The City Paper article suggests the absolute number of crashes should track people per square mile, and is surprised that we have the most crashes but not the highest population density. That's silly. By that logic, a one-block county with everyone packed into massive apartment buildings should have huge numbers of crashes, while a vast county with nothing in it but a busy interstate and one house should have virtually none.

In reality, we should expect crashes to rise with both the size of a county and its population. Add people to a county and naturally you'd expect more crashes. But imagine you hold the population constant and spread them out over a bigger county. That typically means more roads and more driving. (Of course, this ignores lots of stuff. Counting the number of miles of road in a county might be a better predictor of absolute crash numbers than its area, but the article focuses on square miles, not road mileage, so let's stick with that.)

It's perfectly plausible that Allegheny would have the highest absolute number of crashes, regardless of how our road design compares to other counties. After all, we have the second-highest population in the state, but the one county with more people (Philadelphia county has 25% more) is much smaller (it's 19% of our size).

I found 2014 crash stats by county here. Here are the top counties for crashes, in order, from page 59:

Allegheny 12154
Philadelphia 10627
Montgomery 8104
Bucks 5779
Lancaster 5339
Chester 4676
Berks 4593
Delaware 4546
Lehigh 4501
York 4412

Now, let's approximate the expected number of crashes. If you take each county's population and multiply it by its area^0.3, to account for population being a more significant factor than area in crashes, you get this top ten list:

County Pop Area Expected relative crashes
Allegheny County 1223348 745 8896043.50539799
Philadelphia County 1526006 143 6763275.09188891
Montgomery County 799874 487 5120121.52031427
Bucks County 625249 622 4307151.2350518
Lancaster County 519445 984 4106181.10093658
Chester County 498886 760 3649601.06273238
York County 434972 910 3358719.37211644
Berks County 411442 866 3130141.64029159
Westmoreland County 365169 1036 2931580.53106716
Delaware County 558979 191 2702125.41694098

Notice that the top few entries are identical. I just guessed at the 0.3 figure, but already it's a pretty close approximation of the actual relative number of crashes.