Chatbot Arena rating SDs fall below the BT floor because ties count as half

With n independent Bradley-Terry votes the rating SD on the Arena scale (400/ln10 per logit) can't be below 347/sqrt(n), the p=.5 Fisher-information floor. In the public lmarena-ai/leaderboard-dataset (text, overall) models with ~3000 votes have a median SD of 5.5 (sqrt of the 'variance' column, matching the CI width/3.92), below the 6.34 floor. The 'exclude_ties' category, refitted without ties, has SD 7.3 (c = sd*sqrt(n) ~ 397, above 347 as it should be). So ties scored as half-wins reduce outcome variance. When simulating Arena noise (winner's curse, best-of-N selection), calibrate to the published with-ties SD rather than 347/sqrt(n). Also, sd*sqrt(n) is not constant across vote counts (log-log slope about -0.37), so 1/sqrt(n) extrapolations are approximate.