Anaheim closer Francisco Rodriguez (aka, K-Rod) has a major league-leading 38 saves at the All-Star break. The record is 57 set by by Bobby Thigpen of the White Sox in 1990. With just 67 games remaining in the season, and K-Rod needing just 20 to break the record, what are the chances he pulls this off? Cornell student Max Wasserman, our numbers specialist, explores K-Rod’s chances.

Closers are to baseball teams what Velma is to Scooby-Doo. They don’t really add much but everyone remembers their name.

Okay, sorry for the analogy, but I’m behind on studying for the GRE. Anyway, this week’s adventure into the maths involves closers, or more specifically, Francisco Rodriguez. K-Rod is the best relief pitcher with an incongruous initialized nickname since Byung-Hyun “B.K.€ Kim. But unlike Kim, Rodriguez is good outside of any categories. At the all-star break, Rodriguez has amassed a staggering 38 saves in relief for the Angels, that’s 10 more than second-place George Sherrill. Thirty-eight saves through 95 games puts Rodriguez on pace to shatter the record of 57 saves in a season, set by Bobby Thigpen for the White Sox in 1990.

However, a Rodriguez record-breaking season may not be quite so inevitable. Save opportunities, in most cases, depend on a team only having a slight lead in the last inning. And in the long term, close games, especially one-run games, come down to luck over anything else. This year, the Angels have been by far the luckiest team, with an 18-13 record in one-run games and an 18-5 record in two-run games. At the All-Star break, the Angels were a major-league greatest seven games above their Pythagorean projection. It would be quite unlikely that the Angels will continue their close-game-winning ways in their remaining 67 games. But that is what they will need to do in order to give Rodriguez a shot at the record. In 1990, the White Sox finished the season seven games above their Pythagorean expectation as Thigpen set the saves record. In 2002, when John Smoltz set the NL record with 55 saves, the Braves finished five games above expectation. And when Eric Gagne tied that record the next season, the Dodgers finished a relatively unlucky two games better than expected.

So the task is to predict how many saves K-Rod will have at the end of the season. Now, here’s where I describe the math techniques I used, so if you don’t want to read it, don’t care, or Wheel of Fortune is on, feel free to skip this section. I’ll let you know when you can pick it up again. Also, I’ve decided to use format “K’Rod” for Rodriguez’s nickname because it makes him sound more like a Klingon.

Math

To obtain an estimate for the number of saves Rodriguez will have in the Angels’ remaining 67 games, we need to determine the probability that he will get a save in any game. This probability is dependent on the Angels entering the ninth inning with a one, two, or three-run lead and Rodriguez not blowing the save. Both runs scored per game and runs allowed per game are simulated by Weibull distributions, a fact that was proven by Brown Professor Steven Miller, who also derived James’ Pythagorean formula. Using these two Weibull distributions adjusted for the number of runs scored and allowed per game for the Angels this season, we can determine three fairly accurate probabilities for the Halos entering the last inning with a one, two, or three run lead. And since probably nobody is reading this, I can type whatever I want Opaque Llama Uterus. [Ed. We love this guy!]

The probability distribution for runs per inning was determined by Baseball Prospectus’ Keith Woolner, and it resembles an exponential distribution, though not perfectly. To use Woolner’s distribution, we need an estimate of Rodriguez’s true ERA. We would normally use Bayes’ theorem to do this using Rodriguez’s current ERA (2.36) and his predicted PECOTA ERA (2.79). However, the theorem requires a distribution for ERA, and as far as I could research, none has been determined. In lieu of a Bayes predicted ERA, the mean of those two ERAs (2.575) is used.

The resulting probability of Rodriguez getting a save in any game is found to be 0.243. Multiplying that value by the number of remaining games gives and expected value for number of saves Rodriguez will get between now and the end of September. The expected value was adjusted still more though by factoring in games that go to extra innings. The probability of Rodriguez getting a save in an inning past the 9th is 0.023. Multiplying this probability to the number of remaining Angels road games, 32, and adding it to the previously found expected value gives us our prediction. Obviously, more could be done in the prediction since we did not take opponents, stadiums, specific players, or other methods of getting saves into account, but Temperate Soul Reaver Tittie Garmin Chipotle. [Ed. Love Chipotle!]

End Math

The expected value for the number of saves K’Rod will earn after the All-Star break is found to be just under 17 (16.98 to be exact). This means that the prediction for Rodriguez is he will finish the season with 55 saves, two short of Thigpen’s record. Obviously, this doesn’t mean that he can’t break the record. However, he will need his team to continue to play just-good-enough baseball for the rest of the season. The Angels do play the Mariners 10 more times this season, so I guess anything is possible.

Still, I can see how tough the life of a closer must be. Some don’t get many chances to pick up saves and they need to produce when they get that chance. If a closer blows even a couple of saves in their few chances, something that could be chalked up to random chance, they may lose their spot in the bullpen. And yet despite this grim reality, Armando Benitez has somehow managed to keep getting closing jobs. That’s one thing I’ve never been able to figure out. I’m guessing he must give a really great PowerPoint presentation to GMs.