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
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
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
.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,
and 98 DP. The Padres had 4301 putouts as a team and fanned 744 hitters. Ozzie’s
.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:
- There is no obvious relationship between a defensive event and its effect
on run scoring. Palmer presents no evidence that an infield assist is twice
as valuable in preventing runs as is a putout, or that an average error costs
as much as an average putout, or that the player making a DP pivot (on which
he gets both a putout and an assist) should be credited with as much value
as a player who makes four putouts.
- Palmer’s estimates of playing time overestimate the playing time of regular
players and underestimate the playing time of substitutes, artificially depressing
the FR for the regulars at a position.
- Palmer makes no adjustment for differences in the distribution of balls
in play from team to team. Ground ball/fly ball tendencies of pitching staffs
and the LH/RH distribution of hitters faced by a team do change the distribution,
and the variations from team to team are not minimal (see Note 3).
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.
- The formula used here applies only to 2B, 3B, and SS. Palmer has different
formulae for the other positions, but the concept for calculating FR is the
- These are rounded to the nearest whole number.
- There are those who argue that a pitcher "pitches to his fielders",
e.g. pitches in such a way as to control the direction of the ball in play,
and therefore a fielder’s ability might be responsible for generating those
extra opportunities. I don’t see any evidence in play-by-play data that such
an effect occurs on a regular basis, so
while I suppose it’s possible I think it’s mostly independent of fielding
skill, and thus it is appropriate to account for differences in ball in play
distribution when evaluating fielders.
Posted: December 18, 2001 at 05:00 AM | 7 comment(s)
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