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I have a dataset of basketball player salaries and an estimation of how many wins they contributed to their teams over the season. So a reasonable thing to do with those numbers would be to divide the wins with their salary to get a number showing the value of their contract.

The problem is that some players have negative production, as in over the season they provided their team with, say, -2 wins. That makes sense basketball-wise but when doing the division, obviously, you get a negative number, which doesn't seem to really describe the value of the contract. A really low number normally would mean the player is out-producing his contract, but that's clearly not the case with negative value players.

So my question is, how would you evaluate those players' contracts?

Here's an example of the data just to be clear:

+-----------------+----------+-------+
|     Player      |  Salary  | Wins  |
+-----------------+----------+-------+
| Carmelo Anthony | 25534253 | 0.16  |
| Rajon Rondo     |  9000000 | -0.51 |
| Pascal Siakam   |  1544951 | 11.88 |
| Stephen Curry   | 37457154 | 14.43 |
| Kevin Knox      |  3739920 | -5.67 |
| Isaiah Thomas   |  2029463 | 0.00  |
| James Harden    | 30431854 | 18.57 |
| LeBron James    | 35654150 | 11.15 |
+-----------------+----------+-------+
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  • $\begingroup$ You may want to describe how you're counting "wins", as I'd expect that to be a non-negative integer. How does someone provide the team with -2 wins, or with 0.16 wins? As you've described it, a low win/salary ratio indicates that the player is overpaid, the opposite of your interpretation - a player with 100 wins earning \$100k has a ratio of 1, but a player with 100 wins earning \$1M has a ratio of 0.1 (they are only as good as the \$100k player, but are paid 10x as much). A negative ratio indicates that you're paying someone to help you lose! I'm not seeing the problem here. $\endgroup$
    – Nuclear Hoagie
    Jun 25, 2019 at 18:52
  • $\begingroup$ Wins are calculated from other data to (hopefully) sum up to team wins. So when team A wins 44 games in a season, we could estimate that Player X contributed, say, 7.44 of them. It's not as clear as counting pitcher wins in baseball but a rough estimate. -2 would mean indeed the player made the team perform worse than they would have without him. $\endgroup$
    – Clayton Johnson
    Jun 25, 2019 at 19:36
  • $\begingroup$ Say two players make 10$m each. One contributes 0.01 wins, the other -0.01. I would expect their value to be almost exactly the same - how could I get there mathematically? Or players who are exactly at 0 wins - how could I compare their value to players who, say, are paid a lot more but contribute a little more? $\endgroup$
    – Clayton Johnson
    Jun 25, 2019 at 19:46

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Well, I figured out a way to do it that satisfies me.

I calculated the average cost of a win for the whole league, then calculated how many wins each player should produce based on their salary, then compared that to their actual production.

Peace!

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