Short-term trends in rolls, however, can lead to something of a butterfly effect with long-term consequences.
Consider this example, which I don't think is the least bit far-fetched:
You and I start out playing two characters, mechanically-identical in every way including starting gear and xp, in the same party. In the field we meet some nasty foes intent on capturing anyone they can (for whatever reason, not relevant here). Your dice get on a hot streak for that encounter; you beat your foes, evade capture, and get away. My dice, on the other hand, run cold; and my character gets beaten up and captured.
While in captivity I can't do much, so minimal xp and no treasure for me while I'm there. You, on the other hand, carry on adventuring; let's say you go back to town, recruit some more people (including my replacement PC!), then come back, beat the adventure, and successfully rescue my original character along with any other captives. In so doing you've quite reasonably earned xp (or a level or two) and gained treasure-reputation-etc. along the way which I have not, meaning our originally game-identical characters are now not identical at all.
And all of this disparity stems from a brief run of rolls in the encounter where I got captured.
Further, even had we not been game-identical to start with (i.e. our rolled stats were highly disparate) the same sequence could just as easily have occurred: my character with a stat average of 15.2 gets captured while yours with the stat average of 11.5 gets away, and by the time they meet again you're two levels higher than I am and rocking considerably better gear as well.