The first example isn't Bayes, it's basic without replacement probability. The difference is important. The second example is another example of bias. Configurations you find amusing don't shift the value because you can't use that evidence to logically update a prior belief.
Are you disputing that the probability Holmgren would be injured in game #1 goes up dramatically relative to his probability of being injured in some game in the middle of the season, under the condition that he is actually injury-prone? Edit: Sorry, the example was about the envelope -- but same point. Probability that first guess would be correct relative to probability that 50th guess would be correct goes up significantly under the condition that the person making the guesses has external knowledge about the contents. Are you disputing that finding the glass a week later with the ink bunched together wouldn't be strong evidence that there is an attractive force causing that to occur? You seriously wouldn't draw that conclusion?
Way to try to distract from the obvious - Chet Holmgren has spent too much time close to the event horizons of smaller black holes and is showing early-onset spaghettification.
let me know the winning numbers next time then. Let’s be real. This was a half assed event. Don’t act like this was a playoff game after a years worth of work and preparation. Guys are working to get into shape after an offseason and that’s always a scary situation for players…it happens every year. But feel free to message me in a few years if it is decidedly concluded that Chet is physically unable to play nba basketball due to repeated injuries. I’ll be happy to congratulate you on the amazing analysis that a super thin 7+ ft dude might injury problems.
Kind of a strawman. I'm not predicting he'll be physically unable to play NBA basketball in a few years. I do think there's a good chance he'll have an injury-riddled career, like Porzingas or Yao. Of course, it's not something I'm hoping will happen. Your point seems to be that he might be more injury-prone now given that his body was under-developed and he's trying to get into NBA shape still, but as he fills in physically there's no reason to assume this will be recurring problem for him. That's fair. We'll see how it turns out.
I believe durvasa is formulating the envelop problem such that there are two hidden states (cheating, fair) and it is unknown whether the statistics correspond to a fair state (replacement probability stats, as you mentioned) or they correspond to a cheating state (unknown probability stats but deviating significantly from fair). So the Bayesian aspect is to determine the relative likelihood of being in a cheating vs fair hidden state. The complication is that we don't know what the stats of the cheating state would be and we also have high uncertainty in the priors for the cheating and fair state.
Right. One can apply "Bayesian" reasoning even when they don't have precise numerical quantities to work with. If some guy claims to have found Big Foot and posts all manner of "evidence" on his blog, a rational person is still justified in being highly suspicious that there is fraud going on, absent any exact stats or knowledge about that guy's background. It's a judgment call how suspicious vs how credulous they should be in light of whatever evidence is posted or whatever credentials the bloggers claims. Anyway, yes, this has gone far afield of the thread topic. Sorry for the derail. Wish Holmgren an effective recovery and long career. He's an incredibly intriguing player if he can live up to his potential and remain healthy.
Your last sarcastic line seems to undermine your whole post. "We still don't anything, certainly not that he's injury-prone. But if it turns out that he is injury-prone, good job on making the completely obvious prediction that he would be."
Yea same, I just couldn't resist joining the nerd talk. So glad we got Jabari. Even when healthy, Holmgren seemed to fall down at strange times, like his body just didn't work with what he was trying to do.
I think the superficial eye test of Chet is that he’s very frail looking, which would lead one to believe he is injury prone. It makes logical sense. However, I also believe that there are times when the eye test doesn’t always match up with reality. Simply, there is a chance for a person slight of build to have a successful nba career. I understand both sides of the argument I’m just not pretending to know the future. An personally, I don’t like dancing on a guys grave, so to speak. It’s unfortunate to see young , and very unique , talent get hurt
