Why does the number of strategies I tried matter?

Because the best of many tries looks good by luck. The Sharpe ratio of the best of 50 random strategies isn't the Sharpe ratio of a strategy; it's the maximum of 50 noisy numbers, and maxima are biased upward. The more variants you tried, the higher the bar a result has to clear.

Details

• Count every trial: parameter tweaks, different universes, different horizons, and the ones you "just looked at once". If you can't count them, you're probably undercounting.
• Deflated Sharpe ratio (Bailey and López de Prado, 2014): adjusts for the number of trials, sample length, skew and fat tails, and estimates the probability that the true Sharpe is above zero.
• A stricter significance bar: Harvey, Liu and Zhu (2016) proposed a t-statistic of at least 3 for new factors, rather than 2.
• Pre-registration is the cheapest fix: write down the strategy and the pass bar before you look at results.

In Backtest Auditor, you say how many variants you tried, and the Deflated Sharpe Ratio raises the bar to match. If you understate the number, the check is too lenient.