Unless by speed you mean quick reactions. That might help for catching a lizard by stamping on its tail. (I did that as a child: the tail came off so it wouldn't have been many calories.)
I imagine persistence hunting as being a big thing in olden times. You'd need to have a long-distance runner's physique, and ability to follow tracks. Also bow and arrow: skill in moving quietly, and aiming well, obviously.
When it involves mostly running for hours, sex probably matter much less.
Well in a way. "Less" would be accurate than it might matter in contests of strength, but it's still hugely relevant. I think the older races may even be more informative since that would be more of contests of raw athleticism as opposed to the extreme diet/supplemental/developmental process that high level athletics is today.
There's obviously no data, but I would bet any of the top 10000 long distance women runners outruns Usain Bolt in their category. Regarding persitence hunting, it's prohbably easier for humans to hunt cheetas* than to hunt horses.
The general assumption is that men are more likely to be the hunters: I'm not contradicting this, just pointing out it's not definitive. The previous poster was stating it as fact, and the first commenter was being questioned for daring to question said unverified fact.
Often the assumption is based on the need for speed and strength, but a lot of hunting (even of big game) was trap-aided, and primarily called for practised skill rather than simple strength and speed.