^
Great questions. I hope some of our figure skating historians will supply the details, but as I understand it, the original purpose of the short program was to give Janet Lynn (who was bad at tracing figures but great at free skating) a chance to win a world championship. It didn't work out, but that was the goal.
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The question of the thread, however, is this. What is the best way to combine the results of the short and long programs to produce an overall winner?
I'm no historian but ... the original purpose wasn't just to get Janet Lynn a championship. And again, her problems weren't figures per se but (comparitively) weak competitive nerve - a concept that was not well understood back then.
Anyway, AFAICT there were several main purposes of the SP
a. Make sure no more Schubas or Nepalas would win major titles (basically that worked (at least after Nepala's last Bratislavan hurrah) all the champions afterwards were at least pretty good if not always the most spectacular freeskaters )
b. Generate more tv coverage in big competitions
c. Make the 'compusory round' more visible
d. ???
And it wasn't until the _9th_ season with the SP that skaters were competing for ordinals and factored placements. The WC and olys from 73-80 were all still decided on cumulative points.
Again, the controversial Lake Placid Ladies competition would have had three different winners depending on how the scores (assuming those would all still be identical) were counted.
system actually in use : Poetzsch
system from 81-88 : Fratianne
system from 89-90: Fratianne
just SP and LP (not counting figures)
total points (system used) : Fratianne
with factored placements: Biellmann
(also interesting: the scoring method actualy used was the only one that keeps Biellmann off the podium she's at least bronze in any other system).
So there is no one ideal method. Any method will generate some competitions that are too close to realistically call and others where the 'wrong' skater wins.
One way to test the 'ideal' method would be to have a large panel of highly trained judges do phantom judging at umpteen different competitions (just putting the top six skaters in rank order with no points) and see which way of processing the scores given by the real judges most closely matches their picks. (this will obviously never happen)
What we're left with is personal bias. My bias is that if there is one part of the competition that's scored very differently from the rest then factored placements are the way to go (I think 81-90 was the overall fairest period in scoring), but otherwise I'd prefer total point count (either 6.0 or CoP).
The few competitions where one skater puts themself out of reach are more than balanced by the broader field with podium possiblities.