"Expected" ROI

[caddie444]

Alright, I'm wondering how to figure out how close a given player's ROI (using sample size and hard data) is compared to their expected long term ROI.

Example- I just moved up in levels, and running a little bad, my ROI over 300 $6.5o 6-max SNG's is ~%15. (I'm purposely using a small sample size)
Based on the 300 sample size , and at my current skill level, what are the odds that my "expected" long term ROI is higher/lower than the %15 I have thus far achieved? I think standard deviations are needed to figure this out but haven't done these calculations in a while.

What if the sample was 500 matches? 1000? etc




Obviously the more matches you've played, the closer your Actual ROI will be to your Expected ROI (Assuming your skill level remains constant)

Anyone have any clue how to compute this?

[elitemob]

Check this out:

http://www.sitandgoplanet.com/sitand...urly_Rate.html

http://www.sitandgoplanet.com/sitand...ng_Levels.html

cheers,
elitemob

[taipan168]

I also put a table of expected long-term ROIs and ITM percentages in the FAQs.

[jdubs]

Check this out:

http://www.sitandgoplanet.com/sitand...urly_Rate.html

http://www.sitandgoplanet.com/sitand...ng_Levels.html

cheers,
elitemob

thanks good find!

[caddie444]

From :
http://www.sitandgoplanet.com/sitand...ng_Levels.html

The chart below shows the statistical likelihood of a given sample of SNGs being a true indication of your ROI.

100 games: ~23%

300 games: ~40%

1000 games: ~66%

2000 games: ~82%


Thanks, this is what I was looking for! So for the example I gave, the %15 ROI I achieved at that level only has a %40 chance of being my true expected ROI. Anyone have any idea how this was calculated though?? It'd be interesting to know how large a sample size would need to be for the true indication to approach %100 accuracy.

[elitemob]

Hey mate,

this is a classic application for confidence intervals:

http://en.wikipedia.org/wiki/Confidence_Interval (FYI)

This is pure math/statistics though. Unfortunately they didn't link the source (the original post in the 2+2 forums) and I didn't have time to search for it yet.
If I get the chance I can break down the math. You'll never reach 100% btw, the value will asymptotical approach (?) towards 100% (hope that's the right term in english, I'm German, so I'm kind of at a loss of words here). Ok, let me rephrase that. With an infinite sample size, you would of course be 100% certain of your "true" ROI. I think that's easier to understand

If you want to have a visual impression:
- take a piece of paper
- draw two axes, x - no of games, y - ROI%
- put in the 4 coordinates you have
- draw a curve matching the 4 coordinates (use a curve template)

Anyways, perhaps the link helps a bit to understand.

cheers,
elitemob