@hdporterand @SouthJamaica, how the high balance is determined varies from bank to bank. Chase and Capital One use the highest balance anytime in the cycle. AMEX uses the highest statement balance.
High balance has nothing to do with FICO. But as mentioned, it may or may not affect underwriting. And it does serve as a "fake" limit on charge cards when the three Experian 98 scores are involved. The bankcard and auto versions of these scores are probably not widely used. However, the "classic" version of this score is important because it's used for mortgage lending.
@WomanITGeekdid the right thing in letting the 11K balance report. The temporary scoring hit will be noticeable because FICO will view the card as maxed. But it has to be done from time to time until you feel that the card doesn't need any more "limit increases." The main thing is to do this during a month where you're not applying for credit. Even though the score that's pulled may not be one of those Experian scores, depending on ones's profile, an $11K balance might be a liability just because it's there.