If you want to do an interesting experience, doing sprints teach your brain to think faster (because it has to keep up with the information of your steps).
Sprinting is all fast-twitch muscle and technique. It has little to do with your brain. Anyone who ran track knows that short sprinters are the dumbest guys on the team. The smartest runners are the distance guys. Out of the whole team, the smartest guys were the ones who specialized in the oddball events like steeplechase, triple jump or discus.
As has been pointed out, the comparisons are only useful pertaining to the same brain before regular exercise is present and after. You can't glean much from comparing one person to another because baseline intelligence varies too much to account for.
Now, what you are describing may be a case of self-selection. It may be possible (though I do not concede this point) that smarter people tend to gravitate toward the more oddball sports. That doesn't indicate that sprinting does not benefit the brain. Here's a thought experiment:
There are 100 people at the pool and 50 life jackets. People are allowed to choose to use a jacket or not, until all jackets are gone. You may find that better swimmers on average choose not to use a jacket. That does not indicate that the life jacket is not useful for swimming.
Sure, whatever. The original point about your brain moving faster to keep up with your feet is stupid in any context. There's countless techniques in nearly every athletic sport about how to shut your brain down so that only your muscles and autonomic nervous system are doing the work. Athletic speed has no effect on other forms of intelligence. If anything it has a negative effect because sprinting is anaerobic and therefore is cutting off oxygen to your brain. I have no idea what you're getting at with the life jackets.
It's tough to use intuition to bring any real insight to bear on biological systems, I'd be really interested in finding some real research into the matter.
Re: the lifejackets I was demonstrating that the effectiveness of the jackets is not effected by who chooses to use them. I was pointing out that saying less intelligent people gravitate towards sprinting does not prove that sprinting has no positive benefits on intelligence.
That conclusion really doesn't follow from the stated proposition. The proposition is that doing sprints will make you smarter than you are now, not that it will make you smarter than someone else who doesn't do them. The only conclusion about Usain Bolt that you can reach from the stated proposition is that he's now smarter than he was before he started sprinting. </pedantry>
I read the point as "doing a high speed exercise makes your brain have to work at a faster rate". Sprints being the example chosen as increasing the brain processing speed. Which is quite interesting because there are other activities that require high speed mental abilities. Playing an instrument in a thrash metal band for one. According to this theory, a member of Megadeth would be a faster thinker than a classical musician. Interesting thought.
My point is that you can't draw conclusions about two different people this way. If playing speed metal is a good mental exercise, then the only thing you can conclude about Dave Mustaine is that he's smarter now than when he started playing. You can't conclude that he's smarter than anyone else, no matter what activities they participate in. The classical musician very well may have started out at such a high IQ that no amount of mental exercise will allow Dave to catch up.
I am not sure about the heavy metal / classical music approach. There are many classical music that are very challenging by themselves, even more than some heavy metal songs (which usually are 'play the same note at light speed'). I've heard of an author whose name escapes me now that composed songs that weren't suposed to be played due to the sheer difficult of them.
When you sprint, your brain must fire every signal, and process every step so you can keep your balance. Sprinting is, by definition, running as fast as you can, which also means running as fast as your brain can process it. By training it, you train your brain to think at a higher speed than it normally would.