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MIT staff blogger Ben Jones

An American Idol Math Question by Ben Jones

You guys are all good in math; help me out with this one.

You guys are all good in math; help me out with this one. My mom pointed this out last night, and unless I’m missing something, I agree with her that American Idol’s voting system may have some issues.

Did you see the numbers on Wednesday night, when Elliott got voted off? Each of the three top contestants received 33.xx% of the votes – statistically it was a 3-way tie.

Let’s do the math, and please correct me if I’m wrong:

American Idol has a finite number of phone lines. The phone lines stay open for two hours following the show. Seacrest said that 50 million people registered their votes, roughly 16.67 million for each contestant, give or take.

So – if each contestant’s phone numbers (they each get two), within those two hours, can handle a finite number of calls – then it’s always going to be a tie. Voters just max out each contestant’s phone lines for two hours – the system is not actually measuring anything.

Let’s put it another way – if 200 million people try to register votes in that two hour period, and each contestant’s phone lines can handle ~16.67 million votes, then we’ll never really know what happened because all votes beyond the 16.67 million will be lost. What if Elliott had, for example, 100 million people who wanted to vote for him, and Kat and Taylor each had 30 million, but only 16.67 million people were able to get through to register their votes for each contestant?

This would explain why the three contestants essentially tied; the difference in votes was statistically irrelevant, in my opinion. (It would be different if there were one telephone number for all three contestants and callers voted by pushing a button.)

When it’s THAT close, you really have to wonder. Someone tell me I’m wrong so I don’t lose sleep over this.

30 responses to “An American Idol Math Question”

  1. dan jang says:

    you definitely raise some good points.

    If this is true, it’s a great find.

  2. John says:

    I’ve not watched the show for a while, so I’m not sure, but can’t votes be cast through text-messages?

  3. Shannon says:

    Nice. Good call.

    And yeah, votes can be sent through texts but only for Cingular customers- so ultimately whoever wins the competition is decided by how many of their fans use Cingular Wireless.

    I would love to check that out… That would make for some serious statistical fun.

  4. Christina says:

    Mittens at prom!

    [I tried really hard to get everyone to spell out MIT with our fingers but they were being total party poopers.]

  5. Vu says:

    I say American Idol should have a 2 hour telethon, kind of like the ones you see when people are trying to raise money. It’s a crazy idea, as there will be too many calls to keep track of anything, but I can see American Idol making a lot of money out of this. The further behind they see their favorite in the voting, the more they would want to call in.

  6. Dan says:

    Interesting point, but it’s kind of sad that people will cast 50 million votes +/- in two hours for a pop star contest, but will only cast 100 million votes in a presidential election. America needs to reexamine its priorities.

  7. Geoffrey says:

    So why don’t they open presidential elections to phone-line voting? I mean, Idol already has enough safeguards to prevent any statistically significant vote-stealing….

  8. Yes, as someone who’s interested in American idol, i think you have quite a few logical points here.

    However, there’s a website,, which tries to predict, in ‘real-time’, who will be voted off each round. It works on a basis different from simply counting the sample number of votes received by an idol. The website owners have a large sample size of people trying to call for their favourite idol, and they measure the busy percentage signal for an idol – that is, how many calls out of 100 don’t get through- assuming that the busier a line is, the more voters are trying to get through at the same time. Using this, they predict the idol likely to get the most number of votes.

    This is quite strange, because if one looks at their raw figures, sometimes the person they predict to be #1 has the least votes registered out of all the contestants each round, but obviously has a higher busy-percentage.

    An interesting thing to see is that their method seems to be mostly correct in predicting who will be voted off.

    If, the number of votes were suppressed because of the finite number of votes registered per line, maybe using the ‘busy-percentage’ would not be a very accurate tool since it would be quite irrelevant?

    Because, assuming that elliot had a 100 million viewers, and only 16 2/3 million can vote, then the busy-percentage would not be a good indicator of his chances because even despite a low busy-signal, an idol would still receive the (supposedly) maximum finite number of votes, say 16 2/3 million?

    I hope this does make sense =P…

  9. Syed Raza says:

    The question becomes in this case: why is website quite accurate in its predictions if the ‘maxed-out-votes’ theory is correct?

  10. Omar '10 says:

    Haha, I was wondering the same thing with a Puerto Rican program (Objetivo Fama) which had the same voting system. I guess it’s true that if the lines can only handle a certain number of calls at the same time the voting will only measure how fast the people hang the phone. I mean, if you are being confirmed that your vote was registered, just hang so another call might get in. But it’s true what you have said, it’s not really telling how many people want to vote for X person.

