Quote:
Originally Posted by Male30Dan
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You just don't get the importance of getting confidence from a single win and building off of that toward multiple wins. If you somehow thing that playing game 5 on the road is somehow equal or better than playing game 5 at home while down 3-1 I just don't have much else to offer to convince you otherwise.
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I think assuming the games are independent and have no impact on each other is a reasonable null hypothesis (such is the typical stance of null hypotheses). Some people think wins have a positive impact on future games (momentum) and others think they have a negative impact (letdown). Personally, I find that we see too much of both to believe either one is a genuine force.
Even if you disagree, let me expand on this a bit then I'll address the alternative.
If the games are independent, then their order simply does not matter. Consider the case where you're down 3-1 but still have two home games. Either
A) You have Game Five at home. The good news is you have a good chance to win that game and extend the series. The bad news is the best you can do is force another road game.
OR
B) You have Game Five on the road. The bad news is that you're now more likely to lose that game. But the good news is you have a chance to win, with BOTH remaining games at home. In other words, there's a higher risk but also a higher reward if the game is won.
Mathematically, it all evens out. For the sake of example, let's assume your odds of winning a home game are 60% and your odds of winning a road game are 40%. Then your odds of winning Games 5-7 in scenario A are (.6)(.4)(.6) = 14.4%. In scenario B, the odds are (.4)(.6)(.6) = 14.4%.
What you're proposing is a conditional probability model. That is, the games are not independent; rather, past games impact the win probabilities of future ones. Perhaps in scenario A, winning Game Five increases the likelihood of getting that road win in Game Six to 50%, and a win there in turn builds momentum such that your overall win odds are 70%. Then your odds of winning the series become (.6)(.5)(.7) = 21%. Whereas in the other scenario, perhaps only the odds for Game Seven are increased to 70%, in which case your odds of winning are (.4)(.6)(.7) = 16.8%.
There are two issues I have with this model. One is that I find it too complex to justify the decisive conclusion that you draw from it. Sure, maybe (maybe!) in the specific case you have home field yet trail 3-1, you are better off playing Game Five at home. But to truly evaluate the worth of having this game at home overall, you cannot just analyze this scenario. You have to analyze it under all possible scenarios and weight them accordingly. You may be down 3-1, but you may also be up 3-1, and it could also be 2-2. Mathematically, you have to set up a win probability matrix with each scenario weighted properly. Maybe Game Five is good to have at home when down 3-1, but maybe it's not all that likely you trail 3-1 in the first place. And maybe the consequences of the other scenarios outweigh them. Maybe.
Secondly, and more importantly, in order to abandon the null hypothesis, you have to come up with strong observable evidence that the null hypothesis is false. You can't just feel it in your gut that the guys are more confident and roll with it. You can point to the 2008 World Series and say it was all momentum, but then I'll ask you to explain the 2010 NLCS with the same analysis.
The way I see it, treating the games as independent is as reasonable as any other theory, with the side benefit that it is easier to analyze.