Morning Mike, honestly I don't susbscribe to that kind of thinking anymore. I think that koi are tosai for about a year, Nisai for about a year sansai for about a year and then adults for the rest of their life ( 20- 26 years).
So Unless the hobbyist is a tosai or nisai freak, or going to trade out fish once they are no longer in the 'puupy phase', I think a koi pond should be built for adult fish.
So to my way of thinking, a pond needs to be 5 feet deep. This provides swimming dimension, volume for footprint , security and parameter stability. From here, if you want to house jumbos, are a paratrooper type or just love ringing every ounce of genetic potential out of a fish then keep digging! 6-7-8-9 feet ( I think ten and twelve or fifteen feet does get a little ridiculous and more about penis size than function) .
As far as ratio goes, I do think it is wise to make the surface greater, the deeper you go to get the most out of the two considerations - environment and atmospheric contact and also the fish's needs.
the one warning I would give a beginner- be careful what you wish for! IF you make a pond very deep, you have to MOVE all that water. Filters need to be large, turn over huge and pumps- numerous! Treating is a bear, as is just simple netting. And the water and electric bill will be 'impressive'. So it is one thing to get the pond constructed and another to run it long term! I suspect that on the 'two coasts' a 30,000-40,000 gallon pond costs as much as $4000-$5000 a year to run and heat? And $1000 or so to feed. This can get very wearing on a person over the long haul. And in retirement, it can represent a real drag on a fixed income. So for the average middle and upper middle class hobbyist, maybe 7,000- 15,000 is best? Then we are talking about a prototype pond being what? 20 X 10 X 5 = 7500, 22 x 12 X 5 feet deep = 9900 gallons. 24 x 12 X 6 = 12,960. 24 X 14 X 7 = 17,640.