I never posted OBP and Slugging % as being correlated. I added things to my initial post (p-value for statistical significance of the correlation), but you missed on what I posted in terms of the statistics. Too bad. The funny thing about them, however, since you brought it up, is that OPS is used as a primary tool for valuing a player under Sabermetrics. Two very correlated statistics being combined to assign value to a player seems redundant, yet it is accepted by a large portion of the Stat Geek community. EDIT - I see you edited your post to accuse me of posting something that I never posted, and that you also edited away your snarky "Too bad". No need to lie about what I posted, BC
OBP and Slugging being correlated seems to be an argument for using them in a combined sense. Wouldn't this mean that any correlation between PER and usage may actually be beneficial, at least in terms of looking at a similar data set in a different manner, and then combining them to perhaps better utilize both results as an overall value?
There is no "conclusion" to reach. It is a simple linear regression. I'm sure you can find the summation equations online or look up the matrix method of least-squares. Total rebounds and rebound % "measure different things" but it wouldn't be surprising to see a correlation considering they are based on similar basic stats. I'm not suggesting anything about those stats. But if they are built on the same basic stats, I wouldn't be surprised to see a correlation. You're the one assuming a linear correlation, I have no idea what form of regression would fit the best. I asked you if you could do it and you got pissy. If you want the data to back up your claims, go ahead and pull the raw data like I did. Nobody ever said correlation is a bad thing. But you trying to use it to explain the variance in per isn't working, as suggested by the r-squared value. Damn, dude. You just love trying to be bitchy. You started this thread claiming there "is a STRONG correlation" between per and usg. I posted what the stats say the strength of that correlation is. You started with a hypothesis about a correlation, and when somebody posts the actual data, you claim you don't see how it relates to the thread? Um, no. My data / analysis says exactly the opposite. You might want to look into a stats course. The p-value is ~0, as expected.
I "started" with this. "there appears to be a consistent correlation between a high usage rate and a high PER." For some reason, you decided to apply that to all players, regardless of PER. Perhaps you just read the first post incorrectly? If so, thanks for the formula, but it's no wonder we aren't on the same page. You supplied data to a question that I never asked.
Alright, what is a "high PER". If you want to see what the data says, you have to define what "high" means. Let me know and I'll do a new linear regression on players with a per above "x".
PER above 18 would be a decent data set, if you get the time. Thanks! I think we were on the same page, but speaking different languages because of the other "noise" in the thread. Mea culpa! I was completely misunderstanding what you were showing in terms of data. I'd love to see the correlation if it exists, between a relatively "high" PER of 17, and the impact of usage rate on that player's PER. The problem with doing this, as I see it, is it still won't account for why one player has a PER of 17 and a usage of 25, while another has a PER of 17 and a usage of 18. My primary point is that the latter player is more valuable, and would have a higher PER if they had a higher Usage rate. I just don't know the weight of usg and its impact on PER.
That works out to be: per = 0.26 * usg + 14.8 r-squared is terrible at 0.27 The "correlation" gets weaker for players at the higher PER. That is what the other posters and I have been saying. There is a correlation between PER and usg, that shouldn't be a surprise because they are comprised of many of the same basic stats. The real data shows a correlation, such that on average a player with a higher usg will have a higher PER. But the r-squared value being so bad says that you can't use this analysis to explain the variance in PER on a per-player basis.
I'm not really wondering about the PER variance, per se. I'm wondering if players are being used correctly, among other things, based on a usage basis, considering their PER.
This is what he meant: http://easycalculation.com/statistics/learn-regression.php http://easycalculation.com/statistics/learn-correlation.php Just in case anyone here wants to do something similar.
Anyhow, I just emailed John Hollinger a rather lengthy post regarding this, asking for his thoughts on PER, and how he sees usage rate impacting a player's value. Thought it would be fun to see if he answered it!
That is where the correlation coefficient from my regression comes into play. On AVERAGE, a player's PER will increase by 0.5 for every 1pt increase in usg%. The regression applied to players with a PER above 18 shows that increasing usg% has a smaller effect on increasing PER, at about 0.26 PER increase per 1pt increase in usg%.
So there are diminishing returns, which makes sense. If there weren't, you would just put the ball in the hands of your best player every single possession. There are two competing dynamics here: on the one hand, using more possessions gives you more raw opportunities to do something. However, the more possessions you use, the less you can pick and choose your best chances. As you increase your Usage, each added possession is an increasingly difficult chance, which makes those possessions used less effective.
