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Originally Posted by PairTheBoard
Evidently your method can be improved upon in the mixed 4x400 freestyle relay. According to your method it shouldn't matter which order you swim the males/females as long as they are the fastest two male and female swimmers. But statistics show that swimming the females last is better due to psychological factors.
My method had nothing to do with a non-medley event.
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In the extreme example I gave above I'm not saying there's a better solution than the one you'd get using your method. I am saying it's worth knowing that in this extreme case the solution is automatic and obvious, requiring no such calculations. And if someone swam a male in the last leg claiming to have used your method it would be clear they had made some kind of mistake.
You are cheating. To know what you are saying is "worth knowing" you have to have all the data to calculate and do the calculations.
I'm presuming that in medley events that you don't get to pick the order of strokes. If you do, and there are indeed some factors that matter for that, you still pick the smallest sum of times that satisfy the constraints of the competition
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Similarly, I'm saying it would be worth knowing if the actual mixed 4x400 medley has such an overpowering automatic best order. It looks like that's not the case. The built in advantage looks on the order of about 1 second. If that can be overcome then your method would show it. However, even then the statistical psychological advantage to swimming females last as mentioned above might overrule the solution using your method. Note the fact that only the U.S. swam a male in the last leg.
My method would clearly not show such a thing, as it ignores it completely.
I have a feeling that you would mostly come up with the same answer for most teams that I would*, but my method would have fewer errors. For instance, Iceland (if they had two more swimmers) would be correct (have no choice but to) put a man in for the breaststroke and a woman for freestyle regardless of your method's results.
Also, I doubt it (if it is indeed an effect that isn't simply due to differences in the size of male/female time disparities for each stroke) is psychological factors. To show that, you'd need quite a bit of data to rule out other factors. Swimming in calm water, riding the wake of another swimmer, passing the wake of another swimmer, and a bunch of other swim-related stuff that I know even less about. You'd also need a robust method for removal of data for instances of lost-cause, etc.
*For the same reason as both methods would come up with the same answer if you were considering a mixed medley for pissing for aim, pissing for distance, chugging a beer and doing push-ups.