  11. John says:

    Why not online voting?

  12. Syed Raza says:

    Yeah, Quentin you’re right.

    The difference between 33.68% and 33.08% on last show roughly equals 41 2/3 more calls per second for the person who got the most votes.

    Despite everything, that seems to be an emphatic margin.

  13. I’ve thought about this during past seasons. I think that the results may still be accurate, for a different reason. More callers, even to a “full” line, will still be able to squeeze into spaces between other calls. It certainly decreases the signal-to-noise ratio. That raises an interesting attack, though. Voting for your opponent and staying on the line for a long time would actually hurt them.

    The mysteries of American Idol voting…

    Of course, it would all be solved if they said one phone line = one vote.


  14. another Dan says:

    I think you’re absolutely right. Separate phone lines and enough fans to max out each contestant’s votes within the 2 hours. 3 contestants – 33.33% each and in this case only a .35% margin of error. Even with what Quentin Smith said, who knows what the other votes would be past the 2 hours – the people in the first 2 hours could have just so happened (and be statistically possible) to like Taylor or Katherine better.

    This I gotta tell my mom.

  15. Lerh Feng says:

    Now that you mention it, your logic does appear airtight. Oh my…now I’m going to lose sleep too!

  16. Adnan Esmail says:

    I agree with you completely. Perhaps they could have the six lines split among the thee candidates, rather than having people vote to individual lines.

  17. Adnan Esmail says:

    I agree with you completely. Perhaps they could have the six lines split among the thee candidates, rather than having people vote to individual lines.

  18. Hicks Fan says:

    I think the AI system may be awarding persistence. Most voters are going to call in as soon as the voting starts. Most of these calls will be from voters with no previous AI voting experience who decide impulsively to vote in the finale. Most of them will get busy signals. After repeated failures to get through most of them will say “The heck with it, he (or she) doesn’t need my vote tonight.”

    Only the most persistent and organized fans (including those with auto-dialers) will continue dialing throughout the two hour time slot. Towards the end of that time slot after the impulse voters have given up, calls from the most persistent fans will get through and be counted.

    I think more of Taylor’s fans are organized and experienced enough to persist throughout the two hours so I predict Taylor will win!

  19. Christina says:

    I think Ben, or someone, should do a big ‘ol post with their own takes on each of the living quarters!! Yes. Yay!

  20. JKim says:

    MORE Mittens at prom. Except, we call it ball. And also, there are only two of us. woot.

  21. Rob Golden says:

    In answer to the question : why has DialIdol been correct when the phone lines have been maxed out?

    The number suggest the phone lines were only maxed out last week when the vote volume was at its highest and the number of contestants the loweest to date.

    In previous weeks this was not an issue.

    It remains to be seen whether it will be tonight.

  22. As an old computer nerd who has not seen a math class in 30 years, I have become hooked on DialIdol. Not American Idol (AI) but watching the minute by minute results of DialIdol. The producers of AI claim that they do not have bottlenecks – and I believe them. The bottlenecks are before you get to AI. So more phone lines would not help.

    I setup DialIdol for my wife. We live in the home town of Taylor Hicks. In the 2 hours voting windows, my DialIdol will place 600 phone calls but only 12 will get thru – or a 98% busy rate. I have checked and the busy rate holds true of any vote of an AI singer in our area – regardless of who you are voting for. The local interest in AI is big, since we have had 3 finalists in the last 4 years.

    At the same time, the busy rate over the entire EST and CST time zones, per DialIdol, is from 85% for Taylor to 40% for the loser. If the bottleneck was at the AI end of the lines, you would not see the 98% vs 85% difference in busy signals. For the last 6 or 7 weeks Katherine has been on or near the bottom at this point.

    At 11:00 EST, the east coast can no longer vote – but California cuts in. By looking at the raw numbers and subtracting the east coast numbers from the running total, it looks like the busy rate drops to below 20% for the highest vote getter. With 18 million people in Southern California alone, the telephone companies must have a very large telephone infrastruture just to support daily life. Add that the AI lines probably end in the area and would be for all practical purposes a local call.

    At this point, Katherine a local girl and more in the image that the “valley girl” sterotype is looking for, now quickly climbs in the numbers. Other have observed that she gets the highest % of cell phone and text message calls. In Southern Cal. cell and text are not just available, but almost a way of life.

