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Happy's Adjusted Cumulative Distribution Function for NFL ATS Picks (and O/U)
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Cumulative 2010
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There are two main factors that go into our picks; the confidence (a complex function of the standard deviation between the predictions of several different predictive models), and the delta (the difference between the average casino line and the weighted average spread projected by our models).  The delta is used in concert with the historical standard of deviation of NFL outcomes relative to the spread to determine a raw cumulative distribution function (z-statistic).  We then take the raw z-statistic and adjust it on the basis of the confidence.

Specifically, our adjusted cumulative distribution function is equal to the raw z-statistic times the confidence plus 50.0% all divided by the sum of the confidence plus one.  This means that if the confidence is zero the adjusted z-statistic is 50.0%, i.e. a coin toss.  This will not beat any juice (52.4% needed for most casinos US bettors have access to).  Our results in weeks 1-4 are based on the raw z-statistic, but we generally only bet on high confidence games.  Starting in week five we report the adjusted cumulative distribution function as our probability of winning each individual event.

We have posted several blog posts about setting realistic expectations for sports betting.  We now publish out expectation values each week on Wednesday (the same day we make our picks).  We also update our expectation value pages by highlighting in green our actual results.  Finally, we are tracking our year to date results against expectation values.

Prior to week five we were evaluating expectation values based on the raw cumulative distribution function.  Starting in week five we began using the adjusted z-statistic.
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