What other factors do we need to consider when determining a bankroll for tournaments?
How does ROI and ITM% affect this?
The obvious answer is that it affects your variance.
So how do we determine variance and standard deviation for tournaments?
Variance is still simply the average of the squares of all results, and winrate total $won/#tournaments.


$109 buy-in, 100-player MTTs, same prize structure (35%/21%/14%/10%/6%/4%/3%/3%/2%/2%), same opponents, and neither you nor your opponents ever get any better


Let's suppose you finish in every place with equal probability. Then the standard deviation would be $440, or 4.04 buy-ins.

The standard deviation of your observed ROI after n tournaments would be 404%/sqrt(n). If you want to have a 95% confidence interval of +- 10%, you need your standard deviation to be 5%, so n=(404/5)^2=6,531 tournaments.

That is more than most individuals play, so it is almost impossible to get a high confidence of your winrate (ROI)

If you are a winning player, your distribution of places is not uniform. This will tend to increase the standard deviation. If you make k times as many final tables, with an even distribution at the final table, your standard deviation will increase by almost a factor of sqrt(k). for k=2, the standard deviation would be $606, or 5.57 buy-ins.

Here is an application:

Your bankroll should be at least c*SD^2/ROI, where SD is standard deviation and c is a number that depends on your risk tolerance and ability/willingness to move down if you hit a bad streak. (based on the "kelly criterion" in the post below.) Most people seem happy with a value of c between 2 and 4. (1/2 to 1/4 kelly)

If your ROI is 40%=0.4 buy-ins with a SD of 5 buy-ins, then your bankroll should be at least c*5^2/0.4 = c*62.5. For c=2, that is 125 buy-ins. For c=4, that is 250 buy-ins.

For comparison, the SD for 1-table SNGs is about 1.7 buy-ins. In LHE, it is about 15 BB/100 for online full games, or 17 BB/100 for 6-max. In NLHE, it is about 20-60 BB/100.

If you know your win rates in each game, you can use these to determine what gives you the best hourly rate for your bankroll.