Hi Alex,
The ideal depth of a koi pond is 3 times the length of your largest koi. This is from the famed breeder Mr. Hiroji Sakai of the Sakai fish farm of Hiroshima.
I believe that the desirable depth is three times the length of a koi body. For example, I believe the ideal depth for a 50cm koi is 1.5 meters, and for an 80cm koi is 2.4 meters. If too shallow, the back becomes warped.
Rgds,
Dennis