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June 5, 2003

Lies, Damned Lies

Solving a Ninth Inning Quandary

by Nate Silver

NEW YORK (May 28) -- Ball four. With the Yankees batting in the bottom of the ninth and the score tied 5-5, Red Sox Manager Grady Little ordered the bases walked full, preferring that his nominal relief ace, Brandon Lyon, face Yankee catcher Jorge Posada instead of the strikeout-prone Alfonso Soriano or the slumping Jason Giambi. Perhaps Little should have consulted with nerd-in-residence Bill James first. The move backfired, as Posada walked following a borderline call on a 2-2 pitch, sending Hideki Matsui in a slow trot home and blowing the game for the Sox. Long live the curse.

Stop me if you've heard this one before. Any loss to the Yankees causes consternation from Barnstable to Bangor, and especially one with so many elements to pick on. Poor performance by the bullpen? Check. Questionable managerial decision? Check. Controversial call by the umpires? Yessiree, Bob. The reaction from the local scribes was fairly tame, in no small part because Bob Ryan is still serving his suspension for being a moron, but make no mistake: This was exactly the sort of loss that enables Red Sox Nation's impulses toward self-destruction (this column brought to you by Samuel Adams Lager).

But while the loss was painful for Boston fans, it was also the sort of game that Diamond Mind and Strat players love. The bottom of the ninth was a classic chess match, with classic endgame strategy. As D.H. writes:

"Statheads...often lament the intentional walk with an argument that usually goes like this: With a runner on third and one out, the expected runs scored for the inning are X. With the bases loaded and one out, that number is Y (higher than X). This argument normally makes sense, but in a situation where one run is all that matters, the manager should instead try to maximize the probability that no runs will score...Does walking the bases loaded with one out make sense on this basis?"

It goes without saying that the situation that Grady Little faced was unusual. As D.H. points out, the only thing that each manager need concern himself with is whether that one essential run scores. All the strategic elements of the game--hitting, baserunning, pitching, defense--are profoundly different under these conditions. For convenience sake, let's give the situation a name: THNT (Tie game, Home team at bat, Ninth inning or later, runner on Third).

When THNT arises, the visiting manager effectively has three ways to play his hand:

• No intentional walk--runner on third.
• Intentionally walk one hitter--runners on first and third.
• Intentionally walk two hitters--bases loaded.

Is there a built-in, structural advantage to beginning the endgame in any of these states? Under THNT, and with one out, the potential outcomes can be summarized as follows:

• Home team wins: Any hit, or sacrifice fly.
• Visiting team "wins" (sends the game into extra innings): Double play.
• Add an out, stir, and repeat: Strikeout, any other out.