Odds of a Major Downswing in SNGs?

[PartySNGer]

I've tracked every $55 SNG since Party started allowing 10 tables, whether I was drunk, on tilt, whatever. Since then I've played 1540 $55s with a ROI of 14.5% (including a recent downswing). In October and November, my worst 300 SNG stretch was winning $1300. Over my last 299 SNGs I have lost $582.

OK, I've seen posts where Irieguy says even the best players will lose over 100-150 SNGs. I'm just wondering what the odds are that a long term 15% ROI player could lose 11 buy-ins over a 300 SNG stretch. I'm not even overly pissed, just wondering how big a statistical anomaly this is. I imagine there's less than a 1% of this occurring. Hopefully, Irie or someone will know more.

[KenProspero]

If you play long enough, pretty close to 100%

[pzhon]

The standard deviation per SNG is about 1.7 buy-ins. In 300 tournaments, it is sqrt(300)*1.7 ~ 29.4 buy-ins.

You expect to be up by .15*300 = 45 buy-ins. Losing 11 buy-ins or worse is 55.5 buy-ins below average. That's 1.885 standard deviations below average, which happens about 2.97% of the time.

That's quite likely to be an underestimate if you are not completely sure what your win rate is. If, a priori, you felt there was a 20% chance that your win rate was 13%, 14%, 15%, 16%, or 17%, it would be much more likely to lose 11 buy-ins, and you would also have more evidence that your win rate is more likely to be 13% rather than 17%.