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I recently got really interested in the NBA (thanks to Mark Cuban). Google led me to detailed statistics of NBA players, for example, as found here.
If you just look at the statistics (without looking at the Position column), would you be able to tell the position of a player?
I think you wouldn't, you could differentiate groups of positions (PG & SG from PF & C) but exact position no.
First, you would start by looking at Rebounds and Assists, if a player has around 8+ rebounds he is almost always a C or a PF, likewise if a player has around 7+ assists he is probably PG or a SG. The numbers I picked are arbitrary but the more the number goes up the clearer the position (PG or C). Now again there are exceptions like Jokic who averages around 7 assists or Westbrook, Simmons and Doncic who average 8+ rebounds. In that case you can then look at Offensive rebounds and mainly blocks, very rarely does a guard have more than 1.0 blocks per game, so that would tell you that a player is probably a guard even thou he has a high number of rebounds.
After that it gets harder and harder to tell because there are different types of players for every position. For example, if a certain player has a high number of FG attempts per game and all other numbers(like rebounds, assists and so on) are low then he is probably a Shooting Guard whose main job is to score. But even that is not 100% telling because he could be a scoring Point Guard like Irving who is listed as PG but plays like a SG. Or he could be a scoring Small Forward like Paul George. There are types of players like Strech Fours who are PFs that play away from the basket and shoot more three's and so on.
And I won't even start with Lebron who could probably effectively play everything from PG to C.
So, unless the numbers for rebounds or assists are clearly showing that a player is a PG or C, my answer would be no, you can't tell which position a player plays based on stats. Now if you add player's height to the equation then that could be a different story.
EDIT: So to clarify why I picked "arbitrary" numbers that I picked. If we look at, for example, the year by year leaders in assists per game it looks like this. You can see that in the past 20 years highest number of APP is around 10,11 and before that It's more or less the same if we exclude Stockton who is one of the best true PGs ever. Almost all of those players are guards, primarily point guards, which of course makes sense. You usually can't average that many assists per game unless you organize the play which is Point Guards' main job. That is why I picked 7, because it's close to the usual highest average and around that number it gets clearer that a player is a Point Guard.
Same goes for rebounds only the number is higher. As I said, it's not an exact science, but the higher the number of those two stats the clearer the position a player is playing.
