Class size vs star rating

Class size vs star rating

Submitted by michelin on February 3rd, 2010 at 8:56 PM

There is always a debate about the significance of recruiting rankings when teams don't have the same number of recruits.  Here's the question for this year.  

Is it fair to rank UM's class higher than OSU's, as a number of the recruiting services have done, with rivals not even putting OSU in the top 25?

Some argue that OSU’s class is only ranked lower because they had a smaller class size. But how does class size affect the impact of the recruiting success of the entire class.
 
We can get a very crude idea of the impact by asking a purely hypothetical, simplified question.  Suppose you have a class the size of UM’s and each recruit has an independent, 50-50 chance of succeeding.   Then the likelihood that more than half of the recruits succeed is itself, coincidentally, 50% (see link).  By contrast, the chance of success of the same number of recruits in the smaller class for OSU is only 2 %. 

But what if we raise the chance of success for OSU's recruits (with an average rank about 6% higher in scout or rivals, as I recall)? Let's be generous and say that each of OSU’s recruits has a 10% greater chance of succeeding than UM’s.  Then the chance that their class succeeds as a whole (more than half contribute) is still only  9%, less than a fifth of UM’s.  

This oversimplified analysis admittedly ignores possible dependencies, heterogeneities, different degrees of contribution, and the fact that recruiting more players today may lead to more spaces next year, or vice versa.  However, it’s uncertain how important the latter is. 

UM’s large class this year may also be due to the smaller size of prior years (after attrition) as compared with OSU’s.  So, prospectively, it is possible that we will be able to recruit as many as OSU in the coming few years—somebody might check this out.   So, possibly, this year, we just made up a lot of ground and evened the playing field in numbers, while also making this year's class a lot more likely to succeed than OSU's.


http://www.stat.tamu.edu/~west/applets/binomialdemo.html