College hoops, probability, points per game

[JTG51]

This one may be easy for the probability experts, but I'm no sure how to solve it and I think it's interesting.

The University of Connecticut Men's basketball team is averaging 89 points per game, good for second highest in the country. They have scored 91, 67, 76, 116, 97, 59, and 117 in their 7 games.

In their 6th game (vs UMass) they scored only 9 points in the first half. From a strictly statistical point of view (ignoring how good the other team's defense is, etc) what is the probability of a team that averages 44.5 points per half scoring only 9?

I'm not sure how much information is needed to solve this. Just in case the scores by half are needed, they are:

48/43, 37/30, 38/38, 59/57, 53/44, 9/50, 51/66

Thanks.

[lorinda]

Maybe you could do it by working on the probability that they score each minute, or each second and tackle it that way?

I would imagine (Basketball is one of my least favorite games) you could assume that a team either scores in a 20 second period, or doesnt, and that they wouldnt score twice in this time.
That way you can get a probability that they only score in four (I assume) 20 second periods in a half.

That make any sense?


Lori

[marbles]

Interesting question, but virtually impossible to answer for the following reasons:
1. The data in the sample (12 total halves if you ignore the UMass game) is nowhere near statistically significant. 30 trials is commonly cited as a good ballpark minimum, so MAYBE you could get a reasonable number after 30 games, but not after 7.
2. You simply gloss over the statement "ignoring how good the other team's defense is." I assume, as a fan, you know just how ridiculous this is, particularly in college basketball. UNC-Asheville and Sacred Heart (116 and 117 PA by UConn) have no semblance of defense. UMass, meanwhile, has given up more than 80 only once this season, and that was to Indiana. The fact that all three teams are terrible does not make the comparison apples-to-apples.

[JTG51]

"I assume, as a fan, you know just how ridiculous this is, particularly in college basketball. "

Of course that's true. I thought it was a somewhat interesting probability question burried inside a real life example. Without ignoring the quality of the other teams defense, the question would truly be impossible to answer. I was trying to simplify the situation to make it a solvable math problem. Kind of like all the problems in an introductory physics book on projectile motion when they say, "ignore the effect of air friction for now".

I guess the question is harder than I thought. I figured there's be a relatively simple solution, maybe using standard deviation that I didn't know.

[marbles]

"I guess the question is harder than I thought. I figured there's be a relatively simple solution, maybe using standard deviation that I didn't know."
-It's not that the question is hard to answer, it's just hard to answer it and have any faith in your results. You just have to take some pretty wild assumptions.

If you take results of the other six games and assume that present and future results are normally distributed around a mean (not true) and that the sample is statistically significant (also not true), you have a mean of 47.0 and a standard deviation of 10.6. That would put this result of 9.0 at roughly 3.6 standard deviations from the mean... Or, in short, wildly unlikely.

[JTG51]

There we go, that's kind of what I was looking for.

Thanks.