## New “Production” Essay

Production,” (PRO), usually expressed as on-base percentage (OBP) plus Slugging Average (SA) has caught on as a common measurement of offensive capability since it was published in John Thorn and Pete Palmer’s Total Baseball in 1989. On-base percentage measures the percentage of times a batter reaches bases per plate appearance (PA). Slugging measures the number of bases a batter realizes per at-bat (AB).

When they are expressed as decimals, these numbers can be added up. Mathematically, though, there’s a problem. The denominators of these two expressions are different, and, as you recall from middle school math, fractions with different denominators cannot be added together.

To truly add these numbers, both plate appearances and at-bats must be in the denominator of both fractions. So the formula for OBP must be multiplied by at-bats and the formula for SA must be multiplied by plate appearances. Follow the steps in Table 1 on the following page.Table 1. Reconciling OBP and SLG denominators

OBP = Hits(H) + Walks(W) + Hit-By-Pitch(HBP)/Plate Appearances (PA)

PA = At-Bats(AB) + Walks(W) + Hit-By-Pitch(HBP) + Sacrifices(Sac)

OBP = Hits(H) + Walks(W) + Hits-By-Pitch(HBP)/ At Bats(AB) + Walks(W) + Hits-By-Pitch(HBP) + Sacrifices(Sac)

SA = Singles(S) + 2*Doubles(2D) + 3*Triples(3T) + 4*Home Runs(4HR)/At-Bats(AB)

The only way to reconcile the fractions is to do the following:

Hits(H) + Walks(W) + Hits-By-Pitch(HBP)/
At-Bats(AB) + Walks(W) + Hits-By-Pitch(HBP) + Sacrifices(Sac)
+
Singles(S) + 2*Doubles(2D) + 3*Triples(3T) + 4*Home Runs(4HR)/
At-Bats(AB)
=
PRO = AB*(H + W + HBP) + (A + B + W + HBP + Sac)*(S + 2D + 3T
+ 4HR)/
AB*(AB + W + HBP + Sac)

PRO =
(AB*H + AB*W + AB*HBP + AB*S + AB*2D + AB*3T + AB*4HR + W*S +
W*2D + W*3T + W*4HR)/
AB*(AB + W + HBP + Sac)
+
HBP*S + HBP*2D + HBP*3T + HBP*4HR + Sac*S + Sac*2D + Sac*3T +
Sac*4HR)/
AB*(AB + W + HBP + Sac)

PRO =
H + W + HBP + S + 2D + 3T + 4HR/
AB + W + HBP + Sac
+
W*S + W*2D + W*3T + W*4HR + HBP* S + HBP*2D + HBP*3T + HBP*4HR +
Sac*S + Sac*2D + Sac*3T + Sac*HR AB*(AB + W + HBP + Sac)

You can see that PRO, in its expanded form, is a difficult equation to understand.

We need a more easily understood equation. I suggest the one at the top of the next column, which I call “new production” (NewProd).

NewProd = W + HBP + CI + S + 2D + 3T + 4HR/ Plate Appearances

NewProd = W + HBP + CI + S + 2D +3T +4HR/ AB + W + HBP + Sac + CI

This equation encompasses the essential components of on-base production–walks, hit-by-pitches, catcher’s interference (CI), and hits of each type–in the numerator. The denominator is plate appearances, so the equation measures simply the number of bases a batter gets per plate appearance. Four is the highest possible result. The great benefits of this equation are that it is easy to understand–no drastic manipulation of denominators–and it follows mathematical rules.

Table 2 illustrates the top twenty-five players in terms of NewProd given at least 502 plate appearances. The 1999 correlation with PRO is 0.98. You can also determine the percentage of NewProd emanating from on-base percentage (OBP) and slugging (SA). Sammy Sosa had the highest percentage of NewProd emanating from SA–95 percent. Bob Abreu had the highest percentage emanating from OBP–72 percent. Mark McGwire had the highest NewProd number. These results are consistent with our perceptions of these players. Sosa does not have a high OBP but has a high SA. Abreu does not hit a lot of home runs but does have a high OBP. None of us will be surprised to learn that McGwire accounted for 0.753 bases for every plate appearance.

I expect and welcome challenges to NewProd. I acknowledge the high correlation between runs created and PRO, when we evaluate team offensive production. The correlation declines for individual players, though. Combining this with PRO’s violation of mathematical precepts, I think it makes more sense to use NewProd as an index of individual offensive performance.

Mark Kanter lives with his wife Lynne Glickman in Portsmouth, Rhode Island. He has been a member of SABR since 1985. He has a fan of the Phillies since 1966.

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