How to figure the probability of players ending up on a team

[louisvillekid]

Was trying to figure this out. I realize that you have to take out the fact that players have contracts and are tied to teams barring a trade.

But start of last season UK had 31 players on rosters, some doubled up, or even triple on same team.

But taking just random chance like a drawing.

31 players if each were lucky enough you could have one per team and an extra on one.

If it was just a random draw for all 31 to land on a team, but at least one landed on a contender, like whats the odds that out of the 31 players at least on gets on a top 3 contender?

There was a tweet going around yesterday about how Cal had coached for 26 years and has had 33 first round picks and not one had won a nba champ. Only one former player had won a champ and he went undrafted out of memphis but was on the Heat riding the bench when they won a champ.

So me and buddies thought the chances seemed crazy that out of all the first round picks none had got a champ.

But there is a lot of variables. So we were just thinking probability on just 31 random draws on opening day, what odds would one of the 31 have at landing on a top 3 team?

Any ideas how figure this out?

[peacebyinches]

The dirty way to figure this out would be to say that each year there was only one player of his being drafted, with 31 teams picking (3 of which would be in the top tier) and this 'event' happened 33 times. The chance that none of the players was drafted by a top 3 team would be:

(1-(3/31))^33

or about 3.5%.

Since there were multiple first round picks in the same year (since he only coached for 26 years) then you have to tweak the odds a minor amount to account for the 'without replacement' part of this scenario (i.e. adjusting the odds for a single year where there would be 2 players NOT being picked by one of the 3 best of 31 teams) and incorporating that, so the odds decrease for the 33 picks somewhat, but it won't be significantly different than the approximate 3.5% chance that none of the players get drafted by a top 3 team using the shortcut.

[louisvillekid]

The dirty way to figure this out would be to say that each year there was only one player of his being drafted, with 31 teams picking (3 of which would be in the top tier) and this 'event' happened 33 times. The chance that none of the players was drafted by a top 3 team would be:

(1-(3/31))^33

or about 3.5%.

Since there were multiple first round picks in the same year (since he only coached for 26 years) then you have to tweak the odds a minor amount to account for the 'without replacement' part of this scenario (i.e. adjusting the odds for a single year where there would be 2 players NOT being picked by one of the 3 best of 31 teams) and incorporating that, so the odds decrease for the 33 picks somewhat, but it won't be significantly different than the approximate 3.5% chance that none of the players get drafted by a top 3 team using the shortcut.

appreciate it