Pitcher Win Values Explained: Part Four

As we talked about last night, pitcher replacement level is set at a .380 win% for starters and .470 win% for relievers. However, because of the differences between the AL and the NL, as well as varying offensive levels over the years, that means that there isn’t a fixed mark that we can point to as replacement level FIP that works for each year and each role.

However, since we’ve got the .380/.470 marks, we can derive those numbers with just a little bit of work. Let’s walk through the process, first using a 2008 American League starting pitcher as our example.

The league average runs per game in the AL last year was 4.78. The FIPs that are displayed on the pitcher’s player card here at FanGraphs are scaled to ERA, but for the win values, we modified the formula slightly to scale it to match league RA. However, there’s a shortcut if you want to take a pitcher’s traditional FIP and have it match up with the league RA – that’s dividing his FIP by .92.

For instance, a 4.40 FIP divided by .92 will give you a 4.78 FIP. That .92 is the ERA-RA bridge, and allows us to conclude that 4.40 would be a league average FIP in the American League last year. So, a pitcher with a 4.40 FIP in a neutral park would be a league average pitcher. Or, put back into win% terms, a .500 pitcher.

Now, because we’ve set replacement level at .470 for relievers and .380 for starters, we know that a replacement level FIP for an AL reliever will be a lot closer to 4.40 than it will be for a starter. How much closer? Running the numbers through the formula gives us a 4.68 FIP (traditional, not scaled to RA) for an AL reliever and 5.63 for an AL starter. So, if you’re looking at a pitcher’s FIP here on his FanGraphs page, and that pitcher happens to be in the American League, those are the numbers you’d want to compare him to in order to see how far away from replacement level he is.

For the NL in 2008, the numbers are 4.45 for a reliever and 5.37 for a starter – the lack of a DH drives down the league’s offensive level, and so the performance of a replacement level pitcher will appear better in the NL than in the AL.

Remember, these are park neutral numbers, so if you’re looking at a player who pitched in a park that significantly effects offense, you’ll have to adjust his FIP to account for the park effects. If the NL starter that we were looking at pitched in a park that suppressed offense by 5%, then a replacement level for that park would be 5.10, not 5.37. Thus, you’d want to use the lower replacement level for his home innings, and the league average replacement level for his road innings. Assuming equal distribution, that would make the replacement level FIP 5.23 for that NL starter pitching in a park with a park factor of .95.

As you can see, the run environment that the pitcher exists in has a substantial effect on the replacement level value. But the impact of run environments don’t stop there, and are further complicated by the fact that starting pitchers have a significant impact on their own run environment. The expected offensive level is a lot lower in a game where Johan Santana is pitching than where Cha Seung Baek is pitching. In order to calculate the runs to wins conversion for each pitcher, we have to take into account that a pitcher impacts his own run environment. We’ll talk more about this later this afternoon.

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Dave is the Managing Editor of FanGraphs.

11 Responses to “Pitcher Win Values Explained: Part Four”

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  1. Jim C. says:

    I’m tired of you constantly ragging on Cha Seung Baek.

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  2. Torx says:

    With regards to the wonderful work you have all done here (with which I will waste many, many hours), I’d like a clarification.

    If a ballpark suppresses or inflates offense by x%, why would you adjust the FIP by that same percentage?

    If I understand FIP correctly, only one of the variables can be affected by park conditions. Does FIP scale appropriately with park conditions such that you can make this calculation? Or should you do something in the order of “since Safeco Field suppresses offense by x%, you adjust the FIP by x over y% since there are park conditions that do not factor into HR?”

    Thanks again for the great work!

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    • Dave Cameron says:

      Parks actually do have an impact on walks and strikeouts. Dave Studeman covered this in the Hardball Times Annual a few years back.

      And, that’s actually somewhat besides the point. Regardless of what factors the park actually impacts, the win value of a run changes with the environment. In a park where you only have to score three runs to win, a 5.00 FIP is much less valuable than it is in a park where you have to score six runs to win.

      If we were projecting future performance, component park factors would be necessary. For retrospective valuation, it isn’t.

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  3. azruavatar says:

    There’s still little explanation as to how the 38% is actually derived. A link to an old tango post in which he says he sets it at 38% but no indication as to how the result was really arrived at.

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    • Dave Cameron says:

      Historical, empirical evidence gives us a .300 win% for a team of replacement level players. To win 30% of your games, however, does not mean that you have a .300 win% run scoring and .300 win% run prevention. Because of the multiplicative effect, a perfectly balanced team of replacement level players would have a .395 offense and a .395 defense.

      Run prevention is divided up between starters, relievers, and defenders, based on their retrospective amount of responsibility. The results of slicing .395 those three ways is .380 for starters and .470 for relievers.

      Read this and this for more data.

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      • Colin Wyers says:

        I’m starting to come around to the idea that the split shouldn’t be even – that a replacement-level team is worse on offense than defense, typically. We know, after all, that our typical replacement-level hitters are also typically average defensively.

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  4. MattS says:

    This is a little bit nit-picky, but it’s not really proper to divide by .92 for every one. Unearned runs occur less frequently for strikeout pitchers and flyball pitchers, because balls in play are more likely to be botched than strikeouts and groundballs are especially likely to be botched. I would think it’s best to re-devise coefficients based on a regression of RA on K/9 BB/9 and HR/9, and then do the adjustments you’ve done to that FIP.

    The goal here is a proper ordering of players. While these effects may be small, you want a consistent estimator that properly orders players by their effects on run prevention.

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  5. Sean Kingston says:

    How do you go from a 4.40 league FIP for the AL to a 4.68 replacement level for relievers and 5.63 for starters?

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    • Noah says:

      Well I think the league average calculation is as follows. For starters:

      4.40 / (.38 / .5) = 4.4 / .76 = 5.79

      4.40 / (.47 / .5) = 4.4 / .94 = 4.68

      So it looks like they messed up the starting pitcher replacement level calculation.

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