40% comes from testing the formulas with micro timers, varying sizes of arrays, running a calculate (say 100 times(per time period)), measuring the time and averaging across multiple attempts with the same formulas. (and the 40% 'maybe' unique to my machine, my installation, the way I hold my mouth and my particular corner of the galaxy !)
Given that the formulae given were always on the same sheet then countif should be the weapon of choice.
I agree that in other circumstances other expressions could be used as being more appropriate.
Yes ... re-reading the original post he does bemoan the fact that a) the formula is on a different sheet b) well actually it's on a different workbook c) well actually that workbook is closed ... no hang on ... he doesn't !!!
I'm really not into "I'm right and you're wrong" stuff unless the other guy is a complete muppet, but if you are so upset by shades of interpretation then "chase that rascally rabbit" if that fills your hearts desire.
IMHO
Array formulae are notorious bottle necks in spreadsheets, followed VERY close behind by sumproduct formulae. Anything you can do to avoid them should be done but each case should be judged on the circumstances and the user. Helper columns usually speed things up but not always, and do you hide them or not ?, what if the user deletes them 'cos he dunt knew wot thay done' ???