> one contest between two teams, rather than the whole competition
I agree with your remarks, oh bountiful one ;)
To have a stab at your underlying question, dixbie, I’d say the sense comes from the equalising effect of the ‘drawn-by-lots’ mechanism – tied together, to be split apart by the sudden death playoff. This sense evidently goes back to at least the 17th century:
tie (n.)
"that with which anything is tied," O.E. teag, from P.Gmc. *taugo (cf. O.N. taug "tie," tygill "string"), from PIE *deuk- "to pull, to lead" (cf. O.E. teon "to draw, pull, drag;" see duke). Fig. sense is recorded from 1555. Meaning "equality between competitors" is first found 1680, from notion of a connecting link (tie-breaker is recorded from 1961). Sense of "necktie, cravat" first recorded 1761. The railway sense of "transverse sleeper" is from 1857, Amer.Eng. The verb is from O.E. tigan, tiegan. In the noun sense of "connection," tie-in dates from 1934. Tie-dye first attested 1904. Tie one on "get drunk" is recorded from 1951. http://www.etymonline.com/index.php?search=tie&searchmode=term
