[GrekeHaus]

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Standard deviation, which is what you guys mean when you say variance, is sqrt(%1(W1-a)^2+%2(W2-a)+%3(W3-a)+%4(BI-a)), where %1 is chance to come in 1st, W1 is money earned for first, a is expected win, %4 is odds of losing, and BI is the buy-in. So, it's certainly affected by your ROI and your place distrubution, not just the payout structure, and how it changes relative to those depends on what they are specifically. For a player with a 20% ROI or so, variance increases as ROI goes down because the terms (W1-a)^2, (W2-a)^2, and (W3-a)^2 increase much faster than the terms that decrease.

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The last part of this statement isn't true. If you take a player who never finishes ITM or a player who always gets first, they will both have a variance of 0.

For people who fall in the middle (everyone), your variance is just a 2nd degree polynomial. For people in what would be a normal range of finishes, they will actually increase variance with a higher ROI because the higher percentages of firsts tend to create bigger swings.