So I thought I'd try to answer this question. I wrote a pickup basketball simulator to simulate games using NBA stats (from Basketball Reference). It follows the following aspects of a standard pickup game (stats used in parentheses):
- If the defensive player steals the ball, the possession ends (Steal %)
- Else, what type of a shot is taken (3PA/FGA)
- If a 2-pointer, if the defensive player blocks the shot, the possession ends (Block %)
- If not blocked or a 3-pointer, if the shot is made (2PM %, 3PM %)
- If miss, which player rebounded the miss (OReb %, DReb %)
- If the offensive player rebounds the miss, the possession starts over
The following rules are enforced:
- Standard pickup scoring is applied: 2's and 1's (3-pointers count as 2, 2-pointers count as 1)
- No free throws. You don't shoot free throws in pickup
- The games are to 21, win by 2
Right off the bat, it's fairly obvious Curry (and the other 3-point shooters) have a big advantage due to the 2's and 1's rule (Grantland wrote about this scoring advantage).
After simulating each possible 1-on-1 combination 10,000 times each, another wrinkle jumped out at me: one of these things is not like the others! I used this past NBA season's statistics, and Carmelo is past his prime at this point. He loses to every other player in this hypothetical tournament (and in most cases it's not even close), so for simplicity, I've dropped him to make an 8-team bracket. Here is the win probability matrix for every single possible matchup, including Carmelo:
I seeded each player based on their predicted overall win totals, which created the following bracket:
|Seed||Player||Round 1||Round 2||Round 3|
Curry wins the tournament most often, but LeBron isn't far behind. The two of them combine to win 54.64% of the time, which favors the pair over the other six players in the field.
Per the win % matrix, the top 5 least competitive matchups (discounting Carmelo):
And the top 5 most competitive matchups:
Some interesting things that jumped out at me:
- Per the simulations, advantages are not transitive. For example, Curry is favored over LeBron, but he beats Davis (66.30%) less often than LeBron beats Davis (68.45%).
- Including defensive performance is huge. Without it, Curry beats LeBron almost 70% of the time, as opposed to 57.36% in the final simulation.
- The length of game matters. If the games are to 11, then the spread of competitive balance is much smaller (games are much closer to 50/50).
Finally, here are the associated predicted margins of victory for each matchup: