Hmm, I’ve never heard pitched used as in "even". But there’s a first time for everything, I guess.
Welcome to the Agora, watermelon. I see this was your first post. Please don’t make it your last, as so many others have…
I looked up the proffered etymology at one of my favorite sites, the Online Etymology Dictionary:
pitch (v.)
c.1205, "to thrust in, fasten, settle," probably from an unrecorded O.E. *piccean, related to the root of the verb prick. The original past tense was pight. Sense in pitch a tent (1297) is from notion of "driving in" the pegs; meaning "throw a ball" evolved c.1386 from that of "hit the mark." Noun meaning "act of throwing" is recorded from 1833. The noun meaning "act of plunging headfirst" is from 1762; sense of "slope, degree, inclination" is from 1542; musical sense is from 1597; but the connection of these is obscure. Sales pitch is attested from 1876, probably extended from meaning "stall pitched as a sales booth" (1811). Pitch-pipe is attested from 1711. Pitcher "one who pitches" is recorded from 1722, originally hay into a wagon, etc.; baseball sense first recorded 1845.
So it would appear that the sense of "heated" (in battle) comes from both sides "plunging headfirst"... which one could argue grew out of the sense of "slope, degree, inclination".
-Tim