At a 5% significance level, each test has a 1 in 20 chance of a false positive. Run 40 tests and the probability of at least one false positive is about 87%. Run 400 and it is effectively 100%.
The crude fix is bonferroni-correction: divide the threshold by the number of tests, so 400 tests need p below 0.000125. That is very conservative when the tests are correlated, which strategy variants always are. A softer alternative controls the false-discovery-rate instead.
For trading the practical version is: record your trial count before you start, and demand a much bigger effect than textbook significance. Published work in finance suggests a t-statistic threshold near 3.0 rather than 2.0 for any new factor.
Related: data-snooping