David, that's really interesting data. I don't have any answers, but I have a few questions or at least things to ponder.
I threw out a half-ass example definition of a measurement formula for shot values. I think to create anything meaningful we'd have to define what we consider to be important elements of determining the presence of shot values. I would think that such a formula should account for a few things:
1. Presence of options
2. Quantifying of risk (as it pertains to the risk/reward option)
3. Quantifying of reward (as it pertains to the risk/reward option)
4. Balance between risk, reward, and the conservative option and how their scoring averages compare (whether or not there is a "right way" to play a given hole)
5. Variety of shots tested by a course (woods, long irons, mid irons, short irons, wedges)
6. Quantifying of how players choose between the options present (with the idea being that it's ideal if each option is chosen with near equal frequency)
Maybe there are other things, and maybe some of the things above really wouldn't matter that much. As for 10 at Riviera, it sounds like maybe it wouldn't score all that high on factors 2 and 3 (probably just a function of its short length). Factor 5 doesn't apply outside the context of the whole course. But it would score pretty well on 1, 4, and 6. For a hole of its length, it may still pose pretty strong shot values. To contrast it with another short 4 that's been discussed a lot here lately, 13 at Kingsley might have a much higher dispersion of scores, particularly on the higher end of the spectrum. But I also suspect that dispersion at Kingsley may occur regardless of whether the conservative or risk/reward option were chosen by a player off the tee. It seems to me that Kingsley's 13th would score higher on factor 6, and possibly higher on factors 2 and 3, but lower on factor 4 because it may not actually have a "conservative" option statistically.
I'm sure you'd also want to weight certain factors more strongly than others, though I'm not sure which ones would be most important. I almost think 4 and 6 are most important, while 2 and 3 are less important. After all, whlie the numbers may tell us, hypothetically, that a feature like the Road Hole bunker really isn't all that dangerous, it still would play pretty strongly into the decisions that players make when they're in the moment. Others may disagree with me entirely though.
Josh makes a good point about standard deviation's role in all this. Tour players are so good that there may never be a tournament hole that consistently generates a wide dispersion of frequently occurring scores. Those guys just don't make disastrous numbers very often. But holes like 13 at Augusta still would offer more opportunity for scoring swings than most, and there would definitely be a way to quantify that.
One last thought: I was talking with my teaching pro the other day about some of the advanced metrics Tour guys use. The "strokes gained putting" statistic has become pretty well known, but it's not the only statistic of its kind. Players now can receive data on how many strokes they gained or lost on each swing during a round. A drive 6 yards wide of center in the fairway may gain .08 strokes while a layup on a par 5 may lose .13 strokes, and they can see that data. I don't know how the formula that evaluates each shot is written, but if the value of a shot execution can already be calculated then maybe that gives a blueprint for calculating the overall shot values present on a hole relative to the options it presents.