Top 4 projection (final)

Name Song WNTS MJs VF Not-safe Probability
Jessica Meuse Since U Been Gone / So What / You and I 48 62.9 21 0.459
Caleb Johnson You Give Love a Bad Name / Travelin’ Band / Maybe I’m Amazed 53 21.4 21 0.253
Alex Preston Too Close / I’m Yours / Yellow 58.667 12.6 24 0.190
Jena Irene Heartbreaker / Bad Romance / Can’t Help Falling in Love 66.667 3.1 34 0.098

Important!

Updated 5:54 PM EST (final)

The methodology for the finals model is described here (though some modifications have been made to replace Dialidol with MJsBigBlog’s poll). The model is 87% accurate on ranking within a margin of error of +/- 3%. Probabilities being what they are, somebody with a not-safe probability of just 0.25 will be in the bottom 3 one out of four times. Please do not comment that the numbers are wrong. They are probabilities, not certainties or even claims. Do not gamble based on these numbers.

Names in green are most likely to be safe. Names in red are considered most at risk for being eliminated. Names in yellow are undecided. The most probable elimination is Jessica. However, anybody being eliminated would not be shocking.

The collective judgement of the internet is that Jessica is going home tomorrow night. This position certainly makes sense. None of the other contestants was ever in the bottom group except Jena, and that was way back in the Top 12. Jessica found herself in the bottom group in both the Top 6 and the Top 7, and we know for a fact that she was in 5th place in the Top 6. Her being safe would be surprising, though not quite at the level of what I would call shocking.

Jessica is also behind in the Top 3 tracker, and has been behind the three remaining contestants consistently. I would caution, though, that the gap between her and Alex was slimmer than it appears.

I must admit, I’m seeing a bit of a turn-around on Caleb in the numbers. Is he starting to wear thin? Weigh in on the poll.

In the past I’ve investigated what is the best bellwether of elimination when multiple songs are sung. It could be that the best performance is the most predictive, or it could be the average. WNTS ratings become so weakly linked with elimination late in the game, at the point where multiple songs are sung, that the effect is hard to suss out. So I have just stuck with the average, since it’s the most obvious metric.

My point is, if Jena had two middling performance, but one barn burner, where should that leave her? I think it’s splitting hairs, but from reading other impressions on the web, I’m inclined to think many people get an average impression for the whole night, and hence the mean WNTS score should hold sway. I don’t personally think that way, but it does seem to be the norm. Either way, she tops the all indices by a comfortable margin.

Below are the updated model performance stats. With only a few extra data points last week, they are mostly unchanged save for a slight contraction in a couple of the error bars.

S13ProbsvsResults

Top 4 Liveblog

This week we’ll whittle down the pool of contestants to the top three, and incidentally see how the top three tracker did this year. The theme is break-ups and make-ups. I really want to hear some Rachael Yamagata, even though I’m sure we won’t: she’s been called the Troubadour of Heartbreak, and for very good reason. Coincidentally her album Happenstance, which is one of my all-time favorite albums, turns ten this year. What? I run this blog; I can shill for my favorite musicians if I want. Full disclosure: that’s an affiliate link, so I get, like, a penny if you buy the album or something. But you should buy the album because it’s great. Ok. Enough shilling: on with the blogging! Continue reading

Final Top 3 Tracker of Season 13

The Top 3 tracker is a long view of the contest, trying to figure out who will end up in the Top 3 based on the current standings. It works in a similar way to the finals model, but rather than week-to-week, it looks at historical information to decide who most looks like a Top 3 contestant.

Here is the Top 3 tracker over time:

The Top 3 looks quite likely to include Jena and Caleb. The race has tightened in the extreme between Alex and Jessica, and one should no longer, in my opinion, be nearly so sure that Alex will make it instead of Jessica.

Jena has been above 80% for five weeks now. Both she and Caleb are the only ones to make it that high in any week except Alex after the Top 8 redux.

Jessica has momentum following Sam’s elimination, based on two weeks where her approval ratings have been improving somewhat. Alex seems to be in a problematic mode: his really amazingly highly rated performances were several weeks ago, and since then he’s oscillated around 65% with no sign of picking up. His popularity is also flagging. That being said, according to the internet, Jessica is more likely to be eliminated. I sympathize with this, since she has been in the bottom 3, and Alex never has. But there is a lot of room for a surprise in this round.

Continue reading

Top 5 projection (final)

Name Song WNTS MJs VF Not-safe Probability
Sam Woolf Sing / How to Save a Life 34.0 50.4 17 0.533
Jessica Meuse Human / Summertime Sadness 77.0 36.3 16 0.490
Alex Preston Sweater Weather / Say Something 63.5 2.8 14 0.452
Caleb Johnson Don’t Want to Miss a Thing / Still of the Night 57.5 4.5 22 0.315
Jena Irene My Body / Valerie 60.0 5.9 30 0.209

Important!

The methodology for the finals model is described here (though some modifications have been made to replace Dialidol with MJsBigBlog’s poll). The model is 87% accurate on ranking within a margin of error of +/- 3%. Probabilities being what they are, somebody with a not-safe probability of just 0.25 will be in the bottom 3 one out of four times. Please do not comment that the numbers are wrong. They are probabilities, not certainties or even claims. Do not gamble based on these numbers.

Names in green are most likely to be safe. Names in red are considered most at risk for being in the bottom 2. Names in yellow are undecided. The most probable bottom 2 is Sam and Jessica. However, anybody on the list being in the bottom 2 would not be shocking.

Final update 6:01 PM EST.

Updated 11:22 AM EST. Jessica now 2nd most likely outside the margin of error.

Initial post 12:53 AM EST.

Alex and Jessica are virtually tied for second most likely to be in the bottom 2 (supposing that they actually tell us what that is tomorrow). Though Jessica had the highest average score on her approval ratings, she is considered second-most-likely by MJsBigBlog’s poll (“Who WILL go home?”) and is only third most popular on Votefair.

I am not as convinced as everyone else is that Alex is totally safe. Only 3.6% of internet voters thought Alex would be eliminated tomorrow, but I don’t think his chances of being in the bottom 2 are anywhere near that low.

As I’ve said time and again, a probability as written above refers to the chance, based on historical considerations, that a person will be in the bottom group. If someone has a probability of 30%, then 30% of such people in the long run will be not safe: that is, either eliminated or just in the bottom 2. It’s fair, then, to ask how many people this season have actually followed the probabilities stated by me over the weeks so far.

Below you can see the model performance so far this season (the format is adapted from fivethirtyeight’s assessment of their NCAA basketball predictions). The predicted not-safe probabilities were binned in bins of 10 percentage points. The dot shows the proportion that were actually not-safe. So for people predicted not-safe in the range of 0-10%, 15% of such people actually were not-safe, well within the margin of error. The confidence interval (95% C.I. based on simple binomial model) is shown in gray. The more contestants in the bin, the smaller this interval is and the more confident the assessment is. So, the fact that only a few people were predicted between 40-50% means that the uncertainty is quite high in that category, and there’s no real reason to fret that only 16% of those few people actually were (N = 6). Note that in the categories with any significance, the dot is well within the tolerance, in some cases right in the middle of the range. The model is possibly still too tentative about people who are predicted 50-60% chance of not being safe, nearly all (8 out of 9) of whom have been—that is, their predicted chance should have been higher—but the result is not statistically significant.

S13ProbsvsResults