Posted by Mike Frohwirth
When St. Louis Cardinals Manager Tony LaRussa announced his postseason pitching rotation, there was jubilation- among the Phillies' fanbase. As Cardinals' ace Chris Carpenter pitched in the division-clinching win on Wednesday, he will be unable to pitch until Game 3. But LaRussa also made the surprising move of holding his 2nd best starter, lefthander Jaime Garcia, until Game 4. Given that this is a five-game series, LaRussa faces the possibility of not even being able to use his #2 starter. Is this a case of LaRussa being "too smart for his own good", or has his selected pitching order actually increased his team's chances of winning the series?
Some important business, before we look at some numbers:
- The Phillies have a sizeable starting pitching advantage over St. Louis. All LaRussa can look to do is to attempt to minimize this advantage. THERE IS NO PITCHING ORDER LARUSSA CAN USE, THAT WILL GIVE THE CARDINALS THE STARTING PITCHING ADVANTAGE.
- There is a lot of randomness inherent in a short playoff series. The "better" team won't win every series, in fact the "better" team might win the series just 55-65% of the time.
- If the Cards win the series, it doesn't "prove" that LaRussa chose the right pitching order. Likewise, if the Cards lose the series, it doesn't necessarily mean LaRussa's pitching order was poorly-chosen.
Let's look at the Cards' "ideal" pitching rotation (The order that pitches the "best" available pitchers (no short-rest starts) as soon as possible, and as often as possible.):
"Ideal" Rotation
Game 1: Halladay v. Lohse at PHI Guesstimated STL Win Probability: 35%
Game 2: Lee v. Garcia at PHI Guesstimated STL Win Probability: 40%
Game 3: Hamels v. Carpenter at STL Guesstimated STL Win Probability: 55%
Game 4: Oswalt v. Jackson at STL Guesstimated STL Win Probability: 55%
Game 5: Halladay v. Garcia at PHI Guesstimated STL Win Probability: 40%
So, what's the probability that the Cardinals win at least three of these games? Well, it's easier to figure out the probability that the Phillies win two games or less, so let's calculate that probability.
P (Two PHI wins or less)= P (Zero PHI wins) + P (One PHI Win) + P (Two PHI Wins)
P (Zero PHI wins)= P(Loss, Loss, Loss)= (.35)(.40)(.55)= .077, or 7.7%
P (One PHI win)= P(Win, Loss, Loss, Loss) + P (Loss, Win, Loss, Loss) + P (Loss, Loss, Win, Loss)
=(.65)(.40)(.55)(.55) + (.35)(.60)(.55)(.55) + (.35)(.40)(.45)(.55)
=.079 + .064 + .035= .178, or 17.8%
P (Two PHI wins) = P (WWLLL) + P (WLWLL) + P (LWWLL) + P (LLWWL)
=.047 + .026 + .025 + .011= .109, or 10.9%
So, the P (STL wins series, with "ideal" rotation)= .077 + .178 + .109 = .364, or 36.4%
We've determined that the "ideal" rotation gives St. Louis a 36.4% chance of winning the series. Are they better off with the pitching rotation LaRussa has chosen?
Selected Rotation:
Game 1: Halladay v. Lohse at PHI Guesstimated STL Win Probability: 35%
Game 2: Lee v. Jackson at PHI Guesstimated STL Win Probability: 35%
Game 3: Hamels v. Carpenter at STL Guesstimated STL Win Probability: 55%
Game 4: Oswalt v. Garcia at STL Guesstimated STL Win Probability: 60%
Game 5: Halladay v. Lohse at PHI Guesstimated STL Win Probability: 35%
Once again,
P (Two PHI wins or less)= P (Zero PHI wins) + P (One PHI Win) + P (Two PHI Wins)
P (Zero PHI wins)= P(Loss, Loss, Loss)= (.35) (.35) (.55) = .067, or 6.7%
P (One PHI win)= P(Win, Loss, Loss, Loss) + P (Loss, Win, Loss, Loss) + P (Loss, Loss, Win, Loss)
=(.65)(.35)(.55)(.60) + (.35)(.65)(.55)(.60) + (.35)(.35)(.45)(.60)
=.075 + .075 + .033 = .183, or 18.3%
P (Two PHI wins) = P (WWLLL) + P (WLWLL) + P (LWWLL) + P (LLWWL)
= .049 + .021 + .021 + .008 = .099, or 9.9%
So, the P (STL wins series, with the selected rotation)= .067 + .183 + .099 = .349, or 34.9%
Takeaways
- The "Guesstimated Win Probabilities" are guesses. Pretty much just looked at pitching matchups/ballparks, and made them up. But even when homefield advantage and pitching matchup are both heavily tilted in one team's direction, the underdog still has, perhaps, a one-in-three chance of winning a single game. The effects of randomness are much more powerful than most suspect. (This randomness is how pitchers as skilled as Cole Hamels wind up with a 74-54 lifetime record (57.8% Win Pct.). Winning percentage is not a good stat to judge an individual pitcher's abilities, but it does serve to illustrate the fact that randomness, as well as factors unrelated to the choice of starting pitcher, weigh heavily in final outcomes).
- With the information we have, LaRussa is better off giving Garcia (his second best pitcher) two starts, rather than giving Lohse two starts. (There may be information we do not have, however. Or, maybe LaRussa feels that, under the current circumstances, Lohse is a better pitcher than Garcia.)
- LaRussa appears to be trading a better chance at winning a possible Game 5, for a better chance at getting to a Game 5. (Given that the Phillies are favored, reducing the series to a single game, and hoping randomness is on St. Louis' side at the end, seems a viable strategy.)
- LaRussa's strategy could be to "steal" one of the first two games, then hope to win the series in four games (with relatively advantageous matchups in Game 3 and Game 4).
- LaRussa may have additional information that he factored into his Win Probability calculations. (What will the availability/effectiveness of injured players Matt Holliday and Rafael Furcal be, particularly early in the series? Will the additional rest for Garcia, who has already thrown thirty more innings than in 2010, tilt the win probabilities further in St. Louis' direction? Perhaps he sees an advantage to keeping Garcia away from CBP? Perhaps Garcia is even fighting an injury concern?)
Conclusion
LaRussa's strategy may, or may not, be a smart one. It may, or may not, be successful in the one five-game series being played. But it doesn't appear to be a stupid strategy, as the current popular opinion appears to be. Plus, there very may well be more factors that LaRussa is considering, of which we are currently unaware.
