Hypothesis 4 is updated based on the following data:
Reputation changes from friendly matches
For this experiment I played a friendly match at home with Modum (Rep 2185) against the third best Norwegian team Brann (Rep 5554), the match odds were 9-1 (home), 4-1 (even) and 1-4 (away) in favor of Brann.
I found that the following results gave me the following changes in reputation afterwards (Sorted by goal difference):
Modum 5 - 1 Brann, +7 Home rep, +7 Current rep, no change for world rep.
Modum 2 - 2 Brann, +2 Home rep, +2 Current rep, no change for world rep.
Modum 2 - 3 Brann, No change
Modum 0 - 2 Brann, No change
Modum 0 - 4 Brann, -1 Home rep, -1 current rep, -1 World rep.
Modum 1 - 6 Brann -2 Home rep, -2 Current rep, -1 World rep.
Modum 0 - 6 Brann, -3 Home rep, -3 Current rep, -1 World rep.
Modum 0 - 10 Brann, -7 Home rep, -7 Current rep, -1 World rep.
From these data I draw that the game predicts the favorite to win by a certain goal difference and sets a threshold there. If the favorite wins by this threshold or less nothing happens, if the difference is greater the manager of the favorite team gains reputation points at the cost of the other manager. Each goal the result differs from the predicted threshold represents either 1 point gained or one point lost for each of the managers (unless the favorite wins, which seems to prevent gain for the other manager). In this case the threshold seems to be between 2 or 3 goals in favor of Brann. Why two thresholds and not one? It's tempting to guess that the game calculates the difference by dividing the reputation of the favorite club with the oppositions reputation. In this case that would mean 5554/2185 which equals 2.54, as you can see quite in the middle of 2 or 3 goals.
This equation does not incorporate home advantage though, so the equation might have more to do with the odds, but then again you would usually play roughly as many home as away matches during a season so it should even out in the long run. 4-1 in favor of Brann is a margin of three goals, but that doesn't explain why a 2 goal margin would be counted as a no change score. More data will be required to fine tune the equation. But for now a seemingly satisfactory equation could be "Predicted goal difference" - "Actual goal difference" = "change in reputation." Given the win is greater than predicted for the favorite, or the outcome (Win, draw loss) better than predicted for the opposition. If this number is positive the favorite manager would lose this much reputation, if it's negative he would gain this much reputation. The opposite holds true for the other manager. This equation predicts that if a draw is the favored result either manager would gain or lose the goal difference as if the equation had no given condition.
World reputation behaves unlike the other two variables, but I'll leave it until I get more of an idea what it does.
If you let your assistant handle the match you get no change to reputation.