    The thing is at 20% rate, a Cal. DialIdol user gets 600 attempts and 380 votes. A Birmingham AL user get 600 attempts and 12 votes. So one California voter is equal to 32 Birmingham voters. In my opinion, based on DialIdol, not personal bias, the 1 vote – 32 votes is the only reason Katherine was not voted off 5 weeks ago and is (not maybe but is) the only reason she is in the finals.

    I have seen the problem for weeks (and even understood it for several years) but did not see a solution. Until now – putting in one set of lines for everyone and then touchtone voting fixes the phone bottleneck problem.

  23. HarmyG says:

    The thing is, Wanninger, is that Katharine doesn’t have the local support the Taylor Hicks has. You can’t assume that everyone in California is voting for her.

  24. Zaira says:

    This is why I love MIT!

  25. Jerry says:

    You are partially correct, in a perfect world there is a finite amount of votes a phone line can receive. But this is not a perfect world, what is happening in my opinion is this. Once you get through, IE do not get a busy signal the vote SHOULD be cast(don’t quote me on that one cause I don’t know). If you hang up and dial again ideally you get another chance and free up the line for more votes quicker. But if you stay on and hear the whole message from the Idol, I know I did listen for the whole thing at least half the time I voted tonight, you tie up the line for longer thus limiting the votes. That is just one of the many factors that could limit votes.

    Others are outgoing calls from your provider say, MCI, if too many phone calls to that number are going out from MCI I would assume that MCIs network could get overwhelmed from time to time and give you a busy signal similar to the same signal you get when it is actually busy. Just a few things I was thinking of while I was voting for Taylor tonight, vote for Taylor Soul Patrol, Soul Patrol!!!

  26. I don’t assume that everyone in Cal. votes for her. I see in the DialIdol numbers that more people in California vote for her than any other singer. And with the 20% busy rate the west coast has so much more influence that they move her off the bottom at the end of voting. Basing my conclusion only on DialIdol numbers, California has able to keep her on the show each week. But she has never been #1 or passed Taylor.

    What was interesting last night is with the 4 hour voting window you had for the first time an overlap of east coast and west coast voters. For the first two hours of the west coast vote, DialIdol showed lines staying busy because of nationwide traffic. Once the east coast dropped off, the busy rate dropped but at first not as much as usual. But Katherine’s vote totals did not shift as much as they have in the past and this AM, DialIdol showed a really big gap of Taylor over Katherine. The obviously answer is this trend was based on last nights performances.

    But I wonder how much was due to human nature. Here is what I mean. You live in the west and until now have been voting of Katherine for 2 hours each week and mostly getting to vote 4 of 5 calls. Now for 2 hours, you get mostly busy signals – and you quit and do not retry. Per DialIdol, the east and south are accustom to busy signals, so people who normally vote don’t worry about not getting in and keep trying.

    What I saw was as the east coast dropped out, Katherine got a small increase in DialIdol, but then the trend reversed and her numbers really dropped. (If you don’t know, DialIdol uses a calculation of busy signals and time frames to create a DialIdol number. The discussions on creating this “number” have been interesting.)

    Again, don’t have proof but it is just an observation. I am curious. I would love to see a true student of human factors and/or statistics (i.e. someone actually qualified to put science to this and not just guessing) get the raw data and write a paper on it.

  27. james says:

    I thought that very same thing the other night. It may be exactly what happened. As we speak, I can not get through to vote for the final.

  28. Lori says:

    I got through at LEAST 40 times for Kathern!!!

    I did not know it was this easy or I would have voted for Chris this many times!! He deserved to win!!!

  29. Israel Lopez says:

    Hmm interesting post.

    @ M Wanninger

    I was sitting here wondering the same thing. What kind of statistical analysis could one do with the raw data from American Idol? Granted there would be very little information that could be gathered from the vote itself; i.e. Geographic Location is probably at most what you could get. No Age, Race, Sex, Income, etc,.

    In anycase,

    I was interested in the statistical information of, how many votes (In a TV show) are sent via SMS.

    A similar show ‘The Apprentice’ from NBC is also doing a vote or ‘Tell Trump.’ I read the rules, it seems that NBC or the organisers for the vote are charging .99 cents for each text message. At this time it reads to be that you are subscribed into a ‘service’ in which you must send a “quit” “stop” “end” message. Where that message itself is probably charged as well. Since nothing states that the ‘quit’ message would be free.

    I bet that is how they finance the “Win 30,000” for telling what your opinion would be. I was wondering to as how many text messages would it take to raise the 30K based on the ratios of ‘free voting vs. charged voting.’ Since a participant is allowed 20 entries, but only one free online entry.