A Statistical Response to Lowry vs. Paul

by BuckeyeBob on Jan 24, 2012 10:06 PM CST

After reading the Lowry vs. Paul fanpost I decided to put together a quick and dirty statistical analysis of my own. As far as if I am qualified to make the claims I am about to, maybe....

Assumptions: statistics come from normally distributed populations (meaning are random samples of this years games for each player), so that means I will use t-distributions and statistics to check these things. Second is that at each stat the variances are equal. while not true they seem to be reasonably within that assumption as far as statistics are concerned.

Now to the Data:

Points

So when I performed a t test on the data thus far this season testing a difference between the two stats (H0: m1=m2 vs. Ha: m1 =/= m2, so if they are equal o) I got the following:

P-value = .643

a P-value above .05 (indicating a confidence level of 95%) means that we fail to reject H0 so that means that the difference between their points is statistically insignificant.

Assists

same test (H0: m1=m2 vs. Ha: m1 =/= m2)

P-value = .869

way above .05 so the difference is statistically insignificant at the 95% confidence level

Rebounds

same test, (H0: m1=m2 vs. Ha: m1 =/= m2)

P-value = .001

YAY! p-value below .05! Difference in rebounds is statistically significant!

Turnovers

same test (H0: m1=m2 vs. Ha: m1 =/= m2)

P-value = .038

.038<.05 Yikes, Looks like the difference in turnovers is statistically significant too.

so what I'm saying here is that.....

Yes. Lowry is a significantly better rebounder than Paul, but they are statistically equal in the points and assists columns. Lowry does have significantly more turnovers. Statistically speaking of course.

No cursing in title. No pirated material, such as links to online game streams. Do not cut/paste entire sections of content from other websites. Thanks.

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Comments

Excellent.

While I believe your analysis might be skewed by the Johnson-Fargo Principal, I basically agree with your conclusion. We can’t all be stalwart loyalists of the JFP.

by lakeytom on Jan 24, 2012 11:31 PM CST reply actions

Good, but you need to look at assists/points/tov

in the context of pace, minutes, possessions. So while there’s no statistically significant difference between their point and assist averages as such, there may be a statistically significant difference between the percentage of teammate possessions they’re assisting and their shooting efficiency (Paul has a massive lead in true shooting and turnover percentage; much smaller lead in assist percentage).

It isn’t that your analysis is mistaken, only that it concerns statistics that don’t really capture what is going on on the basketball court, though that’s more of an issue with the points column than with assists/rebounds/turnovers (point totals don’t correlate strongly with wins — what does correlate strongly are things like offensive efficiency, which is expressed in true shooting).

Beyond that, there are issues with testing the data, since there is probably good reason to believe that these values aren’t distributed normally across the player population, nor that there is normal variation.

Anyways, it’s been like four or so years since I last broke out my statistical “training” (aced the AP exam back in high school!), so bear with me (I think I last did any sort of real statistical work back in a labor econ class I took in 2008).

True shooting is calculated with the following formula:

PTS / (2 * (FGA + 0.44 * FTA))

So if we look at each of their games we can calculate their true shooting for each, then test.

Testing those two distributions (assuming normal distribution and variance) we get a p value of .535, meaning that this is statistically insignificant difference. Of course, I really doubt that these are normal distributions…