Research: Run Value of Major Batting Events in 2012

Chance of Scoring

To answer the first and second questions and compute the Getting On and Moving Over values we will need to know how often a runner is likely to score in a given situation.

This table shows the frequency (using SLW data from 2012) that a runner in each situation ended up scoring. For example, a runner on first base with two outs scores about 22% of the time.

Run Driving Values

Each batting event has some effect on a runner's Chance of Scoring. The effect may be positive or negative, depending on the event.

For example, let's say a runner on first base with two outs is pushed by a walk to second base. The walk has changed the runner's chance of scoring from 22% to 41%, for a net change of +19%. The Run Driving Value of that walk in this situation is +0.19.

Batter Event Frequencies, by situation

Each batting event occurs with differing frequencies depending on the situation. Walks are theoretically more likely with first base empty and two outs than with the bases loaded and no outs. These tables show the frequency of each event in each situation.

Batter Event Frequencies, by outs

For the Getting On value we need to know how often each event occurs, regardless of whether or where runners are on base.

These tables show the frequency of each event by the number of outs in the inning.

Run Values

We now have enough information to calculate the individual components of Run Value.

The Getting On value is computed as the sum of the products of the frequency of the event by out table with the corresponding Chance of Scoring. For example, the Getting On value of the walk is (0.421 x 0.68) + (0.342 x 0.58) + (0.237 x 0.22). In English, this formula is "the probability that a walk with 0 outs will score plus the probability that a walk with 1 out will score plus the probability that a walk with 2 outs will score."

The Moving Over value is computed in a similar way, but the frequency of the event by base and out and Run Driving Values tables are used instead, which makes for a more cumbersome calculation. For example, for a walk, in English the formula is "by how much does a walk with 0 outs increase the chance of scoring for a runner on first base plus by how much does a walk with 0 outs with a runner on first and second base increase the chance of scoring for a runner on second base..." and so on.

The Inning Killer is the easiest value to compute; it is the average negative value of an out, which can be estimated by the average runs that are scored per out (0.46).

Run Value = Getting On + Moving Over + Inning Killer.

Batter Event Frequencies, overall

This table shows the frequency of each event. For example, 26% of plate appearances result in a groundout.

BIP Frequencies

This table adjusts the frequency of each event, considering only Ball In Play events. For example, 34% of the time the ball is hit and is in play, the result is a groundout.

BIP Run Value

The average BIP event is a weighted average (by frequency) of each type of BIP event.

FIP coefficients

Now that we have the last missing piece (BIP Run Value) we can determine the FIP/xFIP coefficients.

First, each Run Value is adjusted by -(BIP Run Value), so that the adjusted coefficient for BIP disappears (by becoming 0).

The final value of the coefficient is the adjusted coefficient multiplied by 4 (the number of innings in a SLW game).

FIP for SLW

Plugging in the coefficients, we have a formula for Fielding Independent Pitching of:

constant + (((5.485 x HR) + (2.928 x BB) + (-1.973 x K)) / IP)

The constant is then chosen to align the league-average FIP with the league-average ERA.