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# Re-introducing the Hall of wWAR: The Hall of Fame Re-populated by a Mathematical Formula

It was just over eight months ago that I released the Hall of wWAR. That project was far and away the most fun I've had with baseball analysis.

Today I bring you an updated version of the Hall of wWAR. Last time, I received a ton of great feedback from the readership and I've slowly been chipping away at a new formula. Now that the Hall of Fame season is upon us again, it's time to pull back the curtain on the new Hall of wWAR.

There are several key differences between the first version and this new version:

WAR/162: In 1872, Ross Barnes posted 5.2 WAR. In 2011, Prince Fielder also posted 5.2 WAR. But which was more impressive? Fielder produced his 5.2 wins in a 162 game schedule. Barnes did the same in a 48-game schedule. WAR/162 projects Barnes’ WAR to a 162-game schedule, making him worth 17.6 WAR/162 (Yikes!). WAR/162 is a much better approach than what I used last time—a lower arbitrary wWAR cutoff for 19th century players. WAR/162 also gives a boost to players who played 154 game schedules and those who missed time because of work stoppages. I wrote about WAR/162 (for hitters and pitchers) on this very site.

Postseason wWPA: Postseason statistics break the "small sample size" rule, but postseason heroics absolutely add to a player’s Hall of Fame case (while being a postseason goat hurts some). Since there is no postseason WAR, how can we capture that? We can use Win Probability Added (WPA), which measures a player’s contribution to his team’s victory. Add up his WPA and you have an estimate of the number of wins he was directly responsible for. I recently introduced a modification of postseason WPA called (of course) wWPA (Weighted postseason Win Probability Added). The theory behind wWPA is that not all postseason series are created equal. I count the LDS once. I double count the LCS. And the World Series? It counts three times.

Variable WAE and WAM thresholds: I had a problem with 19th century starting pitchers having unusually large WAE and WAM totals. The reason is because they were used much differently and accumulated huge single season WAR totals. They absolutely should get credit for that. But the boost that they get from WAE and WAM should be relative to their workload. So, now as the innings go up, so do the expectations of WAE and WAM. I also have lower thresholds for seasons in which the player caught most of the time or pitched almost exclusively in relief.

Hitting and Pitching WAR for all: Now, Sandy Koufax's value takes a hit because of his awful offense while Walter Johnson's is helped. It also means Jesse Burkett takes a hit for some lousy pitching performances. Most importantly, it means we have a better idea of Babe Ruth and John Montgomery Ward's overall value.

Removed most additional position adjustments: Last time I had different wWAR baselines for corner outfielders, middle infielders, etc. Acknowledging that position is already adjusted for in WAR itself, I did away with almost all of them. The remaining positions with different baselines are catchers (their careers don't last as long), relief pitchers (there's just no other way they can compete), and 19th century pitchers (because they're oh so tricky).

Once again, each of these changes came directly from reader feedback. As a result, the new formula for wWAR is:

wWAR = WAR/162 + WAE + WAM + wWPA

Enough math. Let's talk about the Hall itself. Here are some key observations I've made:

