Here’s my now annual ritual — every February I try to find a significant variable to add to my 3-point contest simulator, and every February I fail. It dawned on me this time that what I’m attempting to do is predict something that I call inherently noisy in the field. Open 3-point shots — and these contest attempts are as unguarded as possible outside of a Phoenix Suns-Cleveland Cavaliers game — are tough to predict. Outside of the player’s 3-point percentage, there’s not much that can be used. But my inner Don Quixote won’t cease; I will keep tilting at these windmills.

Simulation building

Here’s a little background: I’ve been doing this for a while. Essentially, I’m predicting the contest score out of the max possible using a set of variables. This is done with a nonlinear function, and I’ve only got two useful predictors: a recency weighted 3-point percentage with the last four seasons, and a dummy variable for whether or not the round is in the finals. Then I simulate the two rounds, keep tabs on who won, and repeat the process a few thousand times until I come to a stable solution — that way I can find the odds on who will win. It’s not perfect, but it’s simple and it works. So how can it be improved?

Let’s look at an obvious variable. Surely 3-point percentage alone can’t predict the contest results well. Not all shooters are the same — some take decidedly easier shots, waiting for the easiest opportunities, while others fire at will even under duress. What happens when you factor in 3-point volume, you may ask? And I’ll stay one step ahead of you: let’s adjust for league averages as well, since. But when you use this as an input into my model, it flails. You can see this visually below; there’s no pattern.

There’s a weak correlation (an r of 0.09) between the two variables, and when you factor in 3-point percentage the model does not significantly improve. Let’s try something else that should be tied to shooting prowess: free-throw percentage. After all, free throws are the only basketball action that’s anything like the contest — unguarded shooting — and it’s an objective measure of accuracy. What do you get there? Nothing, once again: in case you’re wondering, I tried single season free-throw percentage, career, and only seasons from the contest year and before. It was the closest to being significant, but it had a low effect on the results. (By the way, those numbers are indeed correct with those two dots at 95 percent — Jeff Hornacek was an amazing free-throw shooter at the end of his career, while Anthony Morrow and old man Peja Stojakovic are those three closest dots.)

Okay, now let’s get to something that should truly be meaningful. What if we looked at the past performances from players who have been there before? It’s not a straightforward inclusion, but it’s intuitive; you’d think that if a guy did well before, he’d do well again. I’m only looking at contest results from other contests to make it fair — in other words, to predict how well Eric Gordon will do this year, you can look at how he did last year by taking the average of all three rounds (he had a tie-breaker.) The result? Once again, no significance: you get a weak correlation as seen below, that disappears when modeled.

Astonishingly, I did finally find a variable to add to the madness. It was a late addition but it was always something I had considered, aided by last year’s results — a tie-breaker round. Alas, this dummy variable does nothing to explain performance; it’s just helpful in accurately modeling the real results. Players get better the more they shoot — fatigue obviously matters too but through these results you’d need more rounds to see it visibly change the numbers.

Simulation results

Moving on, let’s go to the results. For the 2018 contest, Eric Gordon, the previous year’s winner, is back, along with three established shooters in Klay Thompson, Bradley Beal, Kyle Lowry, the rising scorer in Devin Booker, and two new guys: Wayne Ellington and Tobias Harris. Surprisingly, besides the league-leader in Klay Thompson, the NBA chose few 3-point percentage leaders, as Paul George is currently eighth and no one else is in the top 20. But that’s okay — what correlates well with success is total 3-point percentage over the past few seasons, not just this one. In fact, according to my research the previous season’s 3-point percentage is slightly more important, even after accounting for attempts.

Going into the simulation, the winner, no surprise, was Klay Thompson followed by Paul George, surprisingly. Tobias Harris brings up the rear; he was in the mid-40’s back in January but has slumped since then. He’s the prime example of why you shouldn’t select these players based on their half-season percentages — we’ll see how he does in reality. By the way, I grabbed one random simulation run for the table below — I’m not saying it’s the most likely scenario but you can see how the data are generated.

Results from one simulation run

Player 1st round Tie-breaker Finals Eric Gordon 17 Klay Thompson 26 21 Bradley Beal 15 Paul George 13 Kyle Lowry 17 Devin Booker 19 26 19 Wayne Ellington 27 15 Tobias Harris 19 14

How do the results compare with the perception? I’ve got implied odds listed below. According to the betting market, Klay Thompson is the clear favorite, and he’s only a little overrated there — that’s probably because of his reputation. Eric Gordon is the most overvalued player. Previous winners don’t have an extra edge in this contest, and he’s not a high-percentage shooter. Remember, past performance and volume shooting don’t strongly correlate with success. Kyle Lowry, no surprise, is probably the most undervalued player.

Table: Odds

Player Betting odds% Simulation odds% Eric Gordon 15.1 7.4 Klay Thompson 27.7 25.4 Bradley Beal 8.8 12.6 Paul George 11.1 15.8 Kyle Lowry 8.3 13.4 Devin Booker 12.3 7.7 Wayne Ellington 9.8 10.0 Tobias Harris 6.9 7.7

Normally, a player like Klay Thompson would be grossly overvalued in this contest. The motto here should be bet the field. But this contest has some of the weakest competition in recent history. Typically we see at least two elite shooters with high-tier percentages, and only Klay qualifies now. Thus, with no great competition, his odds increase. But don’t forget the field — even though Harris has some of the worst percentages, for instance, it would not be an anomaly if it happened.

Even after studying this for years, I can’t in clear conscience state this is predictable. The contest is still a mystery for me, and I think it’ll always remain that way. I can show the spread of the results, and it roughly shows a plausible outcome. But I’m still stumped in terms of what predicts the winners; I’ll always be tilting at those windmills.