Southern pitcher update: few data points

Over at Baseball Think Factory, where they have a thread on yesterday’s post here about Tom Timmerman's paper on Southern pitchers, poster Swedish Chef (I’ll call him SC) alertly notes that the southern pitcher data is based on very few hit batsman (search for comment 14 in the above thread).

SC notes that there were originally 20,357 HBPs in the study. The chart on page 27 shows that of those, only 1.9% of them were when the previous batter hit a home run. Also, only 25.7% of HBPs were by pitchers from the South, and only 29.3% of HBPs were against black batters.

Assuming these are “pretty independent variables,” you can multiply them all out and get 29. SC concludes that there are only

"about 30 HBP on black players by southern pitchers and about 90 by non-southern pitchers after a HR (… these numbers aren't in the paper, why not?)."

Timmerman's study concluded that pitchers from the South are much less likely to bean black batters. But these relatively small numbers certainly cast the study's conclusions into a bit more doubt. Even though the results in the paper are said to be statistically significant, could it be just a couple of pitchers creating the significance?

More data would help.

Thanks to Swedish Chef for the catch.