1. Wes Ferrell, to me, was the most surprising new addition. Despite his high career ERA (4.04), Ferrell's pitching career is actually quite similar to Andy Pettitte's. Ferrell threw 2623 innings with a 117 ERA+ and 41.3 WAR. Pettitte threw 3055 innings with a 117 ERA+ and 49.9 WAR. So, two full 4.3 WAR seasons separate them. Substantial, but not enormous. There are two bigger differences between the two, though. Ferrell has a very condensed peak. In his age 21 to 28 seasons, he was worth 42.3 WAR on the mound. That's actually more than his career total. The other eight seasons of his career were under replacement level. This condensed peak really boosts his WAE and WAM numbers. The other thing that sets Ferrell apart from his peers is his offense. He was worth an additional twelve wins at the plate. That not only boosts his career WAR total, but it also boosts his single season WAR totals, which in turn gives him even more WAE and WAM. During his age 21–28 seasons, he was worth 10.3 WAR at the plate. Combine that with his pitching and you have 52.6 WAR in eight seasons (6.6 WAR per season). Now it starts to make sense.
2. Pud Galvin was the most surprising new subtraction. It never occurred to me that Galvin could be bumped. He won 365 games. He threw 6000 innings. He had a 19.1 WAR season in 1884. He was worth 71.3 WAR as a pitcher. But many of the new adjustments tore Galvin apart. In the seasons where he compiled his highest WAR totals, he also threw a ton of innings, limiting his WAE and WAM gains. But the biggest change that kills Galvin is the fact that he was worth –11.8 wins at the plate. It essentially had the opposite effect that it had on Ferrell.
3. The new WAR/162 component allowed the inductions of Charlie Bennett, Ross Barnes, Ezra Sutton, and Paul Hines. These are actually the players I expected that change to help the most, so that was nice to see.
4. Tommy John got bumped (not from the Hall of Fame, rather from the last version of the Hall of wWAR). I'm a big Tommy John supporter. It was nice to be able to say he belonged on statistical merit alone. That doesn't actually appear to be the case, though. However, I'd still put him in. This cold stathead had a touchy-feely place in his heart for the Tommy John story.
5. The first time, we had 66 new players inducted (and 66 booted). This time, it is down to 64. It's nice to see that with more adjusments, we actually had a bit less turnover.
6. Many of the new inductees this time were 19th century players, meaning some of the 20th century players that squeaked by last time didn't make it in this time. That list includes Robin Ventura, Frank Tanana, Billy Pierce, Jerry Koosman, Larry Jackson, and Darrell Porter. Tanana missed by 0.07 wWAR (Frank Chance missed by 0.09). That's kind of a bummer because I really like Tanana.
7. Desipte making no efforts to make it happen, the Hall of wWAR now has the same position player vs. pitcher split as the Hall of Fame (143 position players, 63 pitchers).
8. Center field still lags far behind the other positions. However, it is incredibly top-heavy. Four of the top fifteen players in history (this includes pitchers and players not yet eligible for the Hall) are center fielders. Then, just 11 of the next 200 patrolled center.
9. The only position that had no change from the last version was shortstop. There are 17 shortstops in the Hall of wWAR, and the gap between #17 and #18 is almost 20 wWAR. In fact, the only non-eligible shortstop that fits in that gap is Nomar Garciaparra, and he's closer to the low-end. No other position has such a clear "in" vs. "out" line.
10. I use WAR/norm to normalize all players' WAR totals. This way I can rank catchers (who have a lower baseline) alongside 19th century starting pitchers (who have a higher baseline). The new Top 25 Best Players Not in the Hall of Fame (According to wWAR) are:
1. Al Spalding (139.0 wWAR/norm)
2. Jeff Bagwell (132.6)
3. Bob Caruthers (120.8)
4. Pete Rose (116.1)
5. Shoeless Joe Jackson (115.0)
6. Bill Dahlen (113.2)
7. Ron Santo (110.4)
8. Ross Barnes (105.3)
9. Jack Glasscock (104.3)
10. Ted Simmons (102.5)
11. Deacon White (101.9)
12. Joe Torre (100.7)
13. Edgar Martinez (100.5)
14. Barry Larkin (100.2)
15. Bobby Grich (99.9)
16. Alan Trammell (99.3)
17. Larry Walker (98.8)
18. Dick Allen (98.1)
19. Kevin Brown (95.9)
20. Jim Wynn (95.1)
21. Lou Whitaker (93.4)
22. Wes Ferrell (93.2)
23. Sal Bando (93.0
24. Rick Reuschel (91.9)
25. Thurman Munson (91.4)
This list jives pretty well with my perception of the most egregious snubs of all time. I was a bit surprised to see Tim Raines at #29, though. And again, I was surprised to see Ferrell rank so highly. But the more I dug, the more it made sense.