Spears can be thrown, so they are a ranged weapon (albeit, short ranged). It's also easier to surround a creature with a group of humans and box it in with spears. It's not the 'net animals harvested' that would be impacted, simply the time taken to hunt. Spears probably increased the percentage of successful hunts. You have to imagine to try to kill a deer or a gazelle with a hand axe...the only way to really do it (since you're far slower on foot than a gazelle) is to chase the animal down until it gets tired enough to quit (takes as much as 8 hours of chase). Then, you have to be able to successfully fend off any other creatures hungry enough to challenge you for it (lions, hyenas, wolves, panthers, etc...). The opportunities for the creature to escape or for another creature to intervene are numerous.

Imagine if spears improved hunting success rate by 50%. What do you do with that extra time? Maybe you take up painting, sporting, music making, etc. Maybe you venture further out into the wilds and succeed across a broader terrain (no longer reliant on savannas alone for success).

Maybe your spear technology and additional leisure time leads you to discover other uses for woodworking, etc. Maybe a few hundred thousand years of that (including sexual selection) leads to evolutionary improvements in brain power.