I'm fighting mad. Polls don't give us a clear notion of the likelihood of who will be our next President, and everyone on TV is talking shit! It all has to do with probability. Quit looking at polls and calculate the odds.
My first diary entry on 18 June about the impending Democratic landslide was based on my own half-assed, but elegantly insightful, heuristic methodology. Serious mathematics back up my contention, then and now. Many people think I'm just another progressive politics cheerleader because I spared readers from reading about numbers. I'm even more sure now that Obama is going to win big! This has nothing to do with my wanting that outcome. This is the result of cold-hearted, squinty-eyed, green-eyeshade analysis. Math and statistics majors can skip to the poll. This is a primer in objective reality for the computationally impaired. If you hate numbers, hang in there! This is for you.
Poll numbers show a lot. They tell us who is ahead right now and they are our best guess about what the result would be if the election were held right now. Yet, stupid people seem to think that even if a candidate is slightly ahead in the polls he may be no more likely to win than his opponent if the gap between them is "within the margin of error". The what? There's no such thing, you know.
This statistically meaningless term gets bandied about by the news media as a handy catch phrase to muddy the waters and shepherd the ignorant toward fallacious ideas. The news media pander to the party they favor. When their candidate (usually the Republican) is ahead, it's always a "commanding lead", but when the less-favored candidate leads by a couple of points, they never fail to point out, "The poll's results are within the margin of error."
Again, the what? I took a couple of rinky-dink classes in statistics and this term was never used. What is it supposed to mean? Clearly, they are alluding to the idea that the poll's results may not accurately reflect the exact proportions favoring each candidate in the electorate at large. So what? The poll is still the best guess we have until we ask everyone, that is, have a final poll of the entire electorate on election day.
This is isn't the big problem, though. We all know that the poll results are probably skewed (which means "slanted", not "screwed", Bubba) slightly one way or the other. We instinctively understand that the sampling may have been faulty in that random samples vary between trials. We are easily led astray in our thinking when some commentator (i.e., shameless flack) postulates that the race is a toss-up because the poll's result favoring our candidate is "within the margin of error". This idea is something they like to call, "a statistical dead heat". W.T.F.? What in hell is that supposed to be? Again, this is another phony statistical term intended to distract and confuse the hoi polloi. That's you, Bubba. Sorry for the stereotyping.
I know they're just messing with us when they try to foist that one off. It's as if they were saying, "Well, your guy is ahead now, but it's just as likely that our guy will overtake him before they get to the finish line." Now, that's just stupid, and any ten-year-old could figure that one out. Really, it's not that hard to do. Let's do what scientists call a Gedankenexperiment. We were taught to do this in elementary school with "story problems". Calm down. It won't hurt.
Let's say you're at the track and two horses, Oh Boy Mama and Johnny Mac are going to the post with the same odds. That means that the consensus of those with money on the race is that the two horses are evenly matched. The race starts. You have money on Oh Boy Mama and your buddy has money on Johnny Mac. Oh Boy Mama breaks from the gate and takes the lead. There are five horses in the race, but only two are contenders. (Lower The Barr, Sir Ralph and Doctor Paul are all decrepit nags, probably headed for the glue factory next month.) Johnny Mac is behind Oh Boy Mama, but well ahead of the pack of crippled plow horses. He moves up a bit. Rounding the clubhouse turn, Oh Boy Mama is holding a steady, one-length lead over Johnny Mac. You turn to your buddy and say, "You know, a length is within the margin of error for a horse race. How about an additional even-money side bet before they get to the stretch?"
Duh. You would only expect someone to take that bet if he were a moron, but there are a lot of really, really stupid people in the world. It's worth a shot. Have you ever done this? When your town's professional sports team is in a championship game, but the other team is favored, you can still go to a bar and find someone dumb enough to make an even-money bet with you. Sometimes you'll lose, and the winner will mock and jeer you, but more often you will win. As you take the drunken jackass's money, you are silent. Money is better than bragging. Either way, you leave shortly after the bet is paid off. If you win, you don't want to gloat because it is your team too, and you like them. If you lose, you don't want to listen to insults from the gloating winner and his faint-hearted cohorts who declined your sucker bet.
Why is it always a good idea to take a bet when the odds are in your favor? Winning has nothing to do with how much you want it, despite what every coach and athlete says in interviews. Fans want their team to win, but if their jocks are not as good as the other team's jocks, then they will lose more often than they win. Wishing and hoping have no effect. If she's got terminal cancer, Tinkerbell dies no matter how hard you clap your hands.
It's called probability. When the horses go to the gate at even money, they are deemed equally likely to win in the opinion of those with money on the race. If the odds favor one horse over another, it's because the touts have reviewed the performance of the horse in previous races and think that horse is more likely to win and bet accordingly. Their bets produce the odds listed at post time. Once the race is on and your horse pulls ahead, it becomes more likely that it will win than another who trails behind it. As the lead increases, the probability at that moment increases that your horse will win. The closer the horses get to the finish, the value of that lead increases, that is, the probability at that moment increases that your horse will win. At the track, your bet doesn't change after post time because the window is closed. In Presidential elections, post time is when the polls have closed in Hawaii and enough preliminary results are in to safely "call it". The probability changes continuously right up until that moment when one candidate has 1.0 and everyone else has zero.
