Rich G: are you sure Doak's scale is logarithmic? If so, Tom himself did not base it on 10: he gave more than ten courses a score of ten; less than 100 courses a score of 9, way less than 1000 courses a score of 8, etc.
Jim:
Yes, I have described the Doak scale as logarithmic in the past, meaning that I think the leap from a 6 to a 7 to an 8 is more than just a slight difference. But of course it's not a 10x logarithm, because there aren't millions of golf courses in the world
. If you think of the distribution of courses as something of a Bell curve, with "3" the average course, and there are 30,000 golf courses in the world, every jump up should have about 1/3 as many courses as the previous step. That would give a distribution something like this:
3 or below: 20,000 courses
4: 8,100
5: 2,700
6: 900 courses
7: 300
8: 100
9: 30
10: 10 courses
Which is not too far off the distribution pattern for courses I've rated, considering I'm only trying to see the best of them. I was probably a bit too stingy with the 9's, based on this view, but I didn't start out with a distribution in mind ... I felt my way to it.
This distribution also means that a rating of 6 puts a course among the top 5% in the world, and a 5 is in the top 15%.
As to the topic of this thread, value for dollar depends on how you value the jumps on the scale, a topic on which reasonable minds with different financial means will certainly disagree. Certainly, by the way I've defined the Doak scale, an 8 should be worth a lot more than twice the green fee a 4 is worth. If every point on the Doak scale doubled the value of the green fee, and a 1 cost $1, then a 10 would be worth $512, so that's too strong, because you can't find many courses for $4 or $8. It seems to work more like a 50% increase for each point:
10 - $450
9 - $300
8 - $200
7 - $135
6 - $90
5 - $60
4 - $40
3 - $27
2 - $18
1 - $12
I have to admit that I'm blown away by the rack rate green fees for nearly all the top courses nowadays ... but I do think Pebble Beach is way closer to being worth $500 than Spyglass Hill is to being worth $350 or $400.
The nature of the modern economy is increasing the multiplier, though, as some economists like Mr. Piketty are starting to figure out. It's long been accepted that 20% of the people would amass 80% of the wealth, but it's only recently that anyone thought that there would be no restraint on compounding that principle, so that 20% of the 20% would own 80% of the 80% [that's 4% owing 64% of the wealth, or 0.8% of the people owning 51.2% of the wealth at the next step]. Economics in this age is quickly evolving to winner-take-all, and the winners can afford any green fee they want.