The contest participants may have frustrated some L.A. motorists, but USAA is heralding it as a success. According to the company, phone distraction among all competitors improved by 26 percent, while the speeding scores of the drivers improved by 30 percent by the end of the contest.

In addition to the competition, USAA currently offers up to 20 percent discounts to certain policy owners who agree to let a separate mobile app track their driving.

Other large insurers, including State Farm, Geico, Progressive and Allstate, offer similar opt-in “usage-based” plans based on driving habits or distance traveled. One recent State Farm ad campaign depicts a woman in labor scolding her husband for speeding to the hospital in the family minivan. “Don’t mess with my discount!” she yells.

Cambridge Mobile Telematics, the company that built the app for the L.A.’s Safest Driver competition, stands to gain as much as anyone from the adoption of these plans. In December, the start-up raised a half billion-dollars from Japanese conglomerate SoftBank to expand its usage-based Drive Well program.

Hari Balakrishnan, a co-founder, said the program, unlike many traditional insurance plans that use markers such as age or ZIP code to determine premiums, allows “for rate-setting based largely on factors that drivers can control.” The Drive Well app, which Mr. Balakrishnan described as a “social gamification of driving,” is used by more than 10 U.S.-based insurers already. That includes State Farm, Liberty Mutual, Safeco and Nationwide, he said.