Consider an absurdly hypersimplified scenario:
Every team has an identical schedule, with 10 games against opponents that are terrible and 10 games against opponents that are outstanding. When two teams of similar strength face each other, the average game is tied for 30 minutes, while when two teams of wildly different strengths face each other, the average game is tied for 10 minutes.
In that scenario, a terrible team's season will include 10 games * 10 minutes/game = 100 minutes of play with the score tied against great opponents, and it will include 10 games * 30 minutes/game = 300 minutes of play with the score tied against terrible opponents.
Conversely, a great team's season has 300 score-tied minutes against great opponents and 100 score-tied minutes against terrible opponents.
The result is that even with identical schedules, the terrible team's Corsi Tied will include three times as much play against other terrible teams and 1/3 as much play against great teams. Their "minutes when tied" schedule is effectively much weaker.
The result is that the observed results get compressed towards the mean, as teams play more tied-minutes against opponents of similar strength than against opponents who are much better or worse.
I'm left with three questions:
- Is this effect on strength of schedule actually significant? Does the best team in the league play appreciably more tied-minutes against good teams than against bad teams, or do schedule differences and the randomness of goal-scoring wash this effect out?
- If stronger teams really do play more tied-minutes against other strong teams, does it that have any practical significance? Is there anyplace where we might make different predictions if we knew that the tails of the talent curve were more extreme than we previously thought?
- If the effect has statistical and practical significance, how would we correct for it? I guess an expected Corsi tied could be calculated (and subtracted out), knowing the number of tied-minutes played against each opponent and the opponent's Corsi tied; does that reveal anything interesting?
My guess is that the answer to the first question is no, or that at least the answer to the second question is no. But I think that's worth confirming. Unfortunately, the way my database is set up will make this a little tricky to answer, so I thought I'd see if anyone else can easily take a quick pass at this. If not, I'll dive into it next week.