# Final pre-performance projection

Tonight was a fairly interesting night, with Hollie Cavanagh finally being featured. This, believe it or not, made Chelsea Sorrell the least exposed female contestant, with Hollie pulling up a close second. She has a lot of work to do if she is going to make it to the finals, but many stranger things have happened. Her performance seemed strong to me, and I found myself wondering “What was the problem?” It’s puzzling why they decided neither to show her this year, nor to even highlight that she was a contestant who was shown during last year’s auditions (made it to the final decision last year, as I recall).

Incidentally, the actual lowest exposed contestant this year is Chase Likens, the country music singer who looks oddly like an average frat boy. He received a tiny amount of footage tonight, as the Idol producers swept him, Hallie Day, and Aaron Sanders (aka Aaron Marcellus) under the rug.

Two notes: First, I made an error in calculating Jen Hirsh’s probability yesterday (it’s probably not 83%, as I printed). This was a result of a mistake when normalizing the data, which I explain below.

Second: a bit of explanation on how this works, so that the numbers are not over-interpreted. If you look at the totality of pre-voting shows, tabulate all of the times that people were shown, and then check that against whether a contestant made the finals, you find that the two variables (pre-exposure time and making it to the finals) are correlated to an extreme degree. This does not mean they are perfectly correlated, or that this is even the only variable that matters. It just means that there is very little chance that the two variables are not related. One can quantify what the relationship between the two variables is by doing a generalized linear fit for the odds (called a logistical or logit regression) to get a quantitative idea of what a given about of pre-exposure time implies about your probability of making the finals.

This fit is done with only one variable: screen time. It does not account for performance quality, which is a major factor as well. So, you can reasonably interpret the numbers given below like this: if all of the contestants put in an equally good performance, then these are the probabilities that a given contestant will make the finals. This, of course, assumes that the voting conditions are all the same, which you know is not true. However, it is likely a decent approximation.

In order to normalize the probabilities, I constrained the total of all probabilities for each gender to equal 600%, because 6 people will make the finals out of this group. This is where I made the transcription mistake yesterday, printing Jen Hirsh’s raw probability rather than her normalized probability.

One final note: according to MJ, the addition of a 13th contestant does not affect this, since he will be added after the vote.