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Tuesday, February 09, 2010
Sabre-nerd FIP fight: IP or PA, MaryAnn or Ginger? A Primer on creating a metric
Matt noted that using IP (instead of PA) in the denominator of FIP to look wrong because IP includes batted ball as outs, and the point of FIP is to ignore batted ball as hits or outs. He is 100% correct about that.
However, is FIP “wrong” for having IP in the denominator? No, and I’ll describe for you the reason. First, let’s start off with creating a baseline. It’s not that important what we have in the baseline, but it gives us a starting point. This is what I use:
IP BB K HR BABIP
9 3 6 1 0.300
We have a 9 inning game, with 3 walks, 6 K, 1 HR and a .300 BABIP. With 27 outs and 6 from K, that gives us 21 outs. For the purposes of this baseline, I’ll treat 95.24% of those outs from batters, and 4.76% from runners. So, this gives us 20 outs from batters and 1 out from runners. This is what we have so far:
IP BB K HR BABIP BIPouts
9 3 6 1 0.300 20
In order to get a .300 BABIP with 20 BIP outs, we need to have 8.57 BIP hits. That is, 8.57 / (20 + 8.57) = .300. We have this:
IP BB K HR BABIP BIPouts BIPhits
9 3 6 1 0.300 20.00 8.6
The number of batters faced is simply BB+K+HR+BIPouts+BIPhits. In this case, it’s 38.87. We are now here:
IP BB K HR BABIP BIPouts BIPhits PA
9 3 6 1 0.300 20.00 8.6 38.9
How many runs should that line produce? Using a short-cut BaseRuns formula, I get 4.31. Again, not too important what the BaseRuns formula is. I just need a baseline. And FIP comes in at exactly 4.31. So, we are now calibrated.
Now, what happens if I change K to 2? In order to get every to make sense, I get this:
IP BB K HR BABIP BIPouts BIPhits PA
9 3 2 1 0.300 23.81 10.2 40.3
We get more BIPouts, more BIPhits, and more PA. The number of runs scored according to BaseRuns is 5.20. FIP? 5.20.
Here is how BaseRuns and FIP compares with the K value changing from 2 to 12:
IP BB K HR BABIP BIPouts BIPhits PA R FIP diff
9 3 2 1 0.300 23.81 10.2 40.3 5.20 5.20 0.00
9 3 4 1 0.300 21.90 9.4 39.6 4.75 4.76 (0.01)
9 3 6 1 0.300 20.00 8.6 38.9 4.31 4.31 (0.00)
9 3 8 1 0.300 18.10 7.8 38.2 3.89 3.87 0.03
9 3 10 1 0.300 16.19 6.9 37.4 3.50 3.42 0.07
9 3 12 1 0.300 14.29 6.1 36.7 3.12 2.98 0.15
The third-to-last column in R (baseruns), the 2nd-to-last column is FIP, and the last column is the difference. We see therefore that up until about K=10, the FIP equation holds extremely well, even though it uses IP, not PA, in its denominator. But, as Matt correctly points out, it SHOULD be PA, not IP. And, it’s apparent we are going to pay a price when K > 12. So, yes, FIP will breakdown at those extremes.
Now, what if we DID use PA instead of IP? What happens to FIP? The new formula for FIP becomes the following for the numerator: 13*HR + 3*BB - 1.93*SO. So the “2” becomes “1.93”. And for the denominator, we get: PA*.23. So, we turn IP into PA*.23. This becomes our new results (and I extended the chart to K=20):
K R FIP(IP) diff FIP(PA) diff
2 5.20 5.20 0.00 5.10 0.11
4 4.75 4.76 (0.01) 4.71 0.04
6 4.31 4.31 (0.00) 4.31 0.00
8 3.89 3.87 0.03 3.90 (0.00)
10 3.50 3.42 0.07 3.46 0.03
12 3.12 2.98 0.15 3.02 0.11
14 2.77 2.53 0.24 2.55 0.22
16 2.45 2.09 0.36 2.07 0.38
18 2.15 1.64 0.50 1.56 0.59
20 1.88 1.20 0.68 1.03 0.85
The first four columns is a repeat of the previous table, which shows the FIP equation based on IP. The second-to-last column shows FIP based on the PA-based equation, and diff is the difference between BaseRuns and the new FIP. Now, we see that either equation is pretty close. There’s really not much to choose from.
So, if I’ve got a choice to use 2 or 1.93 in the numerator, I’ll go for 2. And if I have a choice between IP or PA*.23, I’ll use IP in the denominator.
And that’s why FIP uses what it does.
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