The purpose of this is to determine the value of each major batting event (Walk, Single, Double, Triple, Home Run, Strikeout, Groundout, Flyout) and then to use those run values to improve statistical wiffler evaluations.

An event's value can be determined by answering three questions:

- What is the chance that the batter will score as a result of the event?
- By how much does the event increase or decrease the chances for existing runners on base to score?
- In the case of an out, by how much does the event decrease the odds of scoring in the future?

Call the first answer the *Getting On* value, the second the *Moving Over* value, and the third the
*Inning Killer* value. The total *Run Value* of an event is the sum of all three component values.

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.

0 outs | 1 out | 2 outs | |
---|---|---|---|

1B | 0.61 | 0.51 | 0.22 |

2B | 0.74 | 0.58 | 0.35 |

3B | 0.94 | 0.76 | 0.41 |

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 35%, for a net change of +13%. The Run Driving Value of that walk in this situation is +0.13.

0 outs | 1 out | 2 outs | |
---|---|---|---|

empty | +0.00 | +0.00 | +0.00 |

1B | +0.13 | +0.06 | +0.13 |

2B | +0.00 | +0.00 | +0.00 |

3B | +0.00 | +0.00 | +0.00 |

1B/2B | +0.33 | +0.25 | +0.20 |

1B/3B | +0.13 | +0.06 | +0.13 |

2B/3B | +0.00 | +0.00 | +0.00 |

1B/2B/3B | +0.39 | +0.49 | +0.78 |

0 outs | 1 out | 2 outs | |
---|---|---|---|

empty | +0.00 | +0.00 | +0.00 |

1B | +0.13 | +0.06 | +0.13 |

2B | +0.21 | +0.18 | +0.07 |

3B | +0.06 | +0.24 | +0.59 |

1B/2B | +0.33 | +0.25 | +0.20 |

1B/3B | +0.19 | +0.30 | +0.72 |

2B/3B | +0.26 | +0.42 | +0.65 |

1B/2B/3B | +0.39 | +0.49 | +0.78 |

0 outs | 1 out | 2 outs | |
---|---|---|---|

empty | +0.00 | +0.00 | +0.00 |

1B | +0.33 | +0.25 | +0.20 |

2B | +0.26 | +0.42 | +0.65 |

3B | +0.06 | +0.24 | +0.59 |

1B/2B | +0.60 | +0.67 | +0.85 |

1B/3B | +0.39 | +0.49 | +0.78 |

2B/3B | +0.32 | +0.66 | +1.24 |

1B/2B/3B | +0.66 | +0.91 | +1.44 |

0 outs | 1 out | 2 outs | |
---|---|---|---|

empty | +0.00 | +0.00 | +0.00 |

1B | +0.39 | +0.49 | +0.78 |

2B | +0.26 | +0.42 | +0.65 |

3B | +0.06 | +0.24 | +0.59 |

1B/2B | +0.66 | +0.91 | +1.44 |

1B/3B | +0.45 | +0.72 | +1.37 |

2B/3B | +0.32 | +0.66 | +1.24 |

1B/2B/3B | +0.72 | +1.14 | +2.02 |

0 outs | 1 out | 2 outs | |
---|---|---|---|

empty | +0.00 | +0.00 | +0.00 |

1B | +0.39 | +0.49 | +0.78 |

2B | +0.26 | +0.42 | +0.65 |

3B | +0.06 | +0.24 | +0.59 |

1B/2B | +0.66 | +0.91 | +1.44 |

1B/3B | +0.45 | +0.72 | +1.37 |

2B/3B | +0.32 | +0.66 | +1.24 |

1B/2B/3B | +0.72 | +1.14 | +2.02 |

0 outs | 1 out | 2 outs | |
---|---|---|---|

empty | +0.00 | +0.00 | +0.00 |

1B | -0.09 | -0.30 | -0.22 |

2B | -0.16 | -0.23 | -0.35 |

3B | -0.18 | -0.35 | -0.41 |

1B/2B | -0.25 | -0.53 | -0.56 |

1B/3B | -0.27 | -0.65 | -0.63 |

2B/3B | -0.34 | -0.58 | -0.76 |

1B/2B/3B | -0.43 | -0.88 | -0.98 |

0 outs | 1 out | 2 outs | |
---|---|---|---|

empty | +0.00 | +0.00 | +0.00 |

1B | -0.03 | -0.17 | -0.22 |

2B | +0.03 | -0.17 | -0.35 |

3B | +0.06 | +0.24 | -0.41 |

1B/2B | -0.00 | -0.33 | -0.56 |

1B/3B | +0.03 | +0.07 | -0.63 |

2B/3B | +0.08 | +0.07 | -0.76 |

1B/2B/3B | +0.06 | -0.09 | -0.98 |

0 outs | 1 out | 2 outs | |
---|---|---|---|

empty | +0.00 | +0.00 | +0.00 |

1B | -0.09 | -0.30 | -0.22 |

2B | -0.16 | -0.23 | -0.35 |

3B | +0.06 | +0.24 | -0.41 |

1B/2B | -0.25 | -0.53 | -0.56 |

1B/3B | -0.03 | -0.06 | -0.63 |

2B/3B | -0.10 | +0.01 | -0.76 |

1B/2B/3B | -0.19 | -0.29 | -0.98 |

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.

