Hey guys, arena nerd here.
If both are untrained - say, it's a case of road rage between a russian cyka with a beisbolnaya bita and an equally russian gopnik with his sharp, sharp nozh - then baseballs bat has the decisive advantage by virtue of reach. Knife guy isn't likely to have the composure, patience and skill to get close without eating a faceful.
However, if they both have experience and sufficient skill, then the scales might be even weighed in knife guy's favor - if only slightly, since the bat's range and impact power still remain.
Lets break down the tools each fighter potentially has:
Baseball bat: reach, as previously mentioned. The bat's bulk and length give it ample space control, as well as the ability to bully the opponent by pressing the shaft into them and shoving the poor bastard around, directly stiffling their mobility and providing a close-quarters defense. Note that while using the baseball bat to obstruct the opponent, the batter himself is free to maneouver around.
The bat's power gives KO potential with a hit to the head, enough force to fracture or break certain bones, and debilitating damage to the internal organs, meaning a solid whack to the stomach, and knife guy goes down in pain.
However, the design and material of the bat will impede its performance.
The gradually thickening shaft makes it uncomfortable to grip further away from the handle, while the smoothness will make it slippery, especially with sweaty palms. This complicates its use as a close-range leveraging tool, not necessarily limiting your options, but making them harder, less likely to execute.
When it comes to striking, the rounded shape will make it less deadly of a bludgeoning tool, with the large blunt tip being the most prominent case; while the wood itself retains flexibility, making for less rigid impacts with less optimal force transfer.
Finally, the bat is tip-heavy, meaning that it is slow to recover after swings and will tire out the user quickly.
All in all, the batter's strategy shouldn't change much: keep their distance, carefully time their strikes and use the bat to both control the space inbetween and bully the opponent around.
Knife guy: now we assume we've got a smart and cold-blooded cutthroat on our hands. Just with a knife though: no laser eyes.
Since the biggest problem would be getting in, i'll first adress the ways to do so.
Patience and observation are key to success here: if knife guy can catch on to certain patterns and reactions in his opponent's behavior, it will make it much easier to choose the right moment to slip in. Closing distance will inevitably be associated with some degree of risk, so minimizing it with proper anticipation is always an advantage. If knife guy is lucky, or skilled enough, he might just slip in when the opponent's guard is down - say, as they're still recovering from a swing, or simply not expecting it - meeting no resistance at all.
If the pressure from the batter is too thick, then they will have to deal with an incoming swing.
Dodging is one option - however, it may be hard to execute while similtaneously advancing, commiting oneself to motion already. More likely is bracing the strike or deflecting it.
Deflecting simply involves pushing the strike off-course; using the knife to lessen chance of injury is cool, coupling the action together with a dodge is cool as well.
Bracing would involve several factors at once: the further away from the tip, the less the cross-sectional density and velocity of the impact point, meaning it carries less kinetic energy; distributing the force across a larger surface area can decrease the severity of the damage - an example would be using the upper and lower arm together to block a swing, making it less likely for the bones to fracture; moving together with the swing will help absorb it, as the force is transfered into motion, rather than strain, in this case - a diagonal step-in, rather than a straight one mightaccomplish this task. Last, but not least, brace with something that's less likely to get injured or suffer life threatning damage: the knife, arms, shins and thighs. Not the ribs, stomach, back or head.
Finally, there might be a situation where the bat is already in contact with the body: for example, if the wielder is trying to shove their assailant. In this case, knife guy can use his free hand to attempt a grapple; something the batter cannot do, since a baseball bat is too unwieldy to be effectively used in one hand by anyone short of a muscle monster, simply because it's long and tip-heavy.
All the above options can allow to get in without suffering debilitating damage (if executed right), meaning that knife guy remains in proper condition to go absolutely ham on his opponent.
This is where the knife shines: its wielder has one hand free to restrain the opponent and open up their guard; the weapon's weight and length make it very nimble; and to deliver a crippling strike, a knife needs a much smaller range of motion compared to a baseball bat swing, meaning it's both quicker to deliver and to recover from, allowing to overwhelm with repeated stabs and slashes. While it can't knock someone out, the cumulative blood loss and pain from wounds, combined with rapid action can put the person into a state of shock, rendering them helpless against their attacker.
Oh, and they can take off their jacket and wrap it around their free arm, if wearing one. Or their scarf. Old knifefighting trick; takes some time though, plus you can get tangled up in the jacket; a thick scarf can really become a pain in the ass for the opponent though.
To sum it up for knife guy, the options he has for getting in all require tight timing and sharp execution, becoming dangerous if used poorly; but once he gets in, the batter is going to have a bad, bad day.
It's important to remember though: if knife guy doesn't maintain proper control, batter can still retreat and reset the situation.
In conclusion: fuck off. I don't know who wins. Fighting is cool. Killing is an atrocity. Go duke it out with a styrofoam bat and a rubber knife. Have fun. Have a nice day.