cold emailed 15 profs, got 1 reply. normal or did i mess up

so im a junior at a bay area magnet school, math track, aime qualifier. been trying to get into research since sophomore year but kept getting rejected or ghosted. decided to actually cold email this summer instead of waiting for school connections. sent 15 emails to professors at nearby r1 schools. specific, personalized, mentioned papers ive read, asked about summer availability. one replied and said maybe in fall when a grad student leaves. the other 14 nothing. is that just how it goes or should i expect better hit rate. also wondering if i should try different schools or just wait to hear back from the one professor. tbh the whole thing feels kind of random but i know people who got into mit primes and rsi so clearly some people are getting research early. should i keep cold emailing or is there a better approach at this point in the summer.