Okay, so here are the two possibilities we are exploring:

Buy on the open and suffer whatever slippage you may get which is the old school way most of us do it, and

Put in a limit order today at yesterday’s close and if it goes unfilled then buy at today’s close.
Slippage is the issue here since both methods will get you in 100% of the stocks we intend to buy that day. When comparing methods I will reference slippage from a simulated execution from today’s open. As I’m sure you all know, in probability theory the expected value (or mathematical expectation) is equivalent to the probabilityweighted sum of the possible values.
If we calculated EV of buying at the open it would look like this:
EV = 100% * 0.25% = 0.25%
100% percent probability of getting whatever slippage you care to assume  I’ll use 0.25%. A more conservative number might be along the lines of 0.5%. I’ll also give it a negative value because it has a negative to your account.
The expected value of using entry method 2 would look like this:
EV = (52.7% * 0.25%) + (35.8% * 1.13%) + (11.5% * 2.07%) = 0.035%
52.7% probability of the open being below the previous close and we get in at the open while suffering from the same 0.25% slippage as in Method 1,
plus a 35.8% probability of the open being above the previous close and then falling to hit our limit order intraday times 1.13% positive slippage (a figure I just calculated as the average previous close to today’s open change for stocks that gap up on the open but the low is less than or equal to the previous close, over the last 5 years ),
plus an 11.5% chance of opening above the previous close and never hitting the limit and buying at the close times 2.07% slippage (1.82% open to close movement of these stocks intraday plus 0.25% slippage on that transaction since it would be a market order).
According to my calculations Method 2 produces positive slippage on average. The big weakness in all of this is my programming skills, so if anybody cares to independently calculate the probabilities and returns it would be greatly appreciated.