If you just toss the position on the right-hand side of the equation, and with so few data points, it's pretty much a foregone conclusion that the variable will be meaningless. If you would really like to investigate positions, run separate regressions for each position when you get enough data points.
I did this and it does generate different results. But it still does not prove anything. If there are enough data points by position, the class variable should be significant (ie: add something to the model) or not. Just getting different coefficients by position proves nothing, especially with so little data. I could take a number of variables, significant or not, out of the model (inside d, shot blocking, etc) and it would still change the coefficients.
Skill weights are different per position, so you're getting significant coefficients for the position that occurs most often in your small sample.
Maybe, I don't know. But suffice it to say that I will test everything, although as you said the data is rather limiting at the moment.
There is a lot to explore in this, but a lot more data is needed. I'd say 50-100 datapoints per position, in order to be able to read anything from the results.
Even 50 datapoints would imply at least 250 observations. So even if true, it seems like it will be a long time before this study will finish. There was a lot of excitement when the study started but now the data is only barely trickling in.
So, your concern is noted. And while I appreciate that you have a good deal of knowledge with numbers, what you could help more with is a solution to the possible issue of sub-levels on the cap. For example: how to prove they exist (or not) and if they do, how to model appropriately.
Run of the Mill Canadian Manager