there was a numeric definition of sports excitement going around say 15 years ago. I'm sure its been modified since, it was basically the cumulative change in win probability over the span of a match. A more exciting game is assumed to be one where the chance of winning moves more frequently.
They have likely changed the measurement since. There are ways to consider such things as wrong and factors such as time remaining and the potential for change is also part of why a game can be compelling. Needless to say if you follow the idea of that metric then end of game swings usually produce the most "excitement"
\sum_{t}|P_{win}(t+delta)-P_{win}(t)|