So, where can one find the probability that Obama or McCain will win? It just so happens that betting on the outcome has historically been an excellent indicator of probability.
This site gives odds in a format you may not have seen before. Instead of the familiar "5-to-1" style (or "5-1"), it shows a single value greater than 1.00 to two decimal places. Today, Obama's is at 1.15 and McCain is at 4.85. This is how much you would collect in dollars on a winning $1 bet.
Look at it this way. The house is only willing to put up 15 cents against your $1 wager on the junior senator from Illinois. But, if you should be so foolhardy as to predict that the Melanoma Kid will get the keys to the White House, and back that notion up with a crisp $1 bill, then the house will put up $3.85 against that contention, maintaining that you are full of shit. They obviously think that McCain is a longshot and Obama is almost a sure winner. Do you disagree? Put your money down!
But, how do you get the probability from betting odds? Remember, the probability of any future event ranges from zero (impossibility) to 1.0 (absolute certainty). We compute it. Don't panic if you're mathematically challenged. It's pretty easy. It's the reciprocal of the payout value. I told you not to panic! Just fire up the Windows calculator program (%SystemRoot%\system32\calc.exe) and enter the payout for a $1 bet on McCain (4.85). Now comes the hard part. Hit the "1/x" button. What do you see? If it's not 0.20618556701030927835051546391753, then you don't know how to use a calculator. Get a third-grader to help you. Rounded to two decimal places, McCain has almost a 21% chance of being President according to these oddsmakers. For Obama, touted at 1.15, it's 0.86956521739130434782608695652174 or about 87%.
The InTrade site lets people "put their money where their mouth is" by buying and selling bets on future events. Today, I noticed that the probability reflected in the going price for these "contracts" is about 0.78 for an Obama victory and McCain's is about 0.23.
Note that in both these examples the probabilities don't add up to exactly 1.0 (or 100%) because the bets are bartered as independent events. Of course, there is some "error" in this because what people think and bet on doesn't necessarily coincide precisely with objective reality. But, that's not the point. When people put their money on something, that's what they believe using all their powers of perception and analysis. It's much less influenced by wishful thinking and political bias than pundits' predictions.
So, what about the polls? As I stated earlier, they have a lot of important information. Are you wondering how to convert poll results into probability? So was I. Nate Silver's site really homes in on this. Today, he shows that Obama's success probability is 93.8% (0.938) as compared to the complementary 6.2% (0.062) for McCain. That's probability, not percentages in a poll. That's right. Your calculator doesn't lie. His figures show that Obama is more than 15 times as likely to be the next President as McCain! If you're smart, you'll go out and take as many sucker bets as you can from McCain supporters at even money, 2-to-1, 5-to-1 or even 10-to-1 if you have to go that far.
Idiots don't understand probability and can't wade through a discussion like this. But you are smart and want to understand how Mr. Silver gets from a bunch of polls in each state to those composite figures for the whole country. It is very complex. It's called a "Monte Carlo" simulation. It's a series of experimental trials using the weighted probabilities for different outcomes in each state. On each trial, the electoral votes are added up in the 51 winner-take-all contests in the 50 states and the District of Columbia. Senator Obama wins with 270 electoral votes or more 93.8% of the time, which gives him his "win percentage".
The probabilities in each state are based on polls, but I haven't explained how, nor does Nate. I know, however, that the poll's results are a statistical sample. This means that there is a probabilistic distribution of deviation of the real, unknown value from the sample value in a Gaussian distribution. The uncertainty of how accurate the poll is depends on the proportion of the sample to the population from which it is drawn. In other words, there is a "bell curve" draped around the poll's result. The true value could be higher or lower, but the probability that it's not the same as the sample result decreases the further away you get from that sample's result. This measure of uncertainty is called the standard deviation. It's related to the so-called "margin of error" but it would take a couple more paragraphs to explain it. Don't worry about how this is calculated. Just hold onto the idea that the experimental (poll) value is the most likely outcome and that the probability that it's different drops off very rapidly whether you go one way or the other.
Do you want more? I thought not. You can read up on this stuff or take a course in statistics if it's new to you and you hunger for knowledge. Suffice it to say that when someone is eleven points ahead in the polls nationwide, they're probably going to win. How likely is it? Depending on whether you put more stock in the consensus of hordes of people betting blindly on gut feelings or hope, or you prefer the inscrutable complexity of a Monte Carlo simulation, it somewhere between 78% and 93% likely that Obama will win. Get your money down.
Let's have a little poll to see how much you've learned, or already knew if you've ever taken statistics and paid attention.