The Wall Street Journal marveled at a "remarkable quirk" embedded within LeBron James' career statistics. But my research of other stars' stat lines suggests he's the rule, not the exception.
I would have been with the WSJ journalist and would not have guessed the essential slipperiness of this at first blush, although of course it computes if you think about it. Having to hit all three categories and not two is I think what makes it more unlikely than it first seems. Ironically, I think Chamberlain was the most unlikely of the players you sampled to have a matching game, since he got so many rebounds on average. I am operating on the assumption that the higher an average, the higher the standard deviation, and the harder to match.
It's only two categories, but we are sometimes informed that an 11-7 score in the NFL is the first in history, or some such combination, and that is what I am reminded of.
A couple of other brain teasers as I sort this out for myself....if we took some other combination besides the average, particularly in games where the player played a full complement of minutes, the probably of finding a match would decrease. Yet, for a player to be above or below his average in all three categories, is probably at worst only a 1 in 8 proposition, since each individual over/under is just 50%. It is the precision which makes a match unlikely.
The total number of unique pts/rebounds/assists games for a player in his career would also be fun to look at, and probably not too hard to get. This could also indicate what is possible/likely as far as combinations other than the average in each cropping up.
Also might be fun to ask something like, again, assuming a certain number of minutes, what is the probability of a James threesome beating a Chamberlain in all three categories? Or to take two seemingly mismatched players, and ask that question? (Actually, this and other exercises could get tedious after a while.)
Matt, First off I am not a stats guy but I appreciate how you explained this and made it accessible even interesting and folded in some gambling education even. You have many gifts! Okay a stupid question. Are you taking the average over games and working backwards to see if those stats were achieved in any game? It seems to me to be fair you would have to do this iteratively to be fair, starting at the second game. At your first game you would by definition achieve your average as there is only one game. So all players hit their career average at game one. If game two had those exact same stats the career average is met again. And so on. So it would be possible to hit your average at every game along the way with that fact swallowed up and invisible a game later in ones career. Again I am not a stats person but is my thinking correct here? Apologies if this keeps you up at night for years as running every player and every game iteratively to see if an average was achieved will be a lot of computation!
Thanks much, Bill -- first off, I am surprised you're not a stats guy...especially based on your iterative point. A really good point, too. I mean: it's quite possible that all of these guys did hit their career average at a given time, just not at the end of their careers (or at this point in their careers, for the active ones). I am tempted to explore this, at least for the first 10-20 games of their careers. But I think I'll resist that temptation. I am much more likely to check on Larry Bird and John Havlicek and Bill Russell and Bob Cousy and Paul Pierce --- all those Celtics must feel left out after I included so many Laker greats here. I might have to turn in my Boston Celtic passport if I don't do this soon!!
I would have been with the WSJ journalist and would not have guessed the essential slipperiness of this at first blush, although of course it computes if you think about it. Having to hit all three categories and not two is I think what makes it more unlikely than it first seems. Ironically, I think Chamberlain was the most unlikely of the players you sampled to have a matching game, since he got so many rebounds on average. I am operating on the assumption that the higher an average, the higher the standard deviation, and the harder to match.
It's only two categories, but we are sometimes informed that an 11-7 score in the NFL is the first in history, or some such combination, and that is what I am reminded of.
A couple of other brain teasers as I sort this out for myself....if we took some other combination besides the average, particularly in games where the player played a full complement of minutes, the probably of finding a match would decrease. Yet, for a player to be above or below his average in all three categories, is probably at worst only a 1 in 8 proposition, since each individual over/under is just 50%. It is the precision which makes a match unlikely.
The total number of unique pts/rebounds/assists games for a player in his career would also be fun to look at, and probably not too hard to get. This could also indicate what is possible/likely as far as combinations other than the average in each cropping up.
Also might be fun to ask something like, again, assuming a certain number of minutes, what is the probability of a James threesome beating a Chamberlain in all three categories? Or to take two seemingly mismatched players, and ask that question? (Actually, this and other exercises could get tedious after a while.)
Good stuff........more to come in future installments. I've done a deep-dive on Celtic greats.
Matt, First off I am not a stats guy but I appreciate how you explained this and made it accessible even interesting and folded in some gambling education even. You have many gifts! Okay a stupid question. Are you taking the average over games and working backwards to see if those stats were achieved in any game? It seems to me to be fair you would have to do this iteratively to be fair, starting at the second game. At your first game you would by definition achieve your average as there is only one game. So all players hit their career average at game one. If game two had those exact same stats the career average is met again. And so on. So it would be possible to hit your average at every game along the way with that fact swallowed up and invisible a game later in ones career. Again I am not a stats person but is my thinking correct here? Apologies if this keeps you up at night for years as running every player and every game iteratively to see if an average was achieved will be a lot of computation!
Thanks much, Bill -- first off, I am surprised you're not a stats guy...especially based on your iterative point. A really good point, too. I mean: it's quite possible that all of these guys did hit their career average at a given time, just not at the end of their careers (or at this point in their careers, for the active ones). I am tempted to explore this, at least for the first 10-20 games of their careers. But I think I'll resist that temptation. I am much more likely to check on Larry Bird and John Havlicek and Bill Russell and Bob Cousy and Paul Pierce --- all those Celtics must feel left out after I included so many Laker greats here. I might have to turn in my Boston Celtic passport if I don't do this soon!!