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nba finals is a best of 7 series (first to win 4 games). in the nba, home court is decently advantageous, to the point where the home team is generally expected to win.

this past week saw the phx suns win g1 and g2 at home. not an unexpected result, but the probability of them winning the entire series also increased substantially (60% prior to g1 to 88% post g2).

my non-qual understanding is that they have banked two wins. so regardless of whether or not the predictive models expect them to win home games 1 and 2, they have proven it. by proving it, they have changed the parameters of the predictive modeling - no longer is it a 7 game series, first to 4 wins, but now it is a 5 game series, where phx suns have to win two out of 5, and the bucks have to win 4 out of 5.

so is the 60% actually comparable to 88% since they're talking about different things?

let me know if i can better explain the situation.

the question is: if the suns are expected to win a 7 game series (60% win probability), why does winning games 1 and 2 at home increase their win probability to 88%? if they are expected to win games 1 and 2 (let's say 100% of the time), why would their series win probability increase when the events are occurring as expected?

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    $\begingroup$ Prior belief can be updated, depending on your model. Would need a formulation of the question. $\endgroup$ Commented Jul 10, 2021 at 3:44
  • $\begingroup$ Don’t understand the confusion. Suppose I wanted to know plausibility of tossing two sixes. 1/36. Great. I look at the first. It’s a six. The plausibility of two sixes conditioned on this knowledge is 1/6. $\endgroup$
    – innisfree
    Commented Jul 10, 2021 at 4:50
  • $\begingroup$ Are these probabilities based on how people are betting? $\endgroup$
    – Dave
    Commented Jul 10, 2021 at 4:58

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While winning at home is very likely, there was still a possibility of losing those games at home. The original probability included that possibility, now we have seen the first two games and there's no longer any uncertainty about their result.

Depending on how the probability is calculated, it may also reflect an updated belief on how the teams stack up relative to each other (obviously a lot was known from the rest of the season already on that, but this is still also extra information one can take into account).

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  • $\begingroup$ ok, that all makes sense. then what happens if the bucks win their home games, g3 and g4. Then the series becomes a best of 3; and each team has won their expected games. and we can assume that the positive extra information learned about the suns are countered by the positive extra information learned about the bucks. in that case, one would assume that the sun's series win probability would move from 88% back to 60%, but i'm pretty sure it doesn't work like that - so how can we explain that change? $\endgroup$
    – Joe
    Commented Jul 10, 2021 at 17:04
  • $\begingroup$ thanks. then what happens if the bucks win their home games, g3 and g4. Then the series becomes a best of 3; and each team has won their expected games. and we can assume that the positive extra information learned about the suns are countered by the positive extra information learned about the bucks. in that case, one would assume that the sun's series win probability would move from 88% back to 60%, but i doubt that's correct. said another way, if the sun's win probability for a 7 game series is 60%, in a vacuum, there win probability for a 3 game series should be 60% as well. $\endgroup$
    – Joe
    Commented Jul 10, 2021 at 17:10
  • $\begingroup$ That would definitely shift things back the other way. Given that they were favorites to win a 7 game series, they'd be favorites to win a 3 game series, but with a lower probability (even ignoring everything else like "momentum" etc.), because in 3 games the better team would be less likely to win, because in 3 games more things happen just by chance than in 7. $\endgroup$
    – Björn
    Commented Jul 10, 2021 at 18:09

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