Extremely low, hereabouts.
Having lived on the East Coast as a kid and getting bitten by ticks there many times over many years it'll most likely be from that prior experience if it ever turns up (as arthritis).
Most medical descriptions of the disease state that the Lyme spirochete is only transferred after a tick is well attached-- 48 hours is what is usually mentioned. Being allergic to the anticoagulant that they inject before burrowing their jaws deeply to begin sucking blood, wherever I get even nipped by one the burning is immediate; the swelling is longer lasting than other insect bites or stings. So I'm an unlikely candidate for Lyme, myself.
(California incidence of Lyme has historically been so low one wonders if the clusters of it aren't found around certain quack doctors?)
Having said all that, ticks are certainly vectors for other nasty diseases as well besides Lyme Disease, e.g. Rocky Mountain Spotted Fever, so they do have the potential to be more than simply annoying.
