Great topic! Love to hear others thoughts!
I've grown up with these same things being said. Honestly, in coaching I've not seen that it is or isn't true. We've gone first and won many times. We've gone first and not won many times. I think it largely depends on the competition and how many teams there are.
I feel that in allstar competitions this isn't really true. With the ranges and scoring grids, I really feel like it's more fair and the order doesn't effect it. Your routine either hits the scoresheet and meets the maximums or it doesn't. From there its all about your choreo, performance, and execution.
At UCA though, I really think the order plays into the scoring. I cringe most when we're the team following the current national champions (happened to us 3 weeks ago). I'm not sure if first is always the worst place in order to go, but I definitely think the order plays a big part with subjective score sheets. I especially hate how much scores can vary with how big the divisions are at nationals. I love deep competition, but I hate that the scoring really doesn't stay consistent. I know they try, but when there are 30 teams in a division, skill level is all over the place, and there is no scoring grid in place, I think it's impossible to stay consistent. By team #12 the judges don't remember what team #1 did. I also hate division splits at nationals, but that's another topic!
