simple ROI question

[guaranteedBluff]

Assuming I've played n multi-table tournaments, my ROI is x, and the average tourney size is p, how do I calculate a 95% confidence interval for my actual ROI?

Do I need more data than what is given?

[pzhon]

Yes, you do need more information.

The standard deviation per tournament depends on the tourney size, but not so that the average tournament size is the key figure, which would be the case if variance were to scale linearly with tournament size, which is not true for typical prize structures. The standard deviation also depends on your playing style, skill, and the prize structure.

You can find some computations in the archives of standard deviations for the assumption that your place is uniform. Here is one. IIRC, the standard deviation was not outrageously large (in buy-ins) even for the WSOP main event, perhaps 13 buy-ins.