It's easy to make a statistic how long the average game takes (30-40 moves, to my best knowledge), but when is the average game decided? (Since cashing in the advantage might take a lot of more moves, even if the outcome is never in doubt.)
To get experiment data, let's arbitrarily say that +2 means a decided game. (So the question can be answered automatically with some megabase search.)
If there is reasonable evidence that this happens much earlier, even already in the opening (see the answer by Philip Roe for Why do players leave so little time for the last moves?), I don't have to think about the why. (I deleted that question.)
