Why do winning teams in the NHL score 2/3 of all goals?

I wrote this back in the fall. The NBA games and EPL games were in November or so.

Longer answer: The percentage scored by winners is a function of average goals per game.

If only one goal gets scored, winners score 100% of the goals. If two goals get scored, winners score 100% of goals.

If the game finishes with a total of 3 goals, there are 8 possible outcomes. 2 are 3-0 and 6 are 2-1. Winners should score 18/24 goals or 75%.

With 4 goals, there are 16 possible outcomes. 2 are 4-0, 8 are 3-1, and 6 are 2-2. The 6 ties can be omitted. Winners should score 32/40 goals or 80%. Here's a table for goals 1 to 10

Additionally, the higher scoring games have more leverage. If you have 1000 1 goal games and 1000 10 goal games, you have 11000 total goals. You would expect the game winning team to have scored (1000 + 6630) / 11000 = 69.4% of these goals. NHL games currently average about 5.3 goals per game. Combine all this and in the NHL teams that win the game should score somewhere around 65-70% of all goals.

Contrast this to other sports. In the English Premiere League games tend to finish with fewer goals. Looking at the last 20 non-tied games, the total score was 31-4. That's 1.75 goals per game. Winners scored 31/35 = 0.8857 or about 88.6% of the goals. Total score in a NBA basketball game is around 200. Looking at the last 20 games, the total score was 2081 to 1884. Winners scored 2081/3965 = 0.5248 or about 52.5% of the total points.