Well we don't know without analysis... Health concerns are mostly long-term, and there's no definitive answer on how much getting hit in the head is required for permanent brain damage. Re: concentration, I'm even less convinced; maybe it's not the getting hit that is bad for concentration but the switch between mental/physical activity. Or maybe concentration improves with more adrenaline.
There are definitely short-term cognitive consequences to getting hit in the head. The nausea you can experience with head trauma can also interfere with thinking.
After suffering a blow to the head, I was given a battery of cognitive tests: Repeat this sequence of numbers, and the like. Three days out I was failing the tests rather spectacularly. At five days everything was back to normal.
Yes, for boxing champions, but even there it's hard to say what is caused by the boxing and what is caused by genetic factors. People often say 'look at Ali!' but there's no way to tell if it's really because of the boxing. But more importantly, note that I said 'how much getting hit in the head is required'. See e.g.
Both from 2007. First one says that amateur boxers do get brain damage, second one says they don't. (there are the top google hits, I looked into this deeper about 5 years ago; at that time there was very little research done, let alone consensus.)
Point being, the question is: does getting hit in the head pose linear risks/ I.e, simplified, do a number of cells die for each punch or kick to the head? Or does it require a certain threshold of damage for there to be any cognitive effects?
I don't compete in any sport but I've trained plenty of full contact sports over the last 10 or 15 years. I've been punched and kicked in the face a lot, with and without gloves, been knocked out briefly once, been choked out several times. Still my head/brain has taken nowhere near the amount of punishment a pro or even good amateur fighter gets; my brains gets plenty of time between trainings to recover. I can never know for sure if my training has caused brain damage, and if it did, in what form that will manifest itself (or has already, maybe), but I don't have reasons to believe it affected my cognitive functions. Maybe it did and the damage caused decreased intelligence, making me believe that it didn't :)
Kind of funny, but not really meaningful. There are different priors. Prior probability that water is actually medicine: ~0. Prior probability that repeat head trauma causes damage: >0. If you'd ever seen an MRI of diffuse axonal injury you'd have a different perspective.
A good example of a priori knowledge: "All bachelors are unmarried". This is true, because it's so by definition, it's probability == 1. The effect of boxing is not so obvious as you claim (prior probability that repeat head trauma causes damage: <1), and should be verified. See also roel_v's responses in this sub-thread.
Please reread what I wrote instead of setting up a strawman; you'll see that I did not write "=1" but instead >0. We have prior knowledge on this from evidence.