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Got Variance?

Posted By: Nack Ballard
Date: Sunday, 23 May 2010, at 6:10 a.m.

In Response To: Got Variance? (Daniel Murphy)

The 95% confidence interval in the 1296 trial rollout for the best play is .574 - .614, and the longer rollout comes in at .577. That's ok. For the other play the short rollout says 0.506 - 0.552 and the longer rollout comes in at .546. That's ok too.

It is worth noting that whenever one play is at the top of its range and the other play is at the bottom end of its range, that there is a parlay involved. Forgiving the plays as being independently inside their ranges glosses over that parlay.

In this case, both plays that Stick rolled out are within the 95% confidence interval, but not by much -- for simplicity's sake let's say that the first play is on or just outside of the cusp of a would-be 90% confidence interval and the other around 83+%. In that case, Gnu is saying that there is only 1 chance in 10 that the first play ended up so far from eventual (infinitely rolled) equity, and only 1 chance in 6 that the second play ended up so far from eventual equity, and keeping in mind that in half of those scenarios they would have strayed in the same direction.

That is, if you are to believe the way that Gnu estimates/calculates confidence intervals, the chances of the two plays being this far afield in opposite ends of their ranges is around 1/120. Yet it seems to me that this sort of "wild" occurrence is noticeably less uncommon.

Nack

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