but it is my perception that in a given game, if you score more points than the other team, you are likely to win.
I've been meaning to get to this and finally wasted an hour this morning on it. Point Differential (PD) is a stat that is completely accurate over a single sample size (one game) and terribly misleading over virtually every other sample size.
I first learned this in the mid 80's when the Niners had a couple 10-6 seasons with great PDs. An analysis of the PD would say they were a top 5 team in the league both those years and both years they got spanked out of the playoffs in short and embarrassing fashion. They were in fact an average team that ran up wins and PDs against a weak division and played 500 ball against the rest of the league.
This season has a cool situation with three teams, the Ravens, Cowboys and Charges all having PDs that are at the high end of what one would expect for their records. Raves +231, 13 wins, Cowboys +78, 7 wins, Chargers +2, 5 wins. One would expect the Cowboys to be about zero and the Chargers to be negative.
I tested two hypothesis. First I eliminated the two highest and two lowest PDs from each team. I was attempting to factor out lopsided games that would have an oversized effect on PD. Results
Ravens 231 = 163 (Average 15.4 = 14.8)
Cowboys 78 = 51 (Average 5.5 = 4.6)
Chargers 2 = -17 (Average 0.1 = -1.6)
In each case the average PD dropped when factoring out the lopsided games but not enough to factor back to an expected average. I should test three teams that under preformed PD, I suspect in those cases removing the lopsided games would move their averages in the other direction. I could do more testing but I think the conclusion is lopsided games over the course of a season are a minor factor in PD.
Next I tested for PD vs opponents with winning vs losing records.
Ravens WInning = 112, 14.0 per game, Losing = 119, 17.0 per game
Cowboys Winning = 11, 1.4 per game, Losing = 71, 10.1 per game
Chargers Winning = -38, -6.3 per game, Losing = 49, 5.4 per game
It would be worth testing this over a larger sample size. From this sample PD against teams with winning records looks to be a very accurate predictor of wins. Based on the 14/g, 1.4/g and -6.3p/g one would expect the Ravens to have a lot of wins, the Cowboys to be about 500 and the Chargers to have a losing record, all of which are true. PD on its own and PD vs teams with losing records does not correlate with the wins each team has across the sample.
Interesting because the Chargers PD has been cited as proof of 'bad luck' and the Cowboys as proof of 'bad coaching' but this analysis says each team performed exactly as expected.