Hi, I'm having some trouble calculating the amount of bets I need to place to have 95% confidence in my ROI, and the current floor/ceiling to what my ROI could be. Can anybody help?

Avg odds: 4.5
Bets placed: 155
Std Dev: 2.07
ROI: 57%

There is no way to do this. I mean there is a formula where you can calculate confidence intervals with a given standard deviation and number of plays, but it doesn't even apply in this type of situation because markets change. It's fine for blackjack or VP or probably even single table tournaments (you could actually just search for one of these calcs and it would work out for you) or something but not sports or horses.

Furthermore even if markets stayed the same the formula would still suck. It would vastly overrate your chances of being a winner. What I mean by this is that pretty much no one beats the horses unless they are getting extremely strong info of some sort, or in some cases getting highly favorable rebates + market arbitrage.

This means that no matter how well you have done over whatever sample you have been betting, it is still a huge favorite that you were the one guy who got lucky, unless your methods are revolutionary, or there is some reason to think the market is soft. So no matter what your ROI or average odds is, from a baynesian perspective you would need a much larger sample to know you were truly a winner than the traditional formulas would suggest. Right now I would put your 95% confidence interval at like, whatever the vig is +/- 1%.

Total Bets:
Wins: 54
Losses: 101
155
Win %:
34.84%
T-value:
1.98
Standard Deviation:

3.83%
Win % Confidence Interval:

27.28% - 42.40%

https://sportsbettingcalcs.com/betti...#ci_calculator

Using the ROI calculator 27% winrate equates to 21.5% ROI and 42% winrate equates to 89% ROI