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There are $82$ games in a regular season, and the current record is held by the Chicago Bulls, at 72-10. As of yesterday (March 4th 2016), the GSW season performance stood at 55-5. Assuming they maintain this record or do better,they need to win at least 18 of their next 22 games. I calculated the probability of them breaking the Bulls' record as ~7.4%, since each game's outcome is a binomial probability, and the probability of them winning so far is 55/60. I used the following code in R:

p = 11/12 #55/60, their current record
q = 1-p
i = c(0:22)
(choose(22,18)*(p^18)*(q^4))/sum(choose(22,i)*(p^i)*(q^(22-i)))

But if they keep winning, the probability p of their winning a game will keep changing. How can we take that into consideration while calculating the overall probability?

Jimmy R.
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KVemuri
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  • "the probability of them winning so far is 55/60" -- perhaps you could use Laplace's rule of succession? – shardulc Mar 05 '16 at 16:45
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    unless I am misreading, your code computes the probability of them losing EXACTLY $4$ of the next $22$ games. That's not what you intended...you wanted the probability of AT MOST $4$. Thus you need terms corresponding to $3$ losses, $2$ losses, $1$ loss, and no losses. – lulu Mar 05 '16 at 16:49
  • Probability should be used to express/measure randomness. In the outcomes of the games of the GSW there is no randomness (at most little randomness), so using probabilities makes no sense to me. – Jimmy R. Mar 05 '16 at 17:02
  • Thanks for your answers. lulu: you are absolutely correct, an error on my part. Changing the code accordingly gives me a probability of 0.96,which is more in keeping with the current situation. @JimmyR: your comment is valid, and maybe I'm not expressing myself all that well, but over 22 games, there are a possible 2 raised to 22 outcomes, or of which i want to know the possibility of just one, or a handful. Since the probability of each of those events occurring is equal, doesn't that make it a random event? – KVemuri Mar 05 '16 at 17:52
  • You can use https://en.wikipedia.org/wiki/Beta-binomial_distribution for modeling. – A.S. Mar 05 '16 at 20:19

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