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I am admittedly not great with probabilities, so I am soliciting the help of the community. I am watching game 3 of the NBA Finals and I am trying to work out when it makes sense to milk the shot clock.

I started by trying to work out Miami's possible attempts given different possession times. e.g. If San Antonio is able to maintain an average of 21 seconds per possession, how many attempts does that leave Miami? So I took, Time Remaining/21 + Miami's Average Possession.

That is where I got lost. How can I model situations with multiple variables? What sort of insight is there on this problem. I realize it is harder than can be explained in a few paragraphs, but any resources would be great.

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    $\begingroup$ For those of us that don't understand sportsball, you will probably be able to get better answers if you clarify what it is you actually want. e.g. What is "milk the shot clock?" $\endgroup$
    – Thoth19
    Jun 11, 2014 at 2:52
  • $\begingroup$ At the end of a quarter, play is stopped. I think "milking the clock" occurs near the end of the quarter, where one team "holds" the ball to waste time so that when possession changes, the opposing team has too little time to do anything before the quarter ends. You can think of this as a "continuous" version of Nim, perhaps. $\endgroup$
    – angryavian
    Jun 11, 2014 at 3:04
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    $\begingroup$ I just found this short paper that studies the "2 for 1" situation, which is slightly related. $\endgroup$
    – angryavian
    Jun 11, 2014 at 3:07
  • $\begingroup$ @Thoth19 Not a basketballer, eh? Here's a reference. In the NBA, when a team is on offense, they must at least hit the rim of the basket within 24 seconds of gaining possession. This is to ensure that teams don't just get up by a few points and then run out the clock. $\endgroup$ Jun 11, 2014 at 4:04
  • $\begingroup$ I think everyone did a pretty good job of explaining "milking the clock". To maybe whittle down exactly what I am looking for, I assume that if a team forgoes good shots to try to lengthen their average time per possession, their shooting percentage will suffer. After a 20 point halftime lead, what is the lowest shooting percentage San Antonio would need to shoot in order to maintain their lead for the remainder of the game? Assuming a 21 second time of possession and that Miami's average time of possession doesn't change. I'm starting to work it out wit some of the posted resources. $\endgroup$
    – thellama
    Jun 13, 2014 at 18:38

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hope I can be of some help. I watched the game last night too, it was great. Spurs were really dominant the first half.

Anyways, your initial calculation is correct. Finding the amount of time Miami has the ball is a simple subtraction of 60mins-SpursPossessionTime for the entire game. However, this doesn't give any insight to help with plays. Maybe using smaller intervals, like each quarter is a better start.

For your other question on modelling things with multiple variables, Linear Regression is your answer. This is a modelling technique in which you choose what variables you want to include, to try and match your existing data.

So for example, say I have a list of scores for the entire Miami heat season. I want to make a model that can accurately determine how many points Miami will score on any given game. I want to use each starter as a variable. So it would be MiamiPoints = intercept + C1*Lebron +C2*Wade + C3*Bosh + C4*Chalmers + C5*Haslem where each C is a coefficient of the variable. Now, MiamiPoints would be a list points for each game, and each player would contain a list of points they scored each game. So looking at last nights data,

98 = intercept + C1*22 + C2*22 + C3*9 + C4*2 + C5*0

Once regression analysis is performed, we can get coefficients which help us make the right side get as close as possible to the left side. Now, there are also techniques that tell you when you have too many variables, not enough variables, bad data etc. But regression analysis is definitely a sound way of trying to model things with multiple variables. But choosing the variables is another story entirely, which requires thorough analysis of the game. The example I showed is a pretty bad way to determine points Miami scores, since they are a team that rely on other players, other factors. Also using the formula before the game would be hard because you would have to predict how many points each player will score. I hope this helps in any way!

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