WAR for Pitchers

Editor’s Note: This page is slightly out of date and will be updated in the future. Some important changes since it was originally written: WAR uses FIP plus infield flies as strikeouts, FanGraphs now uses FIP-specific park factors, and reliever WAR includes a leverage component. 

While it was relatively simple to come up with the offensive statistic to base WAR around for position players — wRAA is a well accepted, context-neutral stat for measuring offensive value — it was more difficult to settle on how to account for pitching win values. Do you give a pitcher credit for their defense behind them? Do you focus on their runs allowed, or do you strip that away and focus instead on how well they pitched? Or in other words, how much noise do you leave in, and how much do you strip down to signal?

In order to match up with the theory behind WAR for position players, FanGraphs has traditionally used a context-neutral statistic (Fielding Independent Pitching (FIP)) in order to express a pitcher’s value to their team. Here are a couple reasons why:

● FIP strips away the influences of team defense, focusing solely how variables that a pitcher has control over.

● FIP also involves considerably less regression than other ERA Estimators like SIERA and xFIP, making it a better measure of value added. While SIERA and xFIP estimate a player’s hypothetical home run and BABIP rates based on different criteria, FIP uses a player’s actual home run rate in its calculations.

● These factors make FIP a good middle-ground option. It strips away the impacts of defense and measures a pitcher’s skill, but it doesn’t merely regress away abnormal results. If a pitcher should have allowed 20 home runs (based on his regressed home run rate) but actually gave up 30 home runs, he was a less valuable pitcher to his team than a stat like SIERA or xFIP would have you believe. Those two stats are better at predicting the future, but FIP is better at capturing past value.

Recently, FanGraphs has also started calculating other additional win values for pitchers. Learn more about them here: Fielding Dependent Pitching (FDP).

The next step — turning a pitcher’s FIP into a win total — is no easy thing. Brief explanations of the steps are below, but you can find more detailed information in Dave Cameron’s WAR series (linked at the bottom of the page).

Replacement Level. While league average changes on a year-to-year basis, replacement level stays the same: a .380 win% is the replacement level for starting pitchers, and a .470 win% is the replacement level for relief pitchers. Replacement level FIP is set each year, and it varies depending on the league the player was in and if they were a starter or a reliever. The American League generally has a higher replacement level, as the DH makes offense more prolific in the AL.

So if league-average for American League starters was a 4.40 FIP, then replacement level would be set at the appropriate mark above that for a pitcher with a .380 win% (in this example: 5.63 FIP).

Run Scale. Since FIP is calculated so that league-average FIP is always the same as league-average ERA, it’s on an Earned Runs scale — not a Runs Allowed scale. For the purposes of calculating WAR, though, it’s important to have FIP values on a runs scale, since that’s the same scale that offensive WAR is based on (see: wRAA). To convert FIP onto a runs scale, you divide FIP values by .92.

Park Adjustments. Replacement level FIP varies depending on the park a pitcher plays in. If a 5.63 FIP was the replacement level for an AL starter, and one ballpark depressed offense by 2%, then the replacement level FIP for that park would be 5.52 FIP — 2% lower than the AL replacement level. Pitchers only play half their games at home, though, so they only need to have their FIPs adjusted by half their home park factor.

FanGraphs uses a five-year regressed park factor in its calculations, as single-season park factors can be flaky and variable.

Run Environment. If an elite pitcher is on the mound, their team typically doesn’t need to score as many runs to win a game as they would if they had an average pitcher on the mound. In this sense, pitchers influence their own run environment, and elite pitchers will have a lower Runs Per Win conversion rate. So while league-average is 10 Runs/Win (just like with position players), star pitchers will have lower Runs/Win rates and replacement level pitchers will have higher Runs/Win rates. The conversion formula is: ((League RA + Pitcher’s RA)/2)+2)*1.5

Put this all together, and voila, you have your pitcher WAR values! It’s not the easiest thing to engineer yourself, but it is possible. And if you’d like a detailed example of how to mathematically carry out these steps, see this piece by Dave Cameron.

Any other questions? Be sure to read through the entire Pitcher WAR introduction series: