One question about the random draw. It happens one time before the competition or every time after each performance? Judging by your probabilities it happens one time before the competition, but that is a bit illogical. It would be much better to have random draw after each performance.
One time before the competition. (By the way, the judges do not know the results of the random draw. This is another thing I don't like about it. Two judges are just sitting there throughout the competion dilligently judging away, while all the time the computer is laughing at them, saying, look at those fools, thinking they are judging a skating contest, ha ha.)
It has to be this way, because if there were a separate draw for each performance then the skaters would not be judged by the same panel of judges.
It would be very interesting to simulate the situation and look what happens. I really think that with less than 3 judges it wouldn't have much effect.
A simulation from scratch would be pretty hard because you would first have to do a lot of research about how the different scores are distributed in actual competitions. With just a bunch of random numbers, you would not get any realistic results.
However, you could just take the numbers from actual contests.
For instance, here are the results of the ladies’ short program from Skate Canada. The Anerican judge and the Chinese judge both survive the random draw and are intent on advancing the fortunes of Caroline Zhang.
The way the marks came out, Caroline is languishing in seventh place.
Rochette 70.00
Czisny 63.52
Nagasu 56.34
Lepisto 55.74
Phaneuf 55.58
Lacoste 55.10
Zhang 54.58
One of the conspiring judges raises Caroline’s Skating Skills component scores by one point, the other judge by only three-quarters of a point to avert suspician. Both of these are well within the allowable “corridor.” They lower Lacoste’s Skating Skills by the same amount. What’s three-quarters of a point, right?
Now Zhang has (75 + 1.00) x .8 SP factoring / 5 total judges = .28 extra points, putting her at 54.86.
Lacoste is lowered to 54.82. Zhang zooms into 6th place!
Now they do the same thing with Zhang’s Transitions score, lowering Phaneuf a smidge in both SS and Tr.
Zhang has 55.14, Phaneuf 55.02. Zhang takes fifth.
Next Performance/Execution and Lepisto. Zhang 55.42, Phaneuf 54.90. Zhang is in fourth place.
Now Choreography. Zhang picks up another .28, Nagausu is diminished by 4x.28 for the four program components scored so far. Zhang 55.70, Nagasu 55.22. Zhang advances to bronze.
Is second place within reach?
Interpretation puts Zhang at 55.98, Czisny drops to 62.12.
Now the two judges give Zhange a –1 instead of –2 on her opening combo and 0 instead of –1. Zhang picks up 2 x 2 judges / 5 total = .80 points. They give Czisny 0 instead of +1 on her 3Lz+2T… Nope, silver is out of reach…. They wink at the tech specialist…Was Alissa's 3F really fully rotated?...