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Monday, August 11, 2008
Translating Relievers into W/L records
Your reliever gets an out. Your chances of winning go up. Your reliever allows a runner on. Your chances of winning go down. You add up the deltas of all the times that your chances went up, and you add up all the deltas of all the times your chances went down. Call the former “Win Advancement” (WA) and call the latter “Loss Advancement” (LA). WA+LA is GA (Game Advancement).
If you start the game at zero, you are marching toward 1 Win or 1 Loss. In a typical win, the pitching team will accumulate 1.8 WA and 0.8 LA. The difference in WA and LA, for every win, is always 1.0. Always. That is, on your march toward a win, you’ll accumulate some good things and some bad things. And in a win, you’ll accumulate alot more good things than bad things. The difference, in a win, will always be +1. Similarly, in a typical loss, the pitching team will accumulate 0.8 WA and 1.8 LA, with the difference always being -1.
So, in an average game, you have 1.3 WA, 1.3 LA, 0.5 wins, and 0.5 losses. The WA and LA capture the ebb and flow of the game, on your march toward the win or loss of the game. There is, on average, some 0.8 “wasted” WA and 0.8 “wasted” LA per game (2.6 GA minus 1 game). In order to align WA and LA to W and L, simply subtract the waste (average of 0.8 wasted advancements on each side) from the total accumulation in each game (average of 2.6 GA) from each of WA and LA.
Before we talk about relievers, let’s look at the last generation’s four greatest starters:
Clemens, Maddux, Pedro, RJ. You can order them however you want. (Curt Schilling, John Smoltz, Kevin Brown, Mike Mussina, and Tom Glavine would be on level below the big four.) Per 9 IP, the Big 4 was on the mound for roughly 1.39 win advancements and 1.13 loss advancements. In their games, they had a total of 2.52 game advancements. Since there was a total of 1.52 wasted advancements, we subtract half of the waste (.76) from each the WA and LA. The Big 4’s WA of 1.39 become .630, and their LA of 1.13 become .370.
So, that’s what our Big 4’s win% becomes: .630. (In reality, their career win% is .647, part of which due to these 4 playing on better than .500 teams.)
As we noted, we want, on average, to subtract 0.8/2.6 WA and LA to align it to our more easily understood W/L record. Let’s look at Mariano Rivera. He has accumulated 289 WA and 202 LA (for a total of 491 GA). In order to convert that to the more easily understood W/L numbers, we remove .8/2.6*492 (or 151) from each of his WA and LA. Mariano Rivera’s W/L record becomes 138-51, for a .730 win%.
That is, Mariano’s actual 66-48 W/L record with 471 saves is equivalent to a starting pitcher going 138-51. For a frame of reference, Sandy Koufax, from 1961-1966, had a 129-47 record. Pedro, from 1997-2004, had a 134-45 record.
We can follow this process for the other relievers. Among the contemporaries (includes stats as starters):
138-51 Rivera
132-65 Hoffman
106-88 Wickman
105-50 Wagner
93-55 Wetteland
91-46 Percival
87-55 Benitez
83-53 Nen
And if we look at some old-timers:
174-115 Goose Gossage
153-106 Lee Smith
142-106 John Franco
125-88 Bruce Sutter
123-94 Kent Tekulve
121-95 Jeff Reardon
112-91 Rollie Fingers
104-64 Dan Quisenberry
97-70 Jeff Montgomery
91-49 Tom Henke
Compare Bruce Sutter and Kent Tekulve’s career, beyond this W/L style representation of WPA. Are there more two players who performed as similarly as they did but are regarded overall as so differently? And, based on these numbers, it would seem that Hall of Fame voters have been too loose in their allowing relievers. You can make a case for Goose Gossage, but Bruce Sutter and Rollie Fingers?
***
For those who want to try it out for other pitchers, here’s a step-by-step:
1. Take the +WPA and -WPA numbers on Fangraphs, and double them. That gives you WA and LA.
2. Add WA and LA to give you GA
3. Take 0.8/2.6. Call this the Wasted Rate
4. Take the Wasted Rate, and multiply by GA. That’s the Wasted Amount.
5. Remove the Wasted Amount from WA and LA.
For example, Gosse Gossage:
1. 203.0 +WPA, 173.5 -WPA becomes 406 WA, 347 LA.
2. 406 + 347 = 753
3. .308
4. .308 times 753 equal 232
5. 406 minus 232 = 174; 347 minus 232 = 115
Gossage has a 174-115 W/L record.
Note that in steps 3/4, you would really want to do it on a game-by-game basis. So, sometimes, you have .25 wasted movements, and other times you might have .50 wasted movements, etc, etc. The average is around .30 wasted movements. (Just an educated guess.)
If there’s enough support for this kind of translation and presentation (i.e., just showing the final record as 174-115 for Gossage), maybe we can friendly push Fangraphs and/or Baseball-Reference to adopt this process.
Hope you digested all that. Here are the big 4’s WPA in W/L style (with real W/L record in parens):
343-191 Clemens (354-184)
319-210 Maddux (353-222)
276-169 RJ (293-158)
192-90 Pedro (212-96)
As you can see, a pitcher’s career W/L record does a pretty decent job at capturing his overall effectiveness.
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We can follow a similar process for hitters. Let’s take the greatest of them all (for whom we have PBP): Barry Bonds. His Fangraphs numbers are 311.25-185.59. Once we follow our process laid out above (with win% in parens):
317-65 Bonds (.829)
How about:
264-127 Rickey (.675)
212-130 Palmeiro (.621)
204-130 Molitor (.611)
200-99 Raines (.669)
178-86 ARod (.675)
175-101 Boggs (.633)
165-75 Edgar (.689)
120-32 Pujols (.788)
***
Now, can we just add the hitters numbers to the pitchers numbers for a team record? No!
If you are following along, we are giving pitchers, for each game, a total of 1 W+L. So, the total at the seasonal level is 162 W+L per team.
Same for hitters.
The reason, here and only here, is because we are trying to mimic the W/L situation. And the W/L implementation in vogue is to give 162 decisions to the pitchers.
Now, if we want to do it the right way, such as giving about 3/7ths to pitchers and 4/7 to nonpitchers (including fielding), we’d have a different implementation.
But, to the extent that we want to give 162 decisions to pitchers and 162 decisions to hitters, what we’ve done here is what you want.