A good counter argument that you might make is that including right tackles might bias the data. The best offensive tackles are often charged with protecting the “blind side” of the quarterback. This also coincides with the position of the opposing team’s best pass rusher (again, to get at the quarterback’s blind side). If the better offensive tackles are going up against the better pass rushers, then the data sets could potentially be very different. PFF has listed the number of games played at left or right tackle, so I’ve simply sorted them depending on which position each player has played more.
These graphs convey the same information. Still, there’s no correlation between arm length and performance. Another interesting thing that you can see from these charts is the wide variation in arm lengths for right tackles vs left tackles. Looking at the left tackle chart, all but 4 of the qualified players had arms between 33 and 36 inches long. Looking at right tackles, that number jumps to 13, and is apparent on both ends of the spectrum. So not only are the guys with tiny arms stuck on the right side, but so are the “long-limbed athletes”.
Any way I break it down, there doesn’t seem to be any correlation between arm length and performance.