Evaluating the Gap Between ERA and FIP

Fielding Independent Pitching (FIP) has displayed an ability to accurately measure a pitcher’s true skill. Fangraphs describes FIP succinctly as “a measurement of a pitcher’s performance that strips out the role of defense, luck, and sequencing, making it a more stable indicator of how a pitcher actually performed over a given period of time than a runs allowed based statistic that would be highly dependent on the quality of defense played behind him…”

This definition recognizes three factors that may differentiate the runs a pitcher is expected to surrender (FIP) versus the runs a pitcher actually surrenders.

  • Defense
  • Sequencing
  • Luck

FIP removes these factors by only measuring the events that are within control of the pitcher and therefore accurately reflect the skill of the pitcher. These events are strikeouts, walks, batters hit by pitch and homeruns. All other events, which are balls put into play, may result in outs, bases, runs, or errors, but are outside the pitcher’s complete control.

The general measure of over- or under-performance of a pitcher’s true skill is ERA-FIP. ERA measures the earned runs given up by a pitcher based on all the events that happen, opposed to FIP’s measurement of runs given the limited events over which a pitcher has complete control. Therefore, the variance between ERA and FIP is attributed to the three factors noted above: defense, sequencing and luck.

But how much of the difference between pitching results and pitching skills are attributable to defense, sequencing, and luck, respectively? And shouldn’t the opponent get some credit for widening the gap between ERA and FIP, either to the benefit or detriment of the pitcher?


I compared Ultimate Zone Rating (UZR), Defensive Runs Saved (DRS), and Fangraphs’ Defensive Runs Above Average (DEF) to ERA-FIP for each team season between 2005–2015 to try to understand the effect of defense on pitching results.

All the metrics have similar correlations, but DRS has the highest adjusted r-squared (correlation coefficient) value (.39), which measures how much of the variance in ERA-FIP is correlated by the defensive metric. Fangraphs’ DEF was right behind DRS (.37) and UZR had an adjusted correlation coefficient of (.34).

The result was somewhat surprising, because DRS and UZR do not factor in positional adjustments (UZR also does not measure catcher or pitcher defense). These metrics measure a player against the average player at that player’s position. They do not measure the difficulty of the position in comparison to other positions.

DEF does apply positional adjustments. Fangraphs uses UZR, not DRS, as the metric they apply the positional adjustments to in order to determine DEF. (see notes below for further explanation of positional adjustments)

Still, the non-positionally adjusted DRS correlates most closely to ERA-FIP. However, it does seem that the advantage over DEF is negligible.

All in all, defense, considered alone, appears to explain 35–40% of a team’s ERA-FIP.


I chose to use a team’s Run Expectantcy based on 24 base-out states (RE24) to measure the effects of sequencing. RE24 measures the change in run expectancy between the time a batter comes to the plate and the run expectancy after the plate appearance. The up and down of these changes will reflect the sequence of events experienced by each team (see notes below for further explanation of RE24)

The relationship between ERA-FIP and RE 24 has a similar correlation coefficient (.38) as ERA-FIP and the defensive metrics. Sequencing seems to play a role nearly equal to defense in determing the over- or under-performance of pitchers.


Defense and sequencing are not exclusive though. The reason that the single in the Bottom of the 9th occurred is likely related to the fact that the shortstop and/or third baseman did not have enough range to get to the ground ball hit between them. Therefore, I measured the correlation of ERA-FIP to defense and sequencing.

Again, DRS+RE24 (.54), DEF+RE24 (.53), and UZR+RE24 (.51) all yielded similar adjusted correlation coefficients.

This suggests roughly 50% of the difference between ERA and FIP are correlated to defense and sequencing. The other half of the difference is not the great unknown, but it’s (sort of) immeasurable.


Luck is part of the other half of the gap between ERA and FIP, but is luck really 50% of what separates a pitcher’s result from a pitcher’s skill?

The skill of the opponent in running the bases is probably a greater part of the other 50% than luck is. This was on display in the playoffs, whether its Lorenzo Cain scoring from first on a single; Daniel Murphy taking third base from first base on a walk, or one of the other examples of aggressive (and smart) base running witnessed throughout the playoffs. These events change run probabilities and create runs. These base running events tend to be less noticed during the 162 game season, but they still happen.

Some of the ability for catchers and pitchers to prevent stolen bases is cooked into the defensive metrics, but not much else is. Fangraphs’ Base Running (BsR) measures the base running abilities of players and teams, from an offensive perspective, but to my knowledge there is no accumulated stat to measure opponents’ BsR. The data is out there. The same measures used to determine BsR would only have to be aggregated from the perspective of the pitching team.

A measure of Opponents’ BsR would likely cover a good amount of the uncorrelated variance between ERA and FIP. There would still be a lot of luck left in play, but probably not as much as there is thought to be now.


Notes:

Positional Adjustments: A shortstop starts with a +7.5 positional adjustment due to the difficulty of the position. Therefore, before a shortstop does anything, good or bad, DEF attributed +7.5 runs saved to the shortstop. Every UZR run saved or lost attributed to that shortstop will be adjusted from the +7.5 starting point. Therefore, if you see a shortstop with a 0 DEF, it indicates that his UZR is -7.5.

RE24: The run expectancy when a batter comes to bat with no one on base and no outs is (.479).If the pitcher retires that batter the run expectancy is reduced to (.257). The difference between the initial run expectancy and post-plate appearance run expectancy will be added to RE24. However, if that batter hits a double, the run probability will rise to (1.08%) and the increase in run expectancy will be subtracted from RE24.