"On the other hand, all the leagues have significantly lower average hotness in the first half compared to the second half, so maybe it’s not just the NBA that has a boring first half problem."
This seems to be a misconception. It stands to reason that the chart will grow jumpier as you near the end of the game. In options lingo, the implied volatility will be more stable the further you are from expiry (the end of the game). Theta decay and all that. The market is basically giving you an integrated forecast from each point in time until the final buzzer, and as that window shrinks you expect the odds to be jumping around more.
Actually, I'm not sure whether it's a misconception or not. What you say about applied volatility is true, but if your excitement is proportional to effect on the odds of the outcome then that is still what you're measuring. I have no idea whether that is actually the relationship, though (but hey, you could measure it!).
Heh, true. I guess what I was saying is that if you freeze a basketball score at 20-18 in the second quarter, and at that point the odds are 52-48 in favour of team leading by 2, and then neither team scores for the rest of the match, then the odds will asymptotically approach 100-0 as you approach the final buzzer. Even though no one is scoring. By the variance measure used here, the second half will appear more exciting, even though nobody scores. Reminiscent of football (soccer) perhaps. The fact that first halfs have less variance is just evidence that they are further from conclusion, not necessarily that they are less exciting, but then maybe the two are linked.
I'd really like to do that actual study - monitor people watching the games, see how heart rate and perspiration match up with odds-based measures of "excitement".
This seems to be a misconception. It stands to reason that the chart will grow jumpier as you near the end of the game. In options lingo, the implied volatility will be more stable the further you are from expiry (the end of the game). Theta decay and all that. The market is basically giving you an integrated forecast from each point in time until the final buzzer, and as that window shrinks you expect the odds to be jumping around more.