Using Bweezy Right

On Tuesday's game against the Houston Astros, the San Francisco Giants were up by three runs going into the ninth inning.  According to official baseball statistics, this is a typical "save" situation.  In such  situation, baseball lore has it that a manager should bring in his best reliever in order to close out the game.  A save is any situation where the following occurs: (1) the pitcher is the finishing pitcher by the winning team; (2) he is not the winning pitcher; (3) he has at least 1/3 (one out) recorded; (4) he does one of the following: (a) he enters the game with a lead of no more than three runs; (b) he enters the game, regardless of the count, with the typing run either on base, at bat, or on deck; or (c) he pitches for at least three innings.

In baseball the best relief pitcher is normally referred to as the team's "closer."  Such a pitcher is generally brought in the game during a situation like the one above between the Astros and Giants: your team is winning by three runs or less.  You bring in the closer (the best relief pitcher) in order to ensure that the opposing team does not make a late inning come-back.  Anyone who watches Giants games will note that Bochey virtually never brings Brian Wilson into the game before the ninth inning, and only does it in save situations.

So is this the best way to make use of our team's best relief pitcher?  The answer is not what one may think.

Tom Tango's book on baseball, The Book: Playing the Percentages in Baseball, offers a wonderful statistical analysis of baseball lore.  Is the sacrafice bunt actually a good play?  When should you walk a hitter?  Does leveraging lefties and righties actually work?  One question Tango addresses is the use of closers.

Tango begins his analysis by noting that a save in baseball is the same, no matter if the winning team is ahead by three runs or by one run (Tango 208-9).  However, Tango notes that from 1999-2002 a closer was brought into the game with a three-run lead 1,034 times (210).  How many times did the closer's team lose?  Only 31 times, which is 3% of the games (210).  Tango also notes that even poor relievers who come in during a close situation rarely lose with three runs or more (1 time out of 25) (213).  So, at the end of the day, a three run lead is almost a sure win in the bottom of the ninth, and good relievers do not seem to help that win any more than do poor ones.  So what about when your team has a smaller lead?  What then?

Tango addresses this issue as well (215-16).  Without going into the math in depth, Tango compares the win percentages of average and elite relievers when they come into the game in the ninth when the pitcher's team is ahead by one or two runs.  For two run leads, an average reliever's team will lose 9.0% of the time.  When an elite reliever is in the same situation, a reliever's team loses 4.9% of the time.  A fairly big difference.  When the pitcher's team has a one run lead, the average reliever will lose 21% of the time, while an elite reliever will lost 15% of the time.  Thus, while bringing an average reliever in during the ninth inning, when a team is up by three, is generally no different than bringing in a true "closer", there is a disparity in one and two run leads between average and elite relievers.

So it seems in Tuesday's game against the Astros, Bochey should not have brought Wilson in when he did (ninth inning, Giants up by three).  Perhaps that is a bit of an overstatement.  It certainly is not wrong to bring in Brian Wilson; but perhaps we didn't optimize him.

That simply begs the question: So, smart-guy, when do bring in the elite reliever?  Only when his team is up by one or two runs?

No.  There are more situations where it is optimal to bring in the closer.  In fact, in the 1970s, one would often see the elite reliever come in during the eighth inning.  Elite relievers like Goose Gossage and Bruce Sutter face more batters than not in the eighth inning, rather than the ninth (217).  Tango goes into an in-depth analysis, using the expected run-distribution over the course of two innings for elite pitchers and average pitchers (219).  Assuming an average reliever come in the eighth inning, when his team is up by one, and pitches through the ninth, Tango found the following results: 65%.9 win in 9 innings; 18.8% lose in 9 innings; 15.3% extra innings.  What was it for elite relievers (like Wilson)? 75.7% win; 11.3% lose; 13.0% extra innings.

Wow.  What a difference.  There is almost a 10% higher chance of winning if you use an elite reliever over the course of two innings rather than an average hitter.  National League baseball fans, which I am, will ask one question: That may make sense, but in the national league pitchers have to hit.  Does that effect the win outcome at all?  Oftentimes a manager doesn't want the reliever to hit, so he will take him out.

I think this is a fair question, and I do not see an answer for it in Tango's work.  That said, it would be interesting to see whether having the closer in over two innings is more valuable than the near-guaranteed out the relief pitcher will give the other team when it is his turn to bat.

Regardless, Tango's research does suggest that it is significantly better to bring your elite closer in during the 8th inning with 1 or 2 run lead, rather than in the ninth inning with a 3-run lead.  I think Bochey should take notice of this in order to maximize Wilson's effectiveness.  It is nice for Wilson that he gets the saves in easy situations where we have a 3-run lead, but since he is the Giants's best reliever he should probably be put to work in situations where he impressive talent will help the team win close games.