Fielding-Independent Pitching may be "nice," but I'm not sold on it as being greater than ERA+, which IS, of course much better than ERA.
There are several reasons.
First, while some singles, doubles and triples that drop in, instead of being fielded for outs, are infielders' and outfielders' faults, not all of them are by any means. Many of them are ... the pitcher's fault. Defensive sabermetric stats remain somewhat subjective; injecting that into pitching stats doesn't totally solve the subjectivity of who's responsible.
Second, FIP is itself not exclusive of fielders. It ignores the man behind the plate and his skill or lack thereof on calling pitches, handling pitchers and framing pitchers.
Third, while where a ball goes may be partially outside a pitcher's control, it's not totally outside. An MLBTR commenter said Fangraphs WAR for pitchers was better than B-Ref's because it was tied more closely to FIP. Ironic, or something, then that the idea that a pitcher still has partial control of where a batted ball goes ... is part of a Fangraphs blogger saying he doesn't use FIP. One part of it, getting a batter to hit to spot, has only increased in the five years since the author wrote, with more teams shifting on defense more often against more hitters and having pitchers pitch to the shift.
Fourth, until we get balls and strikes called by machines, umps are human and subjective.
Fifth, unlike ERA+, FIP is not park-adjusted. Said Fangraphs blogger notes that xFIP exists, but? Fangraphs doesn't use it!
So, we need an FIP+ that like ERA+ is park-adjusted and neutralized to 100 before I'm ready to move on from ERA+.
From there, we could average ERA+ and FIP+ and get PP, or Performance Plus, which, IMO would be the best judge of pitching performance. I can do that myself, without B-Ref doing the averaging, unless it wants to.
Second would be doing a takeoff on Jay Jaffe's JAWS stat. Exact same framework, but base it on WAA instead of WAR, as I think WAA is actually a better estimate of how much a player stands out. I'm using it more than WAR to judge Hall of Fame candidacies, any more. I also use it in conjunction with WAR. If your WAA isn't 50 percent or more of your WAR, you probably were a compiler who didn't stand out. Non-HOFer Dale Murphy is an example, and it's part of my case against him.
Third? Whether on its own, or cribbing from Baseball Prospectus, 538 or others, getting some new stat for relievers to replace saves etc. It's already started down this road by tweaking high-leverage pitching for relievers and offering WAA adjusted and Runs Against-Role Factor. To put it in some classic way, they're both great, but they came from different reliever eras. Is Mariano Rivera greater than Goose Gossage? (By WAR, Rivera, exceptional for a reliever, is. What about, say, Billy Wagner vs Trevor Hoffman? Either against Bruce Sutter?)
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