Well, I don't think any of those three jump layouts is legal (all have 3 different jumps repeated).
Oops. it should have been:
layout without a quad: 3A, 3F+3T, 3Lz, 3A+2T, 3S, 3Lo, 3Lz +2T+2Lo,2A.
layout with one quad: 4T, 3A+3T, 3Lz, 3A, 3Lz+1Lo+3S, 3F+2T, 3Lo, 2A.
layout with two quads: 4T, 4T+3T, 3A, 3Lz+1Lo+3S, 3Lo, 3F+2T, 3Lz, 2A.
The mistakes do not affect the rest of my analysis.
I agree with you and I am very aware that my estimate of the opportunity costs for quads was on the high side. My purpose was to come up with a conservative recommendation: The quad fall deduction should be 7 points, which is conservative given that I assumed an opportunity cost higher than it is in most cases. And hence even with the 7-point deduction, skaters will not "become really cautious and attempt only those jumps they routinely land".
I suspect that the ones who fall most of the time also underrotate most of the time. (It's very hard to cheat a quad and stay up on one foot because of the massive rotational force needed even for 3.5 revolutions.) And the ones who fall on rotated quads have much better percentages of staying upright, even landing cleanly. There are probably also some who often stay upright without fully rotating or landing on one foot -- which traditionally, long before IJS, has been considered a worse failure than rotating and falling.
The 2011-2012 season data show the following frequencies:
Full rotation without fall ==> 61 (64.21%)
Full rotation with fall ==> 10 (10.53%)
Underrotation without fall ==> 3 (3.15%)
Underrotation with fall ==> 13 (13.68%)
Downgrade without fall ==> 4 (4.21%)
Downgrade with fall ==> 4 (4.21%)
The data show that 74.74% of the attempted quads during the 2011-2012 season were fully rotated, 16.84% underrotated, and 8.42% downgraded. With those percentages in mind, what should be the total deduction for a quad fall in order to ensure that a skater would attempt quads only if he could maintain a minimum of a 25% success rate for landing?
Let Y = total deduction for a fall, and assume that the average GOE deduction for an underrotated quad without fall is -2 and for a downgraded quad without fall is -2.5.
(74.74% x 25% x 10.30) + (74.74% x 75% x (10.30 - Y)) + (16.84% x 25% x (7.20 - 2) + (16.84% x 75% x (7.20 -Y)) + (8.42% x 25% x (4.1 - 2.5 x 0.7)) + (8.25% x 75% x (4.1 - 0.7Y)) = 4.1
1.9236 + 5.7737 -0.5606Y + 0.2189 + 0.9094 - 0.1262Y + 0.0505 + 0.2537 - 0.0433Y = 4.1 (Again I use the value of 3T, a liberal estimate for the opportunity cost)
5.0298 = 0.7301Y
Y = 6.8892 (a conservative estimate), close to my recommendation of 7 point deduction.