0 outs | 1 out | 2 outs | |
---|---|---|---|

empty | +0.27 | +0.18 | +0.21 |

1B | +0.09 | +0.02 | +0.06 |

2B | +0.02 | +0.02 | +0.03 |

3B | +0.00 | +0.01 | +0.00 |

1B/2B | +0.01 | +0.03 | +0.01 |

1B/3B | +0.00 | +0.00 | +0.00 |

2B/3B | +0.00 | +0.00 | +0.03 |

1B/2B/3B | +0.00 | +0.00 | +0.00 |

0 outs | 1 out | 2 outs | |
---|---|---|---|

empty | +0.24 | +0.17 | +0.13 |

1B | +0.06 | +0.07 | +0.06 |

2B | +0.01 | +0.02 | +0.04 |

3B | +0.01 | +0.00 | +0.01 |

1B/2B | +0.03 | +0.04 | +0.03 |

1B/3B | +0.00 | +0.01 | +0.01 |

2B/3B | +0.00 | +0.01 | +0.01 |

1B/2B/3B | +0.02 | +0.02 | +0.02 |

0 outs | 1 out | 2 outs | |
---|---|---|---|

empty | +0.25 | +0.09 | +0.14 |

1B | +0.05 | +0.09 | +0.11 |

2B | +0.00 | +0.00 | +0.05 |

3B | +0.00 | +0.00 | +0.02 |

1B/2B | +0.00 | +0.09 | +0.07 |

1B/3B | +0.00 | +0.00 | +0.00 |

2B/3B | +0.00 | +0.02 | +0.00 |

1B/2B/3B | +0.00 | +0.02 | +0.00 |

0 outs | 1 out | 2 outs | |
---|---|---|---|

empty | +0.40 | +0.00 | +0.20 |

1B | +0.00 | +0.00 | +0.10 |

2B | +0.00 | +0.00 | +0.10 |

3B | +0.00 | +0.00 | +0.00 |

1B/2B | +0.10 | +0.00 | +0.00 |

1B/3B | +0.00 | +0.00 | +0.00 |

2B/3B | +0.00 | +0.00 | +0.10 |

1B/2B/3B | +0.00 | +0.00 | +0.00 |

0 outs | 1 out | 2 outs | |
---|---|---|---|

empty | +0.24 | +0.20 | +0.12 |

1B | +0.10 | +0.08 | +0.05 |

2B | +0.00 | +0.03 | +0.06 |

3B | +0.00 | +0.00 | +0.01 |

1B/2B | +0.02 | +0.02 | +0.02 |

1B/3B | +0.01 | +0.00 | +0.01 |

2B/3B | +0.00 | +0.02 | +0.00 |

1B/2B/3B | +0.01 | +0.01 | +0.01 |

0 outs | 1 out | 2 outs | |
---|---|---|---|

empty | +0.21 | +0.15 | +0.13 |

1B | +0.07 | +0.05 | +0.06 |

2B | +0.02 | +0.03 | +0.05 |

3B | +0.00 | +0.00 | +0.03 |

1B/2B | +0.04 | +0.03 | +0.05 |

1B/3B | +0.00 | +0.00 | +0.02 |

2B/3B | +0.00 | +0.03 | +0.03 |

1B/2B/3B | +0.01 | +0.00 | +0.02 |

0 outs | 1 out | 2 outs | |
---|---|---|---|

empty | +0.25 | +0.19 | +0.14 |

1B | +0.06 | +0.09 | +0.08 |

2B | +0.01 | +0.02 | +0.05 |

3B | +0.00 | +0.01 | +0.00 |

1B/2B | +0.02 | +0.03 | +0.02 |

1B/3B | +0.00 | +0.00 | +0.00 |

2B/3B | +0.00 | +0.01 | +0.01 |

1B/2B/3B | +0.00 | +0.01 | +0.01 |

0 outs | 1 out | 2 outs | |
---|---|---|---|

empty | +0.26 | +0.20 | +0.17 |

1B | +0.06 | +0.05 | +0.06 |

2B | +0.01 | +0.04 | +0.04 |

3B | +0.00 | +0.00 | +0.01 |

1B/2B | +0.01 | +0.02 | +0.03 |

1B/3B | +0.00 | +0.00 | +0.01 |

2B/3B | +0.00 | +0.02 | +0.01 |

1B/2B/3B | +0.00 | +0.00 | +0.00 |

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.

