I’m working on a longer piece about song selection, and what choices are smart (statistically speaking) and which are not. For now, I’ve listed below all performances of Beatles songs, along with the breakdown of how well the performance was received and what the voting result was (the final column indicates if that contestant had already been in the Bottom 3). These are listed in order of approval rating. Anything below 50 is considered to have been scored below average (and, indeed, most of the not-safe people are in that half of the table).

There haven’t been too many repeats of any of these. Across the Universe (twice), Let It Be (twice) and Come Together (three times) have worked out well for those who sang them. Oh Darling and The Long and Winding Road have been a mixed bag—they worked for one person, not for another. That’s one reason I don’t put too much stock in analyses that focus solely on song choice.

In the recent weeks, I’ve been saying that to the extent that any variable is important to who is eliminated, that variable was how well the contestant had done lately. That is, there was a significant effect of momentum, and contestants were eliminated even if they had a good week because people stuck with their favorites from the prior weeks.

For the Top 3, though, this isn’t the case. There is good statistical evidence that not only does performance matter, but the performance that matters most is the best performance that a contestant has that evening. The contestant can screw up on two songs so long as they don’t have the worst top-score for the night.

That being said, usually the worst average performer also has the lowest top-number for the night.

Supposing, though, that Haley Reinhart has a bad-to-disastrous run at What Is And What Should Never Be tomorrow night, which is very likely, as long as she comes out and kills it with one of her other songs (You Oughta Know being the most likely), I would still expect her to be safe. We don’t know what Lauren or Scotty will be singing, but historically these contestants have produced generally consistent but not stratospheric approval ratings. This is particularly true of Lauren Alaina, who is perceived (rightly) not to have had “a moment” on the show. This would be the time to do it, if she were going to.

So, no numbers this week. What happens this week is almost entirely dependent on what happens tomorrow night.

By the way, Dialidol has gotten 5/6 Top 3 calls correct. However, 7/9 calls were correct based on the above strategy, which is much stronger evidence.

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)

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.

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

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.

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.

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.

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:

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:

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?

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.