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Notes -
My answer was Bat before looking, but I caught the ETA before I posted so I'll reply in detail.
This all hinges on how one assumes an "average" person to behave, and in who you picture when you imagine an average person. I picture two males, late twenties to early fifties, out of shape but not totally sedentary, blue collar workers. Any time your model changes to make the people bigger or increase physical fitness it is advantage to the bat as strength doesn't scale with toughness, any time you increase courage and willingness to accept injury to win it is advantage to the knife. An additional X-Factor, obviously, is how much baseball experience you imagine the average person having. If you picture your batter having played baseball from tee-ball to high school, I'd give him a much higher shot. if you picture this being the first time he ever touches a baseball bat, much lower. This is going to enter into who you picture when you picture average: a small white town in the USA is going to have a lot more "average" baseball experience than a city in Germany. If you have the hand-eye coordination from years of hitting baseballs, the odds of someone getting in without getting hit get lower.
You "knife people" are thinking that you shoved a neuralink up each contestant's ass and they are now being steered by billionaires with xbox controllers. You imagine they are acting with perfect courage and sangfroid, that damage done to them is only notable for its physical impact and not for the psychological. You picture it as a video game where the knife guy tanks the hit from the bat and then goes in for the kill. This would work, for a person with perfect courage and sangfroid. This is not the average untrained person.
Most people will be unwilling to get hit with the bat, they will be scared of getting hit. While the rational choice is to accept the pain and at worst broken left arm or ribs or some missing teeth and stab the other guy to death, most random people will not be willing to do so. They will be unable to force themselves to take a hit and keep moving. Even if they try to, they will hesitate or feel pain and be thrown off balance mentally by it, they won't close, and they'll get hit again.
If we were to model this in reality with random people, I suspect that the results would be close to random, and that it would take many trials to see any kind of result, because the mental fortitude to murder someone at the risk of one's own life is pretty stochastically distributed, and it would be the defining factor in the match.
A lot of the knife answers seem to assume maximum stupidity from the bat fighter and maximum cunning from the knife fighter. That the only strike someone could do with a baseball bat is a big homerun swing. I'm pretty sure most people would figure out that's not all they can do with a bat within seconds of thinking of it as a weapon, and of how to avoid ending up being knifed. Most importantly, a quick overhead bonk (think kendo strikes) leaves you a lot less vulnerable if you miss than a swing, and if the opponent tries to catch it or to block it they will open up the entirety of their body to kicks. While that is not going to kill or even knock out in one shot, just one overhead bonk connecting is likely more than enough to end the fight; the amount of force in it would be enough to have the opponent reeling for long enough to line up another one, and another one, ect... And as for knife fighters, winning with one requires knowing something that is not really commonly known: you will not incapacitate someone with a knife. The targets that can incapacitate are small and an untrained person is not going to hit them on a resisting target. An expert probably wouldn't even bother either. The way to win with a knife is that you tie them down another way (say, by tackling them to the ground), and THEN you do damage with the knife, repeatedly. But the knife is essentially useless to win if you are not able to tie down the other guy, and with no distractions he has a big heavy piece of wood he's highly interested in keeping between you and him.
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