Basically, if you can run a 4.38 40 then the only way that IQ really impacts your livelihood is that your IQ not be so low that you are literally too dumb to play football.
Right.
However I think it's also important to understand that there might still be a correlation. I.e. let's take out the positions where intelligence comes into SIGNIFICANT play, i.e. QB, OL, maybe something like MLB calling the defense. So we look only at the positions that are dominated by athleticism.
I would not be shocked if you did an IQ test across the entirety of players at those positions and they came out higher than the US average. I.e. let's say the US average is 100, it wouldn't be shocking to me if the average of all tested athleticism position NFL players would be 103-105.
The thing is that the sample size is so small that you're not going to have more than one or two in the entire league that is probably an IQ of >145. That's at the 0.1% of the distribution curve. You'd probably have a few that were >130, which is at 2% of the distribution curve.
But the guys clustered between 100-110 that maybe are driving the averages? They may be "smarter than average", but not by enough to be noticeable. They don't stand out in any way.
But the proportion who have an IQ of <85 (~13%) and a 4.38 time in the 40? They stand out like a sore thumb every time they open their mouths and make you think athletes are dolts. In any other area of life, they'd not be given much of a platform. But because they're athletes, they get a microphone shoved in their face and they have to make words fall out.