Sparked by a conversation I had on UMHoops yesterday, I sought out to figure out if the poor three-point shooting from Michigan this year is a regular statistical fluctuation or an accurate reflection of a team that's objectively worse than they were last year. My point of view is that the difference in the 33.4% shooting last year and this year's 29.7% is not really that out of the blue, and in fact, a fairly reasonable output given the data we have. And a random statistical significance calculator I found online seems to agree with me.
(DISCLAIMER: I did particularly poorly in Stats at Michigan and my logic herein might be flawed or flat-out wrong. I don't think it is and had someone much more knowledgeable on the topic look it over. A few times. I am also trusting that this calculator is doing the math correctly. My numbers come from the ESPN Michigan team page, so if they don't quite match the numbers you've seen elsewhere, this is where I'm getting them. But if my logic is correct here and this is a reputable calculator, then, well, read...)
I went into this experiment assuming that the difference in shooting percentage between the 2008-2009 Michigan hoops team and the 2009-2010 team--33.4% to 29.7%--was not statistically significant. Simplistically, this means that given the data, the 29.7% performance this year is a reasonable and unexceptional fluctuation in the team's output from last year. Furthermore, this would go to show that Michigan may just be the recipient of bad luck and experiencing a regular deviation from their performance last year, rather than being outwardly worse, as some suggest.
Now, someone who is really good with these sorts of things would be able to show you the formulas and explain what everything means. I can give you this:
Well, like I said above, it means that we can likely say--albeit not definitively--that the 29.7% three-point shooting performance the team has shown this year is within the team's reasonable capabilities. That is, we can say that the performance this year is quite likely representative of the team's skill and performance given their outcomes last year. Again, this is not an exact process and is something to keep an eye on going forward, but we can't say definitively we're worse yet.
So my post At what point do we say: They just can't shoot, is mostly right. Though the performance this year may not indicative of the team's talent, it's difficult to say yet whether or not they're objectively worse this year than they were last year, at least for the time being.