Top 4 pre-game odds

I’m actually not all that confident in James Durbin compared to where I was yesterday.

If I were to give my best guess as to the fit to the data, and assume that all contestants performed roughly how they did in the Top 5, then the model predicts the following probabilities (not normalized)

Name Prior Average (4 rounds) Probability of elim.
Scotty 53.333 0.323193
James 58.666 0.219311
Lauren 63.1666 0.164075
Haley 71.666 0.075083

Why is James higher than Lauren? He had a bad week. But, in fact, he’s had two bad weeks in a row compared with the other contestants. Lauren had one bad performance and one good performance. She was in the Bottom 2, and so may be running about 5 percentage points behind where she should have been. Scotty, on the other hand, has been running 5-10 points better than he should.

If you asked me my feeling, it’s going to be Lauren. The model predicts Scotty, then James.

Technical note: it may seem that I have been much more confident in the model in past weeks. There is a very good reason for this. Each round of American Idol decreases the total available data from week to week. In the Top 12, you have 12 pieces of data per season (in this case, about 110 data points). But in the Top 4, you have only 4 pieces of data per season. Yes, they sing 2 songs each, but we don’t get the response from individual songs—we only know the outcome of the vote, which was the result of both songs. As such, I only have 36 pieces of data to begin with for judging the Top 4. Factor in the fact that Dialidol only has results since Season 4, and you’re really operating on about 25 degrees of freedom for a statistical fit. And, well, that just adds up to a crummy statistical significance.

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