And guys have torn acls on “routine” football routes, or routine base runs. It is possible that these things happen sometimes. Again, time will tell.
Yes. But the fact this happened in his first game against real NBA players and people already suspected he’d be prone to this type of injury makes it rather unlikely that this was just a freak accident, I think. If I tell a person to guess a number in an envelope that is between 1 and 1000, and I give them 100 tries — them guessing it at some random point in those 100 tries would not be that suspicious. If they “guessed” it right on the first try, however, it is reasonable to think it wasn’t pure random luck.
Is there any type of theory out there that human bodies have X number of jumps, sprints, turns, etc. in them before something breaks? Similar to how cars have X number of miles in them before they break down. Certain bodies have less in them than others like a Dodge would have less miles in them than a Toyota. Things like maintenance could extend their life, but a Dodge will never be a Toyota and a Holmgren will never be a Karl Malone. I say that cause I'm not buying the criticism of his decision to play in that pickup game.
What if - after they guessed it - i then told you that 1000 people around the world were simultaneously doing the experiment?
If it’s the exact same experiment repeated a sufficient number of times, then yes I would be less suspicious that the guess wasn’t random luck. It’s like a lottery at that point. In an idealized scenario where all NBA players are believed to be physically identical with the same likelihood for injury to start, one guy getting injured in the first game is not reason to suspect they are injury prone. I think it is relevant that in this case we already suspected that Holmgren was the type of player who was especially susceptible to injuries like this. Him getting injured on day one like this is strong confirming evidence, if not outright proof, that the suspicion was true.
In a way, it's the psychological context that makes things like these seem to transcend probability. If you won a lottery, you were just lucky. But if someone had predicted you would win a lottery and you actually did, then the odds of it happening would be staggering. And the whole thing wouldn't seem like just luck even though you could still attribute it to luck.
What we have here is an improbable event -- this kid ruptures his foot on a routine basketball play in his first game against NBA-caliber talent. And a prior theory that a player with his physical frame is susceptible to lower-leg injuries. These are not independent. One being true would make the latter more likely to occur. It is rational for someone to "update their priors" when an improbable event occurs, if that prior is for something that is causally related to the event. It's pretty fundamental to how science works. Obviously, it doesn't prove the prior theory must be true. But it increases the probability that it is true. If he comes back next year and injures himself again with a different lower-leg injury, the probability increases still more. Anyway, that's how I look at it. I welcome people who disagree to argue otherwise.
I actually don't disagree with you. In fact, I had been trying to argue against those who pointed to his lack of injuries in the past and dismissed the injury concern. Just because he had been lucky did not mean that the risk wasn't high. What I am saying is that these things are still probabilities. A prophecy about an improbable event coming true may just be luck, but it could also be that the prophet's power was real. Psychologically, it's more satisfying to believe that it's not just blind luck. The theory about Chet's injury proneness could still be true even if he had a long career without any serious injuries. He could just be lucky in beating the odds.
shouldn't that not matter though? It's already a lottery if you run it once or 1000x. The probability of any number being the right number (or being guessed at all) is 1/1000. Any "time" is as likely as any time to have a matching number, there's no magical Bayes force that kicks in when you run it 1000x that influences any individual run; that's like saying "I got 2 heads in a row, therefore there's a 75% chance the next is tails"
You're right, I should expand. Probability is 1/1000 independent If you test 100,000 people, you would expect 100 of them to get it right. Can you use that logic to update your beliefs post priori to say that 100 of them are cheating? No, you can't, at least not logically. The rules are the same, even when your sample size is 100 (or one person doing 100 trials) There's a lot of bias in these things, and we don't have a big enough sample size of NBA 7 footers to know the real odds. The only think we know is that most NBA teams believed the expected value of skinny 7 footers, even including injury risk, was higher than the expected value of other players. Otherwise, this wouldn't keep occurring. They could be wrong about injury risk. We don't have the data to actually determine that. Until we do, we're just people with opinions.
I thought we were gonna have to put you on suicide watch. It's a Lis Frank injury, one of the worst foot injuries you can have for an athlete.
There are a couple differences with my envelope example. First, each time you make an incorrect guess, you are gaining information by eliminating a wrong answer. So, the probability that you'll guess correctly is actually higher on guess number 50 then guess number 1. But let's ignore that and suppose that the person making the guesses has no memory of their prior guesses. Even then, the possibility of the person having some external knowledge of what's in the envelope increases the probability that they will guess it right on guess #1 as opposed to guess #50. And if it comes to pass that they do guess it right on guess #1, I think a rational "Bayesian" inference would then be to have higher confidence that them having that external knowledge is true. Especially so if they had good reason to suspect it in the first place. You can also consider the classic entropy example. You pour black ink into a clear glass of water, you leave for a week, and then you return. Suppose you find that the ink is all pooled into a spherical globule floating in the water, rather than having spread out. Each possible physical configuration of ink particles within the glass of water is equally likely to have occurred. But the particles clumping in a globule would make us think something else was at work (some attractive force between the particles), while the ink particles spread out randomly throughout the glass would not raise such suspicion (even though the particular configuration you find it in is equally likely to have occurred as the particles being clumped together, absent any other biasing force like the particles being sticky).
Sucks for Chet, but anybody who keeps saying it was just a freak accident is just fooling themselves. Yes it could have happened to anybody, but there's a reason it happened to Chet and not anybody else. It's not like Lebron even bumped him hard, Chet tore his ligaments moving backwards.
