Roland Langrock writes:
Since on your blog you’ve regularly been discussing hot hand literature – which we closely followed – I’m writing to share with you a new working paper we wrote on a potential hot hand pattern in professional darts. We use state-space models in which a continuous-valued latent “hotness” variable, modeled as an autoregressive process, is assumed to affect throwing success probabilities. We find strong but short-lived correlation in the latent (hotness) process, which we claim provides clear evidence for a hot hand phenomenon in darts. Right now, we’re implementing the model in Stan, since we want to incorporate random effects to account for potential player heterogeneity regarding the hot hand effect.
I replied:
Regarding hotness etc., we’ve considered two sorts of models:1. continuously varying underlying ability (thus, the hot hand is a “correlational” phenomenon)2. making a shot increases the probability of making the next shot (a “causal” model)It would make sense to include both factors, of course, but either one of them is hard enough to estimate on its own, for reasons discussed on blog: (a) the binary outcome is so noisy that you’d need lots of data, but if you have a long series, then hotness won’t last so long, and (b) the state variable can only be measured from noisy 0/1 data, so it’s hard to tell whether you’re hot or not just from data on recent successes.
With darts it should be much easier to study this because you have continuous data on how close the shot is to its intended target. For basketball we’ve talked about doing something similar using 3-d ball-tracking data, but that would take a lot of work!