I dont think this is even close to being on topic though if we wrote this much and with such complexity we might even lose die hard skating fans lol.Mathematically, I must disagree that 1) the SP is relatively overvalued, and 2) that the system enables insurmountable leads. Let's look at each of these things individually:
1) SP Relatively Overvalued?. In terms of time elapsed and the quantity of elements and component features judged, the point value of the SP, as a general principle, is pretty proportional to that of the Free Skate, e.g. at a rate of roughly 1 to 2. Therefore, unless one wants to argue that somehow those things in the LP should be inherently and relatively more valuable for qualitative reasons (which would then be disproportionately penalizing SP features), I don't see the logic in this premise.
I suppose one could skew the relative weightings significantly in favor of the LP, such that, for example, a 3Lz in the LP (in the first half) is worth more than a 3Lz in the SP, to make the event "more exciting" with a nail-biting finish. I don't find this persuasive; I mean, why have the SP at all, then? But it could be done. However, let's be clear: this would be a judgment to fulfill a value agenda.
In no way does it demonstrate that the system of giving proportionally equal weightings to SP and LP scores (which is the current system) is either unfair, or that it systematically results in insurmountable SP leads (other than for reasons related to what the skaters themselves managed to do, or not do, on the ice).
The difference between this situation and the figures/free skate dichotomy of yore is that, the SP and the LP are essentially like items; it would be like playing 3 innings of a game one day, and then 6 innings the next. Should a run on the second day be counted as 2 runs, just because it would add a certain frisson to the finish? In the latter case, school figures and the free skate are qualitatively different, and people essentially made the judgment that they they didn't particularly care to have these draftsman-like tracings on ice dictate the winner.
2) Insurmountable Leads in the SP? I'll leave Patrick aside and address Yuna's history only: a 3 or 4 point lead going into the LP is only insurmountable if the leader is cleaner and/or has a higher points ceiling than her competitors. It has nothing to do with the SP being relatively overvalued (see above). I would be willing to surmise that if we did a quantitative analysis, it would show that, as a percentage, Yuna's average SP lead is no larger than her average LP lead. In fact, if we look at her latest World performances, her LP point differential was actually quite a bit higher than for her SP.
In the SP, Yuna's score (69.97) was about 4.7% higher than Carolina's second place score (66.86).
In the LP, Yuna's score (148.34) was almost 10.4% higher than Mao's second place score (134.37).
I would argue that Yuna was relatively underscored in the SP, for various reasons (she was skating in an early flight, she hadn't skated in a major competition all year, actually for almost two years, etc.). Let's even bend over backwards to "normalize" the case, and say she didn't get the infamous "e" on her 3F, and her PCS was judged to final flight standards. Call it 73 to 74 points? Revealingly, the average percentage differential for this range would be right around 10% when compared to Caro's SP score, exactly in line with her LP differential.
In other words, at worst, Yuna's SP lead was proportionally far smaller than her LP lead. At best, it was merely equal to it.
That's one of the benefits of looking at the hard numbers. Unless there is some funny business going on, a close scrutiny, more often than not, reveals the internal consistencies and logic.