I suppose that is why dice are always favored. By giving bonuses to a roll based on stats or specific circumstances, you can put the odds in favor of the player with the best logical chances, but there is still the chance that the underdog can pull an upset by rolling a really good number. Even strategy video games work on this system much of the time.

There are a few problems that you have to deal with though. The first is the fairness of the roll, especially since this is online and there isn't really a practical way to keep track of rolls (that I am aware of). You could always have your GM be a GM in the original sense and only participate in the RP as an arbiter rather than an actual player, but you might not personally want to do that. 

The other problem with introducing too many stats is that it will get players to think of the RP in terms of a game that they are supposed to win. You might want to do that, which is cool, but if you want to focus more on the writing and the storytelling then stats can be a detriment.

On the other hand, RPing without any stats in the way I am personally used to RPing comes with its own problems. For one, you have to rely more on the personalities of the people RPing with you, because a bad egg can really ruin it for everyone if they try to make things too gamey, especially if the other RPers are not steady enough to keep things moving.