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.

Top 4: The winner may already be locked in

The Top 4 continues the trend of being much less about how somebody sings that week, and much more about how they’ve already done. It would be reasonable to say that America has already picked its favorite, and is just eliminating the others one by one until the finale.

This is not to say that it does this indiscriminately. In fact, it probably still eliminates its least favorite quicker. Nonetheless, even if James Durbin screeches out a tone deaf version of a Bee Gees song, my guess is he’ll still make the finale.

The above chart shows the WNTS approval rating for the 4 previous rounds and the outcome (safe or eliminated) that was the result. The points hew relatively close to the logistical regression curve, though the statistical significance leaves something to be desired. Here are variables that are even less well-correlated, though:

  • The contestant’s Top 4 average approval
  • The contestants Top 4 best approval or worst approval
  • Gender
  • Dialidol score

The chart also shows two regions, one that is “generally safe”, above 55, and generally in danger, below 55. There are certainly contestants who were doing well in the previous rounds and got booted. The 3 most prominent ones (the points in the upper right-hand part of the chart) were all women (Tamyra Gray, Latoya London, and Allison Iraheta). However, I wouldn’t read too much into that, as it’s likely statistical noise.

More than half of the people eliminated in the Top 4 fell below this dividing line.

Haley Reinhart is a bit of a puzzle to me. She has seriously underperformed her numbers in the voting, ending up in the Bottom Group when she clearly didn’t deserve it. However, this hasn’t happened for the past couple weeks, and she may have benefited disproportionately from the elimination of Casey Abrams. Scotty McCreery, on the other hand, has consistently overperformed his scores. Were he pulling the votes he deserved, Scotty would have been in the Bottom 2 last week instead of Lauren Alaina. Lauren and Scotty are the two that fall below the line. That being the case, Lauren is probably the contestant in the most danger.

Top 5 Pre-game

As far as who’s going to be eliminated, I’m not going to say anything that isn’t well-known.

Contestant Sex Prior Average Probability of Elim.
Jacob Lusk M 32.5 0.63144
Scotty McCreery M 48.75 0.231642
Lauren Alaina F 55 0.133852
James Durbin M 63.5 0.058627
Haley Reinhart F 65.5 0.04788

There is no point in speculating about how well Jacob would have to do to be considered safe. The model believes that no matter what score Jacob gets, he will be eliminated.

Why is this the case? Funny enough, during the Top 5, America doesn’t vote based on how well the contestant sings. That may seem weird to you, but it doesn’t seem too far off to me. During the Top 5, America tends to shed the contestant who has been doing the worst lately, rather than the one who did the worst that day. There is, in fact, no significant correlation with the Top 5 performance approval and the outcome!

What is notable, though, is that Ms. Haley Reinhart may have moved into front-runner territory. Now, no winner of American Idol has ever been in the Bottom 3 three times, as Haley has (the closest is Fantasia, who was in the B3 twice). However, Haley is probably one of the most improved contestants that I can remember. Even Jordin Sparks started stronger than Haley, and while she did improve, it was not as markedly.

Top 6 pre-game

Contestant Prior Average Prob
Jacob Lusk 41.0 0.217113
Scotty McCreery 48.0 0.158728
Casey Abrams 51.7 0.133645
Haley Reinhart 59.7 0.090357
Lauren Alaina 61.3 0.083084
James Durbin 69.0 0.056084

The Top 6 is going to be an entertaining show. Not that I think the performances will be good (I really don’t), but we can see that the rankings are getting very narrow. A bit of handicapping, though, should perhaps be entertained at this point. Looking at last week‘s prediction, we can say that Scotty McCreery appears to be overperforming by perhaps 6 points, and Haley underperforming by about 5 points. I expect this effect to diminish over time, but assuming it is still present, the rankings would be Jacob Lusk first, and then Casey and Haley essentially in a dead heat.

Continuing the practice from last week, I’ll give the approximate caliber performance needed to keep a contestant out of the Bottom 3 for those at risk, and the score that would put the a contestant in the Bottom 3 for those predicted to be safe.

Contestant Prior
Average
Safe Score/
Not Safe Score
Change from
recent average
Jacob Lusk 41 78 +37
Scotty McCreery 48 77 +29
Casey Abrams 51.66 72 +21
Haley Reinhart 59.66 39 -20
Lauren Alaina 61.33 37 -24
James Durbin 69 25 -44

Jacob Lusk is unlikely to be able to overcome that deficit. Although I would put him at a slight advantage this week, that advantage still requires a level of performance that we haven’t seen from him in many weeks. If Scotty persists in overperforming like he has been, he would need only a 60 to be considered safe according to the model.

In sum, there is a large gulf between the projected bottom 3 (Jacob, Scotty, Casey) and the top 3, if this year is like past years. Whether or not it is like past years is another matter.

As to this week’s being a duet, I don’t know that it changes things much. Last year’s contest saw Michael Lynche go home in what many considered a long-coming elimination. That was in the Top 4, and each contestant did a duet and a song by themselves. Even with the Top 6 doing duets, I would think they will do one by themselves and one in a duet, as only three songs during a show would be fewer than any other episode.

Top 7 Pre-game: Anybody’s game

Now that we’re in the thick of it, any one of the remaining contestants could go this week. No result would be shocking. Based on prior years and based on the average of the previous 3 rounds, the pregame odds look something like this:

Contestant Sex PriorAverage Prob
Jacob Lusk M 44 0.203924
Stefano Langone M 46 0.185417
Casey Abrams M 51 0.144875
Haley Reinhart F 51 0.144875
Scotty McCreery M 57.5 0.103467
Lauren Alaina F 62 0.081281
James Durbin M 70.5 0.050831

Not even a James Durbin elimination would be a total shock. However, if things keep going like they have been, I expect Jacob to go.

We can take this analysis a bit further. Supposing that all the other contestants performed at their recent average, we can ask how much better a performance Jacob or Stefano would need to be predicted to be ranked higher than Casey and Haley:

Contestant Score Needed For Safety Prior Average Difference
Stefano Langone 61.0 46.0 +15.0
Jacob Lusk 65.0 44.0 +21.0

These scores are perfectly achievable. Many times in Idol history a contestant has managed a score on the order of 20 points above his average, or 20 points above his prior performance. It happens. However, I don’t think that this is the most likely week for it, as the theme (Songs from the 21st century) doesn’t particularly suit either contestant.

We can do the same thing in reverse for James and Lauren. How badly would they need to screw the pooch to be in danger?

Contestant Score Needed For Elimination Prior Average Difference
James Durbin 19.0 70.5 -51.5
Lauren Alaina 34.0 62.0 -28.0

Has a contestant ever had a week-to-week swing of 50 points? In fact, it has happened. Anthony Federov succeeded in this feat, getting a 64 in the Top 6 but a 12 in the Top 5. So I would not call James totally safe, but he’s pretty damn safe.

Lauren is another story. Many contestants have had a week where they underperformed by 25-30 points. I’m not ready to call this one safe, but I also wouldn’t put any money on Lauren.