by Kevin Harlow
February 5, 2003
Rob Wood presented the results of his simulations of 5 usage patterns for Stoppers in his More on the Modern Bullpen. What follows is some additional comments on Wood's fine work.
The five usage patterns that he investigates are as follows:
Case 1: Stopper pitches 9th inning if save situation (lead of 1, 2, or 3 runs).
Case 2: Stopper pitches 9th inning if save situation or game is tied (lead of 0, 1, 2, or 3 runs).
Case 3: Stopper pitches 8th and 9th innings if a save situation (lead of 1, 2, or 3 runs).
Case 4: Stopper pitches 7th, 8th, and 9th innings (two innings max) if game is within one run (lead of -1, 0, or 1 run).
Case 5: Stopper pitches 7th inning if a 1-run lead, and the 8th and 9th innings if tied or a 1-run lead (two innings max).
I've summarized Wood's IP and WAA data for each case and added some additional calculated quantities in the following table.
case ip WAA G_est WAA/(9IP) WAA/58G_Est WAA_SP LI 1 42 2.17 42.0 0.47 3.00 1.17 1.86 2 58 3.39 58.0 0.53 3.39 1.61 2.10 3 88 4.09 58.7 0.42 4.04 2.44 1.67 4 142 6.33 85.2 0.40 4.31 3.94 1.60 5 92 5.35 57.5 0.52 5.40 2.56 2.09
case = case number
IP = innings pitched
WAA = wins above average
G_est = games Stopper played in, estimated below
WAA/(9IP) = WAA/(ip/9)
WAA/58G_est = WAA * (58 / G_est)
WAA_SP = wins above average for starting pitcher with *ERA+=200, PF=1
= (ip/9)*(4.86-.5*4.86)/(2*4.86)
LI = leverage index = (WAA / WAA_SP)
The estimated number of games the Stopper appears in, G_est, was calculated from the following equations by solving for G:
Case 1: IP = 1 * G
Case 2: IP = 1 * G
Case 3: IP = (1/2 * G) + (2* 1/2 * G)
Case 4: IP = (1/3 * G) + (2 * 2/3 * G)
Case 5: IP = (0.4 * 1 * G) + (0.4 * 2 * G) + (0.2 * G * 2)
Case 1:
Using your Stopper only in 9th inning save opportunity situations is not an effective usage pattern. Although the leverage index ranks in the middle of the usage patterns investigated, the low number of IP results in significantly fewer wins above average than the other options.
Case 2:
I believe the current typical Stopper usage pattern is closest to Case 2, with the Stopper also pitching a few extra games to keep him sharp during the stretches that there are no situations defined by this scenario. This usage pattern has the highest LI but the second lowest IP. If you were to include the Metamucil appearances the WAA may be about 3.75.
Case 3:
Even with 50% more IP, the WAA for this scenario is only slightly higher than Case 2 because of the huge difference in LI. Also, pitching two innings may result in a slightly lower *ERA+.
Case 4:
Although this case results in the most WAA, the extreme number of IP makes this option not viable. In addition to the likely increased injury risk, the *ERA+ would likely not be as high. Because of the lowered *ERA+, the 6.33 WAA from the simulation overestimated the effect - perhaps it would only be 4.5 or 5 WAA.
Case 5:
This usage pattern results in a high WAA due to a combination of high LI and reasonable IP. However, now the reliever must be prepared to come into the game in 3 different innings and also possibly pitch 2 innings.
The WAA produced by the simulation is based on an *ERA+=200 Stopper. However, there aren't very many of those. For instance, the top 16 pitchers in saves had the following numbers in 2002:
*ERA+ Name
127 J Smoltz
192 E Gagne
147 M Williams
127 J Mesa
151 E Guardado
142 B Koch
172 R Nen
138 J Jimenez
226 T Percival
148 U Urbina
140 T Hoffman
105 K Escobar
166 K Sasaki
216 B Kim
170 B Wagner
172 A Benitez
There are only 2 *ERA+=200 guys on the list, or 3 if you include Gagne who was close, and the average is only *ERA+=159. Given that the *ERA+=159 includes partial innings of 2 and 1 outs, the assumed *ERA+=200 for Stoppers pitching a full 3-out inning is more like an upper end. The differences in the various cases will be smaller than reported from the simulations and possibly even smaller for those cases which require a pitcher to pitch 2 innings more frequently.
The effect of the *ERA+ on the differences between the usage patterns is significant. With an *ERA+=200, the difference between Case 5 and Case 2 is 1.96 wins. What about if the *ERA+=150? Do you have to re-run the simulation? Not if you just want a rough answer. Since the LI is known, you can estimate the WAA.
For example, in Case 2, the pitcher throws 58 innings with a LI=2.10. The league average RPG was 4.86.
WAA = (58/9) * [(4.86 - 4.86/(150/100)) / (2*4.86)] * 2.10
WAA = 2.26
In Case 5, the pitcher throws 92 innings with a LI=2.09.
WAA = (92/9) * [(4.86 - 4.86/(150/100)) / (2*4.86)] * 2.09
WAA = 3.56
Thus, replacing the *ERA+=200 pitcher with an *ERA+=150 pitcher reduces the difference in wins between Case 5 and Case 2 from 1.96 to 1.30.
Conclusions:
The usage question comes down to whether you want to maintain the the current Stopper usage pattern, which is Case 2 plus some appearances, or try the multi-inning, high-leverage usage pattern of Case 5. The 2 additional simulated wins of Case 5 is tantalizing, but is a bit of a mirage since the simulation results overstate WAA. Few Stoppers have an *ERA+=200 (top saves guys averaged *ERA+=159 in 2002) and their ERA is aided by pitching some partial innings. Also, few of the Stoppers currently have many multi-inning appearances. If the simulation used an *ERA+=150 Stopper, which is much more reasonable given the previous factors, the difference between Case 2 and Case 5 is cut by a third to about 1.3 wins, and reduced further to say 1.0 (for a round figure) by the additional appearances outside of Case 2. But even the 1 extra win is possibly too much. Case 5 would require the Stopper to warm up unnecessarily many times. This may increase the injury risk , decrease performance over the course of a season, or negatively affect the Stopper psychology - the exact effect is unknown but most likely negative. So does the reward of an potential extra win offset the additional risk to your valuable closer? I don't think it's worth the risk.
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