If you have 500k to invest, and your goal is to do 1% better than the index funds.. this is easy to compute. You want to make 5k "extra" with your stock market playing. If you consult for $100 an hour, then you need to be able to do this 1% win in <= 50 hours a year (about 1 hour a week).
So you could do this for a year, measure, and see "Yes, I spent 50 hours and I made 5k extra over the S&P 500, so my time paid for itself".
However- did you account for increased risk? Very very likely you got the extra gains by extra risk (say, invest in 10 stocks you think are hot instead of the 500 of an index fund). So some years you will win, some years you will lose. How do you even calculate how more much risk your pick has over an index fund? Wall Street has a way to calculate this risk, I am not sure the average day trader does. How good is a strategy where 80% of the time you gain 1% over an index, but 20% of the time you lose 50% more than the index? (It looks really good while it works, until it doesn't!)
Ultimately, many people who trade for fun are gambling - not much different from picking horse races or football game results.