According to the test of phalanx_man, the effect of lethality is not linear (in a strict sense) but follows an affine function (no power function):
f(x)=2.98 *x + 0.54
(where x is the lethality, and f(x) the killing rate; to be more specific it's the percentage of men of the unit killed in a minute)
This is tested for a solid value of all other effects (attack, defense, etc.), but and that's a very, very big but, there's a ton of methodology problems here:
1) he made only 4-8 data points for every lethality, so the statisical failure is pretty high.
2) he said for himself that lethality showed other killing rates for other battle configurations, so the data seems not be very objective but pretty specific for the situation he tested them in.
3) We only know the effect on killing rate this way. We cannot conclude anything if there is a difference in not dying because of non-working attack or the attack beeing only non lethal. It's still possible, lethality is used as a 1to1 probability after the attack effect has been concluded. I don't see a way to really test this.
4) I don't know how he ruled out more complex non-affine functions. R^2 for his model (and I get the same recalculating it) is pretty high though (R^2=0,9992; so at least his linear model has a high quality).) I did not test for linearity further for now, don't have any real statistic software on this pc.
EDIT: My conclusion is, that phalanx men tests (on lethality) are not very conclusive :(
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