Combinational Game Theory tells us that solved games will always result in a draw if both players play optimally. With non-solved games like chess, one can make a "draw" assumption safely in the start position : no side has played a sub-optimal move ... or any move for that matter.
There are some famous players who have postulated this rigorously but when it comes to computer evaluations, you have to take what the engine says with a grain of salt. They are great at analytical positions but are hit-and-miss in other places including the opening.
Most engines will give White an evaluation of around +0.30 at the start (3/10ths of a pawn) but that is not significant to predict that White will be able to sustain a draw if he tries to only play for one even at Master level play. Nor has Engine vs. Engine competition ever seen a near perfect record of draws all the time. There is too much uncertainty when dealing with complexity like the kind in chess or Go.
In short, the answer to your question really should be "no". There is no such yardstick for draw-depth nor is there any value of attempting to statistically analyze a million games for inferences.
Practically, a draw occurs at the highest levels of play when there is mutually nothing worth playing for (without incurring undue risk).