Man -
175 lbs
25 years old
in good shape
Baboon -
95 lbs
18 years old
in good shape
Hand to hand - No sticks or other weapons
Arena - On the Savannah
A lot of combat between predators is about posturing and confidence, rather than strength or ferocity. If the human convinces himself not to show any signs of fear, the baboon may eventually get the impression he’s facing a much more determined (and certainly physically larger) opponent and back down before he gets hurt. Similarly, humans have successfully faced down angry elephants by simply not giving into fear.
But if it gets to an actual fight, the human is toast. Them puppies is strong, smart, and got wicked teeth.
In my teens, I read a lot of books about big game hunting in Africa and India. In one of them, the author described witnessing a mother baboon fighting to keep her kid(s) safe from a leopard. He was amazed because in this case the baboon won and drove off the leopard – apparently 99 percent of the time the leopard would win. Now, do you know how powerful a leopard is? Any critter that can just put up a decent fight against a leopard, much less possibly win (even if only 1% of the time), is one bad sumbitch.
Maybe if the human studied how baboons fight and knew what to expect it would make a difference, kind of the way that boxers will look at clips of their opponents before the match to train.
My money is on the human… most of the time, if he’s prepared.
Sure, most animals can sink their teeth into a person with a vise like grip that would be impossible for a human to pry open relying on physical strength.
However, a human who’s trained to fight and won’t try to simply flee or panic from such a bite knows how to jam their thumbs deep into the eye socket of the animal.
Peace.
But this supposes that the two are otherwise fairly equal. On the other hand if I study all of Evander Holyfield’s moves and then get in the ring with him, about the best I can hope for is to know which hand he’s going to use to flatten me.
I couldn’t find anything online about the absolute strength of baboons or even the relative strength of baboons compared to chimpanzees but let’s use the chimp as a starting point. Chimps are about 50% larger than baboons (150 lbs vs. 100 lbs average male size) and chimps are extraordinarily strong (Saint Louis zoo throws out a blanket “7 times as strong as a man”). If we scale that down by body size we’re still talking about a monkey that is several times as strong as a person, plus it has fangs and can use all four limbs for grasping.
That indicates a small, fast, strong opponent stabbing away at your repeatedly. My money is on the monkey.
Moriah’s idea about going for the eyes is probably exactly what the baboon will be doing - slashing away at your face. IIRC from previous reading that’s a common tactic amongst various monkeys.
Only tangentially related, but my dad once worked in Ethiopia surveying the land for the purpose of making maps for the US government. He and his workmates were out in the field one day and came up over a hill. Before them was a huge group of baboons. They needed to get through, but the baboons were in their way, so they picked up some rocks to toss into the group and scare them away. Without hesitation, the baboons picked up the rocks, plus some other they saw scattered around, and heaved them all back at the guys, doing some pretty good damage and scaring the crap out of my dad and his friends.
Of course, people have killed leopards with their bare hands before - let me see if I can dig up that photo of Charles Cottar who did while his son was filming back in the day.
Surely after reading the hundred or so existing threads about fights between humans and various animals - ?who would win? - you know they always end up in long-winded arguments between two sides who have two different interpretations of what’s being asked. So I’m assuming you mistakenly forgot to include the most important detail in your question:
Are you asking “is it in any way physically possible for at least one human at some point in history to have won such a fight even by complete freak accident?”
OR
Are you asking how likely it is that the guy you described in the OP would win right now today?
Also what do you consider “winning”, and a “fight”?
Winning
- One animal running away?
- One animal starting strong but then finishing the fight weak?
- One animal bleeding from the face? (you’d be surprised how many people judge the winner of a human fight this way)
- One animal suffering permanent but non life-threatening damage (eg loose and eye/ get a huge scar)?
- One animal suffering injuries requiring human intervention to heal?
- One animal dead - immediatley/2 hours later/next week?
…from what - blood loss/organ trauma/infection? - Is the judging criteria fair? - would the baboon need to tear the human apart to win while the human just has to survive 3 minutes without bleeding to death to win?
- What happens if both animals are seriously hurt?
