If there is a game 7, you still have an inning of league-average lefty Lee rather than 2-3 innings of ace starter Lee, which might be strategically used for a few batters.

PHILLIES 7TH: Feliz grounded out to 3B; Ruiz doubled to deep left center; DOBBS BATTED FOR MYERS; Dobbs walked; LEE RUNS FOR DOBBS; Rollins flied out to shallow center; Victorino walked (Ruiz to 3rd, Lee to 2nd); Utley homered to right (Ruiz scores, Lee scores, Victorino scores); Howard struck out.
4 R 2 H 0 E Phillies 4, Yankees 3

YANKEES 7TH: LEE REMAINS IN THE GAME PITCHING; Texiera struck out; Rodriguez singles to right;

oops, better not give away the ending.

As others have mentioned, I think you'd be better off using more realistic Game #6/#7 win probabilities. Something close to...
Game #6: 0.36
Game #7: 0.32 to 0.35

vr, Xeifrank

Where does the 93% figure come from? If it's based on win expectancy (e.g., the outcome we might expect to observe for the average team up 3-1 in the third playing against the average opponent), then I see no reason to invoke it here. Simply put, the Yankees in no way approximate the average opponent.

The Phillies need to win!!!

Interesting that the chances of winning the series only rose 1.5%. Seems like a very small change for such a big decision.

Personally I thought they'd remove him before the 7th, since he'd already reached 100 pitches and they had a solid lead and they would want to make sure Lee's as fresh as possible for any further elimination games. I was surprised they didn't, and then Lee allowed some runs in the 7th that got the Yankees closer.

Is it possible that the math didn't take this kind of thing into account? It seems logically that the chances of winning should've been significantly higher if Lee was removed after 6 last night.

To call Game 7 a 50/50 game with Lee going on two days rest (even though he had only thrown in the 50s) is probably unrealistic. Also, think about if the Yankees lose the next two games. Joe Girardi will be on a rail out of town. Burnett looked awful on three days rest yesterday. It's been pointed out repeatedly that given his age and elbow history that Andy Pettite is far from a sure thing in Game 6. That leaves Sabathia going on three days rest for the third time this postseason in Game 7. With a 3-1 lead the Yankees could have opted to give everyone an extra day, but they didn't. Now that's the second guess people should be talking about.

Thanks for the comments. You can quibble with the probabilities chosen for Games 6 and 7 (or Game 5), but if you change them it really won't really move the needle on the decision. Ex. if you think the Yankees have a better chance to win Game 7 than 50% (a reasonable thought), this will factor in the same way for both strategies - hence, you'll get the same difference between the two options. Depending on your assumptions, the overall probability of Phillies victory may change a lot, but the difference between the two choices will remain pretty much constant.

The Yankees aren't giving "everyone an extra day" by moving their starters back; they would have substituted a Gaudin start for a Sabathia start. That's a losing proposition, even if Sabathia is pitching on short rest in Game 7.

As for Lee pitching as deep into Game 5 as he did, Charlie Manuel must have more faith in Cole Hamels's current form than I do.

A response to Sky's response. The point made by Devon is that even when you weighted things heavily in favor of pulling Lee, you didn't find that it made much of a difference. That's what is interesting. You started with the assumption that it was a mistake to leave Lee on the mound, and then you ignored your conclusion that it didn't matter.

While a couple of percentage points difference in winning the World Series sounds small, the difference is actually huge considering no manager's decision in Game 5 can have that huge of an effect. To review:

Using Lee to continue in Game 5 increased the probability of winning the WS by 1.5%

Removing Lee and pitching him 2 additional innings in Game 7 increased the probability by 4.65%.

Taking him out is 3 times as valuable as leaving him in. That's not a small difference at all.

If you want to say it's too small to bother with then you'd have to concede that virtually no decision either manager could make in a Game 5 would be worth debating.

Love the thinking. I think the numbers are off a bit, but I think a rational number cruncher could reach the same conclusion with more intensely researched and thought out numbers.

To throw out some numbers of my own...

Game 6 is unaffected, so I'll exclude that.
Win Exp might be 93%, but facing the Yankees in a hitters' park probably brings that down to 88%. Leaving Lee in probably gets it back up to 93%, but pulling him might drop you to the mid-80%s given the stadium, and again, the Yankee bats. We'll say 86%. Three to four innings of Lee in game 7? I'd say the line on that game probably goes from -220/+200 (67.7% NY if you split the difference) in a Sabathia v Hamels with Lee unavailable to -190/+170 (64.3% NY) with a Lee/Hamels 7-8 inning combo. My guess is that a fully recovered Lee would be about a 61/39 underdog vs Sabathia at Yankee stadium, so I'm pretty much splitting the difference.

So you got 0.93*0.323=0.300 leaving Lee in versus 0.86*0.357=0.307 taking him out.

Quick and dirty and VERY close for me. Slight edge to pulling him and having him available for game 7. I would LOVE to see a manager actually do it, but I think it would take a 10 run lead.

Brian,
You are right that the number I use are not perfect (nor meant to be), but since the assumptions I make (Lee is perfect, teams are evenly matched) are the same for both scenarios, the difference between the two scenarios will be relatively unaffected.

As for your numbers, they don't seem quite right. You have the difference between Lee/No-Lee being 8% in a 5-1 game. But you have the difference between Lee/No-Lee being only 3.4% in a tie game. This doesn't make sense, being that as probabilities get close to 1 (or 0), star-players and big plays have LESS of an effect on the probability, not more.

The fact that your heavily skewed numbers still show that Manuel should have pulled Lee is testament to the fact that that should have been the right move.

Sorry, your Lee/No-Lee difference was SEVEN points in a SIX-one game. Same point though.