How many Lebrons does Lebron have in parallel universes?
It's been well documented (such as this reddit post) that Lebron James has averaged 27 points, 7 rebounds and 7 assists over his career, but has never had a game with a 27/7/7 stat line AKA "a Lebron". In this post, we'll explore how often Lebron would "Lebron" if we simulated 1000 Lebron careers. I'm going to assume points, assists and rebounds are independent, but may follow-up this post with some investigation into those relationships in the future. Data is sourced from this dataset containing box scores of all 1,427 of Lebron's games through 2019.
Distributions of Points, Assists and Rebounds
As previously mentioned, this analysis will be using the actual distribution from Lebron's career to simulate the probability of Lebronning, so let's start by viewing the distributions of points, assists and rebounds per game in Lebron's career.
Two things stand out in this distribution: first, 27 is the mode of this distribution; second, Lebron rarely scores 28 points. NEVER BET ON LEBRON FINISHING WITH 28.
7 is the mode of this distribution and it's a little odd that Lebron rarely gets exactly 10 assists.
You can see Lebron usually makes sure he gets at least 6 boards and that 7 is actually the second most frequent amount. Also worth noting, Lebron doesn't actually average 27/7/7 if you include playoff games (as this dataset does). He averages 27/7/8 because he averages 9 rebounds in the playoffs and he has been in a fuckton of playoff games.
Simulating Lebron's Career 1000 Times
To simulate Lebron's careers, we'll use a simple bootstrapping methodology, meaning we'll take random samples—with replacement—of points, rebounds and assists from Lebron's career then combine these samples to create new simulated box scores. (Another way to simulate would be to take permutations of his actual points, rebounds, and assists and shuffle them together randomly, but that feels less like a parallel universe to me.) Each simulated Lebron career will consist of 1,427 games. Let's look at the results.
If 2020 wasn't proof enough that we're living in a fucked up timeline, you can see that Lebron has never Lebron'd in only 18% of the simulated universes. In over 50% of the universes he has Lebron'd twice or more, and in 2 universes he Lebron'd 7 times! Thanks for reading. MJ is the GOAT.