0 outs | 1 out | 2 outs |
---|---|---|

0.394 | 0.263 | 0.343 |

0 outs | 1 out | 2 outs |
---|---|---|

0.353 | 0.334 | 0.313 |

0 outs | 1 out | 2 outs |
---|---|---|

0.295 | 0.318 | 0.386 |

0 outs | 1 out | 2 outs |
---|---|---|

0.500 | 0.000 | 0.500 |

0 outs | 1 out | 2 outs |
---|---|---|

0.378 | 0.348 | 0.274 |

0 outs | 1 out | 2 outs |
---|---|---|

0.342 | 0.279 | 0.378 |

0 outs | 1 out | 2 outs |
---|---|---|

0.337 | 0.354 | 0.309 |

0 outs | 1 out | 2 outs |
---|---|---|

0.343 | 0.325 | 0.332 |

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
(0.394 x 0.61)
+ (0.263 x 0.51)
+ (0.343 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 (0.38).

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

Event | Run Value | Getting On | Moving Over | Inning Killer |
---|---|---|---|---|

Walk | 0.48 | 0.45 | 0.03 | 0.00 |

Single | 0.56 | 0.45 | 0.11 | 0.00 |

Double | 0.79 | 0.54 | 0.26 | 0.00 |

Triple | 1.01 | 0.68 | 0.33 | 0.00 |

Home Run | 1.28 | 1.00 | 0.28 | 0.00 |

Strikeout | -0.57 | 0.00 | -0.19 | -0.38 |

Groundout | -0.47 | 0.00 | -0.09 | -0.38 |

Flyout | -0.48 | 0.00 | -0.10 | -0.38 |

Now that we have the relative values of each batting event, we can use them to determine coefficients for FIP/xFIP. The basic formula (does not account for park factors, etc.) for FIP for Major League Baseball is:

constant + (((13 x HR) + (3 x BB) - (2 x K)) / IP)

The point of FIP (Fielding Independent Pitching) is to estimate a pitcher's performance independent of his team's fielding
performance, so only pieces which are directly under his (and the batter's and the umpire's) control are included.
Intentionally missing from that formula are *Balls In Play* events (Single, Double, Triple, Groundout, Flyout)
since those events are, to varying degrees, affected by his team's fielding.

The coefficients (13, 3, -2) come from a formula which takes two things into account:

- the
*Run Value*of the corresponding event - the average
*Run Value*of a*Ball In Play*(BIP) event

We have the first piece, but we need to determine the value of an average *Ball In Play* event.

This table shows the frequency of each event. For example, 29% of plate appearances result in a groundout.

Event | Frequency |
---|---|

Walk | 0.06 |

Single | 0.20 |

Double | 0.03 |

Triple | 0.01 |

Home Run | 0.10 |

Strikeout | 0.07 |

Groundout | 0.29 |

Flyout | 0.24 |

This table adjusts the frequency of each event, considering only *Ball In Play* events.
For example, 38% of the time the ball is hit and is in play, the result
is a groundout.

Event | Raw Freq | Adj Freq |
---|---|---|

Single | 0.20 | 0.26 |

Double | 0.03 | 0.04 |

Triple | 0.01 | 0.01 |

Groundout | 0.29 | 0.38 |

Flyout | 0.24 | 0.32 |

Ball In Play | 0.77 | 1.00 |

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

Event | Total | Getting On | Moving Over | Inning Killer |
---|---|---|---|---|

Single | 0.56 | 0.45 | 0.11 | 0.00 |

Double | 0.79 | 0.54 | 0.26 | 0.00 |

Triple | 1.01 | 0.68 | 0.33 | 0.00 |

Groundout | -0.47 | 0.00 | -0.09 | -0.38 |

Flyout | -0.48 | 0.00 | -0.10 | -0.38 |

Ball In Play | -0.15 | 0.14 | -0.02 | -0.26 |

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).

Event | Raw | Adjusted | Final |
---|---|---|---|

Walk | 0.48 | 0.63 | 2.51 |

Home Run | 1.28 | 1.43 | 5.70 |

Strikeout | -0.57 | -0.43 | -1.71 |

Ball In Play | -0.15 | 0.00 | 0.00 |

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

constant + (((5.705 x HR) + (2.508 x BB) + (-1.711 x K)) / IP)

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

Run Values can also be used to calculate wOBA coefficients, where wOBA is:

(((c0 * BB) + (c1 * 1B) + (c2 * 2B) + (c3 * 3B) + (c4 * HR))/ Plate Appearances)

Each coefficient is:

(Corresponding Run Value - (Run Value of an Out)) * constant

The run value of an out (combinging strikeouts, groundouts, and flyouts) is -0.487.

The constant should be the difference between the league-average constant-less wOBA (0.548) and the league-average OBP (on-base percentage; 0.398) so that the league-average wOBA is roughly equal to the league-average OBP. SLW uses a constant of 0.728.

Event | Raw | Adjusted (for outs) | Final (with constant) |
---|---|---|---|

Walk | 0.482 | 0.968 | 0.705 |

Single | 0.564 | 1.051 | 0.764 |

Double | 0.793 | 1.280 | 0.931 |

Triple | 1.011 | 1.497 | 1.089 |

Home Run | 1.281 | 1.768 | 1.286 |