Runs Created

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Runs Created (RC) is a run estimator developed by Bill James. First introduced in the 1979, James has continuously revised the formulas in pursuit of incorporating more data while increasing accuracy. The term "runs created" is sometimes used more generally to refer to the result of any run estimator.

All Runs Created versions take the form:

RC = A*B/C

The A factor represents baserunners; the B factor represents advancement of baserunners; the C factor represents opportunity. James has consistently defined baserunners as final baserunners (i.e. removing all runners known to have been put out after reaching base through being caught stealing or retired on a double play). The opportunity factor has consistently been defined as total plate appearances.

Versions of Runs Created in Use[edit]

The basic version of Runs Created, which remains in use today, was first published by James in 1979:

A = H + W
B = TB
C = AB + W

This version can be written equivalently as (H + W)/(AB + W)*(TB/AB)*AB, essentially OBP*SLG*AB.

James later introduced a version that includes stolen bases and caught stealing:

A = H + W - CS
B = TB + .55*SB
C = AB + W

Beginning in the 1983 Baseball Abstract, James has had several "technical" versions of the formula which incorporate minor offensive categories. The most recent version, appearing in the Bill James Handbook, is:

A = H + W + HB - CS - GIDP
B = 1.125*S + 1.69*D + 3.02*T + 3.73*HR + .29*(W - IW + HB) + .492*(SB + SH + SF) - .04*K
C = AB + W + HB + SH + SF

Theoretical Team Runs Created[edit]

Since Runs Created is a dynamic estimator, it is inappropriate to apply it directly to individual batters, as they interact with eight other batters in a lineup. To address this issue, James introduced a formula which estimates the number of runs a team would score with the individual batter in question plus eight "typical" hitters (each with the same number of plate appearances as the individual in question), then subtracts the number of runs the eight typical hitters would created without the player. This difference is the number of Runs Created credited to the individual.

TT RC = (A + 2.4*C)*(B + 3*C)/(9*C) - .9*C

The eight typical hitters are defined so that they add .3 (2.4/8) to their A factors with each plate appearance and .375 (3/8) to their B factors. Thus, a team with just the eight typical players creates (2.4*C)*(3*C)/(8*C) = .9*C runs.

Situational Adjustments[edit]

In addition to the theoretical team construct, James added situation adjustments to the latest incarnations of RC. The adjustments are based on home runs with runners on base and Batting Average with runners in scoring position. For each home run with a runner on base more than expected (based on HR/AB overall and with runners on base), the player gets credit for one additional run. Likewise, for each additional hit with runners in scoring position (based on overall and RISP BA), the player is credited with an extra run.

An additional adjustment is to correct the sum of the individual estimates for members of a team so that it is equal to the team's actual number of runs scored. This is done proportionally, so New RC = RC*(Team Runs/Sum(positive individual RC for team)).

Intrinsic Linear Weights[edit]

Like other dynamic run estimators, one can find the intrinsic linear weights used by RC for any set of input statistics. To find these, one must find the total A, B, and C factors for the entity in question (A, B, and C in the formula), as well as the coefficients for each event in the A, B, and C factors (a, b, and c respectively):

LW (event) = (C*(A*b + B*a) - A*B*c)/C^2 = (B/C)*a + (A/C)*b - (A/C)*(B/C)*c

Once the intrinsic LW have been found, one can use the weights to calculate "Linear RC". If the A*B/C form is considered to be "Classic RC", the theoretical team RC equation simplifies to (1/9)*(Classic RC) + (8/9)*(Linear RC).

Weaknesses of Runs Created[edit]

  • Runs Created is based on a theory of how an offense works, namely on base times advancement divided by opportunity, unlike Base Runs which is based on an identity that is mathematically true. This in and of itself does not mean that the method is inferior, but it means that it is starting from a shakier foundation.
  • RC does not handle the home run correctly, since home runs always result in at least one run. A homer by itself in RC is worth 4 runs (1*4/1 = 4), but a homer along with 27 outs is worth 1/7 of a run (1*4/28 = 1/7). RC also does not adhere to the fact that runs must always be less than or equal to the number of batters reaching base.
  • RC is overly optimistic in its predictions at high levels of offense. Much of this results from the treatment of the home run; in order to properly value the home run in average circumstances, it must be given a very large advancement coefficient.