**0**

Is that good or bad? Should every skater attempt a quad even if he/she has a zero success rate for landing? How about a 25% success rate? I would like to know what the minimum required success rate should be, so we can come up with a scoring proposal accordingly--A system that a skater can yield a "profitable expected value" on that element as long as his/her jump can meet the minimum required success rate. By "profitable expected value", I mean: Expected value of performing a difficult jump (e.g., 3A) - Opportunity Cost > 0. Opportunity cost is the expected value of performing an easier jump of the same type (e.g., 2A). That is to say, the deduction system should be designed as such so that: E(difficult jump with the minimum required success rate) ≥ base mark of the easier jump (i.e., E (easier jump with a 100% success rate)).

We know the base marks for 3A = 8.50, 2A =3.30 , 4T = 10.30 , 3T = 4.10, and the total deduction for a fully rotated but fallen jump is 4 (maximum GOE deduction 3 + fall deduction 1), so what is the expected minimum success rate for landing the jump right now? The answer is 0%. 0% × 8.50 + 100% (8.50 - 4) = 4.5 ≥ 3.30 (the opportunity cost for 3A), or 0% × 10.30 + 100% (10.30 - 4) = 6.4 ≥ 4.10 (the opportunity cost for 4T)

What is the expected minimum success rate for rotation right now? Let R = the rate of fully rotating the jump, and (1 -R) = the rate of being downgrated. To isolate the rotation factor, we assume that everything else is successful, and so there is no mandatory deduction for a fall.

R × 8.50 + (1 - R) (3.30 - 3) ≥ 3.30 ==> 8.5R + 0.3 + 0.3R ≥ 3.30 ==> 8.8R ≥ 3 ==> R ≥ 34% for 3A

or R × 10.30 + (1 - R) (4.10 - 3) ≥ 4.10 ==> 10.3R + 1.1 + 1.1R ≥ 4.1 ==> 11.4R ≥ 3 ==> R ≥ 26% for 4T.

In conclusion,the COP is a funny system that demands a minimum of 26% success rate for rotation but 0% for its landing.

What should be the total deduction for a fully rotated fallen jump in order to maintain a minimum of 25% success rate for landing?

Let X_{n+1}= base mark of the difficult jump, X_{n }= base mark of the easier jump. Y = deduction for a fall.

So we have: 25% X_{n+1}+ 75% (X_{n+1}-Y) = X_{n }

thus, 1/4 × 8.50 + 3/4 (8.50 - Y) = 3.30 ==> 8.5 - 3Y/4 = 3.30 ==> 5.2 = 3Y/4 ==> Y = 6.93 for 3A

And 1/4 × 10.30 + 3/4 (10.30 - Y) = 4.10 ==> 10.3 - 3Y/4 = 4.10 ==> Y = 8.27 for 4T

And therefore I recommend a total deduction (GOEs and mandatory deduction or whatever) of 7 points for a fall in a difficult jump (i.e., 3A or quads).

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