding line and the number of plate appearances. Palmer doesn’t publish his formula for estimating playing time, making it impossible to reproduce his results. In my calculations below I use actual playing time calculated from Retrosheet data to demonstrate the method.
NL SS, in 1978, had 3191 PO, 6199 A, 332 E, and 1105 DP. The league as a whole had 52,000 PO and 9905 K. The AVG(POS,LG) is therefore
.20*(3191+2*6199-332+1105)/(52000-9905) = 0.0777
Garry Templeton played 1353 2/3 of the 1437 2/3 innings played by the Cardinals (0.942 of the total). Templeton had 285 PO, 523 A, 40 E, and 108 DP. The Cardinals had 4313 putouts as a team and fanned 859 hitters. Templeton’s FR (see Note 2) are:
.20*(285+2*523-40+108)-((4313-859)*.0777*.942) = 27
Ozzie Smith played 1327 of the 1433 2/3 innings played by the Padres (0.926
of the total). Ozzie had 264 PO, 548 A, 25 E,
.20*(264+2*548-25+98)-((4301-744)*.0777*.926) = 31
TB7 has Templeton at 23, Ozzie at 26.
The biggest flaw in FR is that Palmer makes no effort to derive event weights from the actual relationship between the defensive events and their impact on run scoring, as he does with his offensive measures. An assist is worth two times a putout based on Palmer’s subjective assessment of its value. Palmer also subtracts errors from plays made, even though not every error adds a baserunner, and adds DPs to the total even though DPs are also counted in PO and A.
FR is flawed in three important ways:
The first flaw above, in my opinion, is the primary reason why most analysts discredit FR. It’s very natural for an analyst, when presented with a formula that looks like:
R = AW1+BW2+CW3
to ask how the developer of the formula came up with the weights. If the developer of the formula doesn’t have satisfactory answers, as Palmer does not, the credibility of the entire formula is questioned, especially when the results aren’t always intuitive and the developer of the formula acts as though the results are just as accurate as the results from other, more rigorously developed formulae that measure other aspects of R.
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