good sample size for ROI calculation

[starchyy]

i was just wondering what the right sample size would be to calculate my sng ROI. one that will take into account all variance.
thanks

[starchyy]

bump

[Mr. Ratface]

I was actually wondering the same thing. I've been looking at my stats on my SNGs and noticed that I had a 60% ROI. My sample size is only 85 SNGs so I know I've been running good and that the size of the sample is too small but how large does it have to be before the stats start to hold any kind of meaning?

[A__theKevlar__2]

1000 sngs is a number i hear thrown around quite a bit

[SGspecial]

[ QUOTE ]
1000 sngs is a number i hear thrown around quite a bit

[/ QUOTE ]

so if you average 3 sngs a day, you have to play for a year before you know you're a winning player?

[QuattroFour4]

If you're averaging only 1,000 S&G's a year, it seems as if you're only playing for fun anyway.

[Paul2432]

The answer depends on what level of confidence you require.

For a reasonable estimate divide 180% by the square root of the number of SNGs. This will give you the SD of your win-rate.

68% of the time your winrate will be within +/- 1 SD.
95% of the time your winrate will be within +/- 2 SD.
99% of the time your winrate will be within +/- 3 SD.

So for example if you've played 10,000 SNGs then you know your ROI +/- 3.6% with 95% confidence.

This assumes the standard 50/30/20 payout structure.

Paul

[starchyy]

[ QUOTE ]


So for example if you've played 10,000 SNGs then you know your ROI +/- 3.6% with 95% confidence.


[/ QUOTE ]

Where does the +/- 3.6% come from? I understand the 95% confidence from the # of SD, but I don't see where the +/- 3.6% comes into play.

[fraz8000]

The ROI you have measured is a sample of your actual winrate.
+/- 3.6 at 95% confidence means take your sample ROI as a percentage (say 20%), then subtract and add 3.6 to find new values (16.4, 23.6).

With these parameters, you can say with 95% confidence that your actual win rate falls within the range 16.4% and 23.6%. For higher confidence levels (say 99%) you would need wider ranges to accomodate more for the possibility that it may fall outside this range. For lower confidence levels, the range is smaller.

[Absalon]

Hi Paul,

interesting Post, but can you tell us where the 180% come from?
It seems to me, your Formula doesn't agree with 2+2 spreadsheet:
I have measured a ROI of +20.1% over 428 Tourneys. So by your Formula my SD should be 9% and I could be sure to be a winnign player at the 95% confidence Level, but not at the 99%, am I right?
But the spreadsheet tells me, my "Winning Confidence" is 99.6% and I can have a 99% confidence that my $/tourney is between 0.03$ and 2.17$ (5+05$ Tourneys).
So, according to you my winning Confidence is between 95% and 99%, but according to the spreadsheet it is over 99%. Another Formula? And why, where does it come from?