UFC 76

[TomCowley]

No, it's not. If you are assuming AN EXACT, KNOWN edge, then of course there is no "variance" to be considered- only the exact, known edge. This entire conversation would be moot if we knew such a thing.

Consider chess ratings. For those not familiar, they range from roughly 1000-2800 (with horrific little kids below 1000). A player, on average, scores 75% against somebody rated 200 points lower 75%. So if we see "2200 v. 2000", with no other information, we would expect a score of 0.75.

Now, let's consider two hypothetical 2000 players. One 2000 pretty much murders everybody lower rated, but hardly ever scores against higher-rated players. The second 2000 has lots of upsets, but also lots of upset losses.

Even though both would have the same aggregate score against a "background" of competition with varying ratings, these two players have vastly different expectations against a 2200. The former will be way under 25%, the latter will be significantly over it.

The latter player's ability to win against higher-level competition more often (and lose against lower-level competition more often), compared to an "average" player of EXACTLY EQUAL NET RESULTS VS. A BACKGROUND OF OPPONENTS, is the variance we're talking about here. If you don't think such things can exist, in chess and in MMA, well, you're just wrong.