[UPDATED August 1, 2016]

For the last couple of years, a coworker and I have been tracking the U.S. candidates' chances to become the next U.S. President. We haven't been relying on polls or on punditry, however. Instead, we've been looking at online bookmakers, and the odds that they offer on various candidates. Our feeling is that polls can be poorly designed, or slanted, or executed with varying degrees of accuracy (they worked great for making Nate Silver's career, but only with a tremendous amount of vetting and weighting behind the scenes). Pundits, of course, are not paid to be right or wrong, but merely to have an opinion and to generate traffic/viewers/ad revenue.

The people who REALLY have something at stake, when it comes to accurately predicting a candidate's chance to win, are the bookmakers. They have their own money on the line, so it is strongly in their best interest to properly ascertain the true odds of a candidate reaching the White House.

Feel free to interact with the embedded Tableau dashboards and explore who was up, who was down, and who could have been good value for money earlier in the campaign.

HOW DOES THE HOUSE ALWAYS WIN?

There's a well-worn adage that, in gambling, "the house always wins." But the house only wins if the odds are slightly--not greatly--in its favor.

The general rule of thumb is that bookies hope to make 5-10% profit on every wager. In a contest between two unevenly matched sports teams, bookies achieve this by offering an even money bet (that is, bet $1 to win $1, or 1-1 odds) that the stronger team will win by at least X points. The house also charges a 10% surcharge (also called a "commission" or "the vig," short for "vigorish") on each bet (pay $11 to make a $10 wager).

Ideally for the house, half of the gamblers will wager on the stronger team, and half on the weaker team. Bettors on the winning side of the wager get their initial bet returned, while the losers don't. The house will therefore pay out $20 for every $21 it takes in, earning 5% of all money wagered regardless of the game's outcome.

However, elections aren't structured this way. There's no point spread or head-to-head competition (even in the general election), so bookies set them up as "proposition bets," or bets based on the likelihood of a particular outcome taking place. In order to ensure that they make money on proposition bets, bookmakers set odds to the public that are probably at least 5-10% worse than whatever they consider the true odds to be.

ODDS TOO HIGH = TOO MANY PAYOUTS

They can't set the odds on any particular candidate too high (that is, assume that an event is less likely to happen than it truly is), because in the long run they will lose money that way. For instance, if they take $1000 in bets at 9-1 odds on something that is actually likely to happen 20% of the time, they lose money.

There's an 8 in 10 chance that gamblers lose, and the book makes $1000

There's a 2 in 10 chance that gamblers win, and the book loses $9000

So, the expected value of these wagers to the book is ((8/10) * $1000) - (2/10) * $9000), or a loss of $1000 per $1000 wagered.

On the other hand, they can't set the odds on any particular candidate too low, because gamblers are unlikely to wager when they clearly are getting the worst of the deal. For instance, you might be willing to take an even money wager that a coin flip would end up heads, because you know that there's a 50-50 chance of that outcome. In other words, you're being offered the true odds on that outcome. However, you'd never take 1-1 odds that the next roll of a six-sided die would be a six, because you know the true odds of that happening are 5-1 (five times it won't happen, and one time it will).

ODDS JUST RIGHT = CONSISTENT PROFITS

In a competitive market (which online gambling is), people will wager at whatever outlet offers them the best odds on any given bet. Knowing this, bookmakers will set lines that approach the true odds but fall about 5-10% short of them. That is, if a bookmaker thinks that the true odds for John Doe to win the race are 8-1, then a competitive book might offer 15-2 odds. Let's assume that gamblers bet $1000 on John Doe under these circumstances.

There's an 8 in 9 chance that gamblers will lose, and the book will make $1000

There's a 1 in 9 chance that gamblers will win, and the book will lose $7500

So, the expected value of these wagers to the book is ((8/9) * $1000) - ((1/9) * $7500),or a gain of $55.55 per $1000 wagered.

This bookmaker is earning a respectable 5.5% profit while still offering competitive odds. While the true odds are, of course, unknowable, It is difficult for the betting public to determine how close to true odds the offered betting line is, so books might actually look to make more profit in this circumstance. (It's more realistic to see a line like 7-1 or 13-2 in this situation.) But competition among dozens of online bookmakers ensure that a consensus, or close to a consensus, odds line will be reached, even as events dictate that the line move over time.

WHAT DOES THIS MEAN FOR US?

Since it is so incumbent upon the bookmakers to get their lines right, we are using an average of those lines as a proxy for the likelihood of any one candidate to be elected. We take the average of all available betting lines, and assume that those lines offer odds that are shorter than the true odds by roughly 10% (to account for the bookmakers' vig). Then, we convert those odds into an Implied Chance of Winning the Presidency.

While these values certainly change over time, we feel that they give the most accurate representation, at any given point, of who is winning and who is losing the race to the White House.