3. A normal plot of the 252 {500Dartboard40} portfolio CAGRs shows the distribution is close to normal. There are 9 outliers, with some of the fat tails remaining. For a normal distribution, 97.5% of results will be higher than the mean minus 2 standard deviations, and 84% of results will be higher than the mean minus 1 standard deviations.

In the last 66 years, S&P 500 Equal Weight had a CAGR about 1.6 higher than S&P 500 MktCap Weight. To beat SPY 97.5% of the time, a S&P 500 Dartboard portfolio needs a SDcg less than 0.8. Over 10 years a depth of 150 is needed.

Depth = (SDpop / SDcg)^2 / yrs = ((31 / 0.8)^2) / 10 = 150 depth needed for 97.5% win rate of 500Dartboard40 over SP500MktCapWeight in rolling 10-year periods from 19570301 to 20230310.

A depth of 40 has a 1.55 SDcg over 10 years, and so had about a 84% win rate.
SDcg = SDpop / sqrt(40*10) = 1.55

      Screen       CAGR  GSD  Sharpe  AT     From       To
  500Dartboard40   12.0  19    0.50   0.9  19570301  20230310
SP500MktCapWeight  10.3  17    0.44   0.2  19570301  20230310
SP500EqualWeight   11.9  19    0.49   0.3  19570301  20230310
SP1500EqualWeight  12.1  20    0.49   0.3  19570301  20230310

https://gtr1.net/2013/?~500Dartboard40:h252::sp500...

In the last 10 years, equal weight trailed market cap weight, and so the win rate was less than 50%.

https://www.portfoliovisualizer.com/backtest-portf...

I calculated rolling 10-year returns for the 252 {500Dartboard40} portfolios and found a 78% win rate over {SP500MktCapWeight} from 19570301 to 20230310.

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