Betting on the outcomes of elections in the United States is a long-time gambling proposition offered by legal bookmakers in the United Kingdom but is only something that has recently begun to occur in America. That raises the question: who is more accurate at predicting the outcomes of these elections, British gamblers for whom this is an established game or Americans who may be new to this form of gambling but, arguably, may know their domestic politics better than foreign gamblers.
To do this, I compared the accuracy of different gambling platforms available to U.S. and British players for the 2020 U.S. Presidential Election on a state-by-state basis. Platforms examined include one U.S.-based prediction market and three British online bookmakers.
Betting on U.S. elections is currently illegal in the United States. However, a few “prediction markets” are given exemptions by the U.S. government if they meet certain conditions, such as operating as a non-profit, limiting participation, and caping investments. While the first online political prediction market was the University of Iowa’s Iowa Electronic Markets, today’s most famous “legal in the U.S.” political prediction market is PredictIt, run by Victoria University of Wellington, New Zealand and Aristotle International in Washington, DC.
The British are legally allowed to gamble on U.S. political elections, and the punters do so with gusto. Dozens of online bookmaking sites offered bets on the 2020 Presidential election, but I could only find three that offered odds on every state (and the District of Columbia) as of the morning of Election Day: Sky Bet, Betfred, and Boylesports.
For action from American players, I was dependent on using share prices and odds collected from PredictiIt and Oddschecker around 8:30 am on Election Day. This time was chosen to minimize data leakage; inevitably, exit polls would begin leaking to the press, and gamblers would act accordingly. Odds and share prices were converted into implied probabilities (accounting for the “vig” or bookmaker’s margin) and rounded to the nearest hundredth.
PredictIt offers binary option contracts: an event either happens or does not happen (Yes or No). A “winning” prediction receives $1/share, and a “losing” share receives nothing. PredictIt traders can buy shares on which party (defined as “Democratic” or “Republican”) will win a state in the Presidential election. Each contract has four prices publicly available:
- bestBuyYesCost: the lowest price to buy one “Yes” share
- bestBuyNoCost: the lowest price to buy one “No” share
- BestSellYesCost: the highest price to sell one “Yes” share
- BestSellNoCost: the highest price to sell one “No” share
To find the implied probability of PredictIt shares, I used the following formula:
(bestBuyYesCost + (1-bestBuyNoCost) + BestSellYesCost + (1- BestSellNoCost)) / 4
For example, on the morning of the election, Joe Biden’s contracts in the Arkansas market (“Which party will win Arkansas in the 2020 presidential election?”: “Democratic”: “Yes”) were trading at:
- bestBuyYesCost: 0.03
- bestBuyNoCost: 0.98
- BestSellYesCost: 0.02
- BestSellNoCost: 0.97
(0.03 + (1-0.98) + 0.02 + (1-0.97)) / 4 = 0.025 ≈ 0.03
There are different ways of representing a wager, but British bookmakers traditionally use “fractional odds” (a.k.a. “British odds”), which do not represent the odds of winning but depict the potential net profit for the amount wagered (“stake”). If a British bookmaker lists Joe Biden’s odds for winning Arkansas as “20/1” that means in the event Biden wins Arkansas, $21 is won for every $1 wagered (profit of $20). The numerator is the net profit from the wager and the denominator is the stake.
To find the implied probability of fractional gambling odds, I’m using the following formula:
Stake / (Stake + Net Profit) = Implied Probability
For example, on Election morning Joe Biden’s odds of winning Arkansas were listed as:
- Sky Bet: 20/1 = 1/(1+20) = 0.05
- Betfred: 14/1 = 1/(1+14) = 0.07
- Boylesports: 16/1 = 1/(1+16) = 0.06
I then calculated a Brier score for each prediction. Brier scores measure probabilistic predictions for binary outcomes. Predictions are the implied probabilities of the PredictIt share prices and bookmaker odds. Truth is measured as either 0 (event did not happen) or 1 (event did happen).
So, to compare PredictIt and the three British bookmakers, I am
(a) calculating the Brier score for their respective 102 predictions (2 candidates x 51 races)
(b) comparing the number of correct state winners.
For example, the truth of whether Biden won Arkansas would be 0 (event did not happen). The error is the difference between the prediction (implied probability) and truth (0) for Biden in Arkansas. A Brier score squares the error, which penalizes predictions for being further away from the truth:
- PredictIt: (0.03 – 0)2 = 0.0009
- Sky Bet: (0.05 – 0)2 = 0.0025
- Betfred: (0.07 – 0)2 = 0.0049
- Boylesports: (0.06 – 0)2 = 0.0036
The mean of all the squared errors for each platform’s 102 candidates/state combinations makes up their respective Brier score. A Brier score ranges from 0 to 1, with a lower score indicating more accurate predictions. A score of 0 signifies perfect accuracy and a score of 1 signifies perfect inaccuracy.
To measure whether a winner is correctly predicted, I consider an implied probability of 0.50 and above as ‘calling’ a state for Trump or Biden. Because the binary options contracts and bets are made independently for each candidate in each state, both Biden and Trump could be favored to win a state. PredictIt had both Trump and Biden above $0.50/share in Arizona, and all three British bookmakers had both Biden and Trump at an implied probability at or above 0.50 in North Carolina.
| Platform | Brier score | State winner |
| PredictIt | 0.0389 | 99 / 102 |
| Sky Bet | 0.0332 | 99 / 102 |
| Betfred | 0.0346 | 98 / 102 |
| Boylesports | 0.0338 | 99 / 102 |
Judging their predictions based on Brier scores, all three British bookmakers were marginally more accurate than PredictIt, although all four had low scores. Based on correctly predicting whether a candidate would win a state (or D.C.), PredictIt, Sky Bet, and Boylesports were correct in 99 out of 102 predictions, with Betfred correctly calling 98 out of 102.
Incorrect predictions for each platform:
- PredictIt: Arizona/Trump, Georgia/Trump, Georgia/Biden
- Sky Bet: Georgia/Trump, Georgia/Biden, North Carolina/Biden
- Betfred: Arizona/Trump, Georgia/Trump, Georgia/Biden, North Carolina/Biden
- Boylesports: Georgia/Trump, Georgia/Biden, North Carolina/Biden
Another scenario I ran was what would happen if I changed the definition of calling a state to an implied probability of 0.50 and above? In that case, Sky Bet was correct in 100 out of 102 predictions and Betfred in 99.
Interestingly, the British bookmakers and PredictIt were similar; 98 out of 102 predictions were identical across all four platforms. Given the availability of websites like FiveThirtyEight and RealClearPolitics that aggregate polling data, PredictIt users in America would not have any information advantage over gamblers in Europe—at least in terms of quantitative opinion data. While PredictIt overestimated Trump’s chances in Arizona and the British bookmakers overestimated Biden in North Carolina, all four called Georgia incorrectly.
That British gamblers are better at predicting American politics than Americans—if ever so slightly—could be attributed to less emotional attachment or ideological connection to the outcome. They might be more objective since they do not have American partisans participating, have a large pool of sophisticated gamblers, and wager more significant amounts of money through bookmakers. Since there is no way to know who is placing bets on each platform, this is highly speculative at best.
Areas for further analysis on this topic include:
- Share prices and odds farther out from Election Day
- Calculate true probabilities
- Use additional scoring rules such as log loss
- Compare with forecast models such as FiveThirtyEight and The Economist
- Analyzing data from bookmakers who did not take bets on every state.
- Examine the relationship between volume of trading and accuracy