From week to week, a given contestant is bound to increase his or her number of votes. This is due to two things. The first is that more people vote as the season goes on (or, at least, more votes come in). The second is that someone was eliminated in the prior week, and assuming his votes don’t just drop out, each contestant should get a share of those. If a given contestant can build a coalition of new or converted voters from eliminated contestants, she can win.
As an experiment, I’ve compiled the numbers of votes that each contestant has gotten on a service called Votefair. This service has a ballot each week on who was the best, and it publishes the raw numbers. The service has decent accuracy predicting the outcomes this year (4 correct projections out of 8, or 50%, much better than my model). They clearly aren’t perfect, but let’s assume that the votes are indicative of what is really going on, plus or minus some error.
Here are the raw numbers of vote tallies for each contestant week-by-week
| Top 12 | Top 10 | Top 9 | Top 8 | Top 7 (i) | Top 7 (ii) | Top 6 | Top 5 | |
|---|---|---|---|---|---|---|---|---|
| Colton | 42 | 96 | 133 | 96 | 141 | 170 | ||
| Deandre | 22 | 30 | 18 | 28 | ||||
| Elise | 17 | 59 | 121 | 75 | 92 | 92 | 93 | |
| Erika | 10 | 22 | ||||||
| Heejun | 21 | 26 | 33 | |||||
| Hollie | 114 | 84 | 83 | 58 | 86 | 138 | 159 | 331 |
| Jermaine | 4 | |||||||
| Jessica | 186 | 251 | 268 | 331 | 414 | 492 | 504 | 544 |
| Joshua | 98 | 44 | 41 | 51 | 76 | 92 | 115 | 194 |
| Phil | 98 | 113 | 158 | 147 | 159 | 244 | 295 | 260 |
| Shannon | 8 | |||||||
| Skylar | 30 | 34 | 25 | 65 | 82 | 102 | 171 | 133 |
| Total | 650 | 759 | 880 | 851 | 1050 | 1330 | 1337 | 1462 |
As you can see, the total number of voters went up over time (monotonically), which I believe to be consistent with what actually happens on Idol. One might raise the objection that the total ratings are going down, which is true, but I think more people may be inclined to vote later in the season as they become attached to someone.
Now, let’s focus on Jessica for example. For the Top 10, you would expect that she would pick up some percentage of the votes cast in the Top 12 for Jermaine and Shannon. She would also pick up some of the 109 new voters that participated. Assuming that these votes are distributed evenly, you get an expected growth or decline from week to week.
Aside: Why could there be an expected decline if the person is assumed to pick up votes? Take Hollie in the Top 10, for instance. She got 114 votes in the Top 12. Assume that she picks up an even share of the 12 votes that previously were for Jermaine and Shannon and the 109 new voters. This would give her 126.1 votes out of 759, or 16.6%. Since her preivous total was 17.5%, her percentage actually drops because she was way ahead of the pack but only picked up an average number, which drags her total down.
Here are the expected percentage changes based on the assumption that everyone takes an equal share:
| Top 10 | Top 9 | Top 8 | Top 7 (i) | Top 7 (ii) | Top 6 | Top 5 | |
|---|---|---|---|---|---|---|---|
| Colton | +0.7 | +5.6 | +3.0 | -3.5 | +1.4 | ||
| Elise | +1.2 | +4.7 | +5.8 | -4.0 | -0.3 | -0.8 | |
| Hollie | -0.9 | -5.3 | -1.5 | -1.2 | +0.9 | +3.1 | +1.3 |
| Jessica | -2.5 | +4.2 | +1.2 | +3.1 | -0.5 | +4.9 | -1.5 |
| Joshua | -0.6 | -7.7 | -1.9 | +3.1 | +0.8 | +0.4 | +1.8 |
| Phil | -0.6 | +0.1 | +4.0 | -1.5 | -2.1 | +5.5 | +2.7 |
| Skylar | +0.9 | +0.1 | -2.7 | +6.3 | -0.1 | +0.7 | +4.8 |
Now, if we take the difference between this assumption and the actual week-to-week percentage change, we see how the contestant is doing compared to this idea, a sort of conversion advantage, or the amount that they are converting votes compared to expectations:
| Top 10 | Top 9 | Top 8 | Top 7 (i) | Top 7 (ii) | Top 6 | Top 5 | Total | ||
|---|---|---|---|---|---|---|---|---|---|
| Colton | +5.5 | -3.1 | -6.8 | +5.6 | -2.0 | -0.8 | |||
| Elise | +3.9 | +1.3 | -10.7 | +4.0 | -1.5 | +0.9 | -2.1 | ||
| Hollie | -5.5 | +3.6 | -1.1 | +2.6 | +1.3 | -1.5 | +9.4 | +8.8 | |
| Jessica | +7.0 | -6.8 | +7.2 | -2.5 | -2.0 | -4.2 | +1.1 | -0.2 | |
| Joshua | -8.7 | +6.6 | +3.3 | -1.8 | -1.1 | +1.3 | +2.9 | +2.4 | |
| Phil | +0.4 | +2.9 | -4.7 | -0.6 | +5.3 | -1.8 | -7.0 | -5.4 | |
| Skylar | -1.1 | -1.8 | +7.5 | -6.1 | -0.0 | +4.5 | -8.5 | -5.6 |
Overall, Hollie and Joshua are the ones who’ve been doing the best, converting on average 8.8 and 2.4 points higher than expectation, respectively, whereas Colton, Elise, Phil, and Skylar have done worse than expectation. 3/4 of those have already been eliminated. Jessica has done basically equal to expectation, with a modest underperformance of -0.2, and would have been eliminated if not for the save.
Phil Phillips is the beneficiary of what appears to be a highly organized publicity campaign on Twitter and other sites. This implies that he has a certain “base” of voters. However, he has proven very poor at converting new voters, at least according to Votefair. This implies that Phil is not a certainty to win this season. It depends on how many votes he actually has in the bank, and whether Hollie and Joshua’s ability to win new voters overtakes this base number that he has.
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