A routine I've seen on this site specifies that the open of the trade day must be greater than (a specified percentage) above the limit price. It won't buy if the Open and the Limit are closer than, say, 3% or 5%. Is this because limit buys generally perform better if the stock opens well above the limit.

What "routine" have you seen? Its name or link could help.

Naturally, now that I need it I can't find it. It was a strategy that looked at same-day price action, specially coded so as not to invoke the danger of peek ahead. I think it used a new WL feature that makes it possible. One comment that I copied from the strategy was: "always Alert for real trading for the last bar" An important line of code went something like this:

if (bar < Bars.Count - 1 && Open[bar+1] > limitPrice * 1.03)

Sorry, that's all I got. Anyway, it made me wonder if there's a general impression that dip buys perform better when the stock opens well above the BuyAtLimit price and then drops down to that Limit.

QUOTE:
if (bar < Bars.Count - 1 && Open[bar+1] > limitPrice * 1.03)

Found something close though not exactly:

GetSessionOpen with Metastock?

This is a feature of the Quotes tool gap filter. See the discussion in the User Guide: Quotes > Quotes Pane > Gap Filter and its Sample Usage.

QUOTE:
Is this because limit buys generally perform better if the stock opens well above the limit.

The idea is that if a stock is gapping down, it's due to an earnings or bad news event, and these are the knives that you may not want to catch.

Thanks, that was where I had seen it. And I appreciate your explanation of the theory behind it.