Has anyone calculated the average Elo rating of a chess computer as a function of the number of half moves or plys ahead it can look. I realise that the Elo is also a function of the choice of move then taken which may differ from engine to engine.
This is an area that academic can write papers on it. The relationships is complicated and might not be quantified.
Essentially, it's a non-linear relationship where the improvement is most obvious in shallow depth. The benefit diminishes as the engine go deeper and deeper in the search.
Look for the "Diminishing Returns" section and you'll know more.
There is a paper, which examines this relationship for Houdini 1.5.
On page 77 you get the relevant table:
depth: elo: 20 2894 19 2828 18 2761 17 2695 16 2629 15 2563 … 8 2099 7 2033 6 1966