I can accept those words.
But I tend to see in truly great commanders the ability to transcend the limitations of their traditions and to adapt, and to get others to follow them.
Of course, it is easier with kings than with generals in a Republic. An Alexander not only commanded armies, but he commanded the treasury and everything else. No general or admiral of any fame of the modern day commands the country itself which supports him.
I think that if one does not apply the strict victory criteria I used: win every battle and grand strategic campaign too, and if one allows for many, many defeats but accounts for the odds faced, then the greatest general of the 20th Century becomes obvious once one sees the name: General Giap.
He won a decisive, strategic victory against the United States of America and its Pacific allies. A bunch of half-armed men in pajamas defeated a superpower and a dozen other powers as well (Australia and Thailand, South Vietnam). And HE didn't win one battle in the field, so poor was his army.
But he won the war.
Brilliantly.
A grand strategic victory.
And then he blocked out the Chinese too.
Now, by those criteria, we get a very different list.
By those criteria, the greatest American general, hands down, was George Washington. He didn't win all, or even most, of his battles. But he was fighting a superpower with militia. And he won a grand strategic victory in the end, and a continent. Washington faced far worse odds, and a far more powerful foe, relatively, than Robert E. Lee did. But Washington won, against the worst odds ever faced by America, in any war.
Washington and Giap stand on the same plane, in that regard. They both humiliated a superpower, by fighting in the field. Washington at least won the final battles. Giap didn't win any major engagements, in the sense that he did not ever remain in possession of the field. But his Fabian tactics left him in possession of the WHOLE field at the end of it all. Not bad for a guy in pajamas!