> So here's bogle point: people who don't index then they're the market where half of them beat it and the other half lose for it (basic math).

Good funds don't have to beat every year. The above logic treats funds' annual performance an independent event from other years. They are not independent events. A fund can underperform/overperform the index in a given year.

Here are some good actively managed funds with their respective index. They do even better compared to SP500.
https://www.portfoliovisualizer.com/backtest-portfolio?s=y&timePeriod=4&startYear=1985&firstMonth=1&endYear=2021&lastMonth=12&calendarAligned=true&includeYTD=false&initialAmount=10000&annualOperation=0&annualAdjustment=0&inflationAdjusted=true&annualPercentage=0.0&frequency=4&rebalanceType=1&absoluteDeviation=5.0&relativeDeviation=25.0&reinvestDividends=true&showYield=false&showFactors=false&factorModel=3&benchmark=-1&benchmarkSymbol=VIGAX&portfolioNames=false&portfolioName1=Portfolio+1&portfolioName2=Portfolio+2&portfolioName3=Portfolio+3&symbol1=TRLGX&allocation1_1=100&symbol2=VHCOX&allocation2_2=100&symbol3=VPMCX&allocation3_3=100