Tension vs. excitement during NBA games

This is related to our discussion of the martingale property of calibrated probability forecasts.

Jeremy Lu writes:

I’m a former student of Dr. Jennifer Hill at NYU and have been keeping up with your blog. I noticed some people write to you with questions and wanted to ask you a question of my own. For some background, I scraped together every NBA game since 1996. Each game has a tension metric, which measures how uncertain the outcome of a game is (detailed calculation here: https://www.inpredictable.com/2020/04/an-update-to-tension-index-with-assist_11.html) and an excitement metric, which calculates how far the probability graph “travels” over the course of the game. There’s been a lot of talk about the NBA becoming boring, so I wanted to see if this could be measured statistically. I’ve made boxplots of the daily median excitement and tension of the regular season. The idea is, if a viewer turned on a random game one day and watched it, how would they perceive how engaging the NBA was? We can see that (at least with this methodology), over time, excitement has increased slightly, and tension has decreased. Regarding excitement and tension — these two variables are highly correlated (Spearman coefficient of 0.91). So my question is: Does it make sense that excitement and tension are positively correlated, but over time, excitement has slightly increased and that tension has slightly decreased? Am I doing something wrong here or simply misunderstanding correlation and trends over time? Is it a sort of paradoxical relationship where looking at individual factors vs. the aggregate is different? (for example, player A may have a higher 2 point percentage and 3 point percentage than player B, but a lower overall field goal percentage, due to the proportion of their 2pt vs 3 pt shots)