What about a combo of the above (eg baboon looses eye and eventually runs away but human started strong with the gouge but then had their jugular ripped open, collapsed helpless in the fetal position, and had to be be saved by a paramedic?
Fight
- Territorial scrap?
- Defending young?
- Rabid/drug induced rage?
- Illogical deathmatch that both animals somehow comprehend and agree to?
All these types of encounters would be fought differently and be judged differently from both animal’s perspectives. I’d consider myself the winner of a territorial fight if I stepped on the monkey’s toe and he ran away. I’d also say I won in an insane random attack from a marauding baboon if I happened to live through it. None of the answers you get will mean much if all this stuff isn’t understood - anything from “100% guarentee yes” to “no way in hell” could be argued succesfully.
Well the reason we won this planet was through intelligence and intelligent use of dominance displays- things that OFTEN come into play in a physical fight with an animal.
Almost always, animals submit to another animal that shows no fear- this is very useful to a human who can think properly at the proper time.
If I personally got into a fight with a monkey-which I’m sure has more strength- I would make more noise&violent motions- I’m betting it would keep me alive anyway. 
I think the biggest strength for animals is most of them are extremely agile. And they are also typically much faster than humans (although many animals that have a higher raw speed couldn’t chase down a human in a lot of situations because humans typically know how to better use terrain and humans are able to outrun quite a few animals, even horses in some cases, over a long period of time/long distance.)
In this particular fight I think the baboon would win most of the time (assuming a physical confrontation actually occurs.) However a human would stand a decent chance if they got lucky with an opening kick to the throat, head area. A baboon probably is stronger than many ordinary people, and definitely has more natural weapons, but a 95 lbs. animal receiving a solid kick to the throat or head area will be in critical physical condition afterwards.
Fighting a wild animal with bare hands is pretty dumb though, we became the dominant species on this planet by using our heads, not our fists.
Also even a lot of the more ferocious predators will stay away from humans if humans make aggressive displays, even some of the big cats (jaguars, leopards, cheetahs, panthers, mountain lions) won’t directly confront a human in a direct confrontation because the human towers over them. Now whenever serious hunger or fear comes into play with a wild mammal the rulebook is thrown out the window. For example several people in California have been killed by mountain lions, and this is a combination of the animals being very hungry and also being in an area where they have grown used to human presence and did not feel overly threatened by them.
I don’t think it would be close. I think a baboon would destroy a human. Humans generally don’t fight with the ferocity of animals. Baboons are very, very strong. They have big teeth. I think a 95lb Baboon would kill a human pretty easily if it really wanted to.
So you are saying a head-butt is the way to go? 
Yeah, I’m thinking your average baboon could rip Ahnold’s arms out if he wanted to.,
Were you watching “The Naked Prey” again?
I remember seeing a demonstration of the strength of a Chimpanzee. A zookeeper gave it a wooden dowel about 1" thick, and the Chimp twisted it apart. I’d like to see any human on the planet try that.
This may also be a bit off-topic but this is what happened to me.
About a month ago I was walking with my girlfriend to the end of Cape Point in South Africa with a bottle of cooldrink in my hand. As we were walking along the path a baboon came towards us. My GF said the baboon wanted my drink so I hid it behind my back. The baboon came up to me, showed me his teeth, went round behind me and grabbed my cooldrink. I had visions of this animal jumping on my face and ripping me apart so I certainly wasn’t going to fight him or any other baboon over a cooldrink, especially after he showed me his nice canines.
Dude, you should’ve fought him. You could have given us the definitive answer.
Plus, it was a cool drink. Where are your priorities, man?
One thing to factor in is that wild animals survive to adulthood by fighting other wild animals–and winning. Most men–even the meanest bouncer in the roughest biker bar–probably haven’t much experience fighting baboons.
One question, though, for anyone with wilderness experience: I have always heard that wild animals are instinctively afraid of fire. Would lighting a torch, or maybe even flashing a cigarette lighter, scare away a predatory animal?
No external tools (including fire) are allowed in this fight. It’s mano a monko.