The 2020 US election offered a fascinating case study for betting market efficiency. Joseph Buchdahl looks in depth at how efficient the market was compared to the polls and what bettors can take away from the event.
I should apologise from the off for writing this article because I imagine nearly everyone is sick of hearing about the US presidential election. As of writing we still don’t know definitively who’s won, even though the major US networks have called it for Joe Biden. That said, by the time you read this I won’t be the least bit surprised if any of you who bet and won on the market are still waiting to be paid whilst Trump continues to drag things through the courts.
Much was written in the aftermath of election night about the failure of the opinion polls to accurately predict the outcome. Yes, Biden was forecast to win, but the margin of victory in the popular vote was considerably narrower than the best estimates had forecast, although arguably well within the 95% confidence limits. Furthermore, contrary to most predictions, the Senate has likely remained in Republican hands whilst they have picked up additional seats in the House of Representatives.
the latest content on your timeline
Articles, competitions and moreFollow Pinnacle
But how did the betting market perform in comparison? It’s an often touted maxim that the best, and possibly only, opinion poll worth paying attention to is the betting market, since this is the one poll that has skin in the game: people’s money is on the line. In this article I’m going to investigate whether this was true for the 2020 US Presidential Election.
A look back at the 2020 US Election winner odds
For most of Tuesday, November 3 the major betting markets had been quoting Joe Biden to win at around 1.5, with Donald Trump correspondingly around 3.0 at best prices. Echoing the forecasting website FiveThirtyEight, who had predicted an 89% chance of a Biden victory when they stopped updating their model, I had tweeted that these odds were far too long for Biden, suggesting the true price was nearer 1.2. My thinking was that whilst the polls had called the wrong result on 2016 there were a number of factors which suggested history would not repeat itself.1) Biden had a bigger lead than Hillary Clinton, and particularly in the swing States.
2) Biden is not Hillary Clinton.
3) Biden is not Donald Trump.
4) Biden is a moderate, neither a progressive nor a socialist.
5) We now know who Donald Trump really is.
6) COVID-19 and the resulting economic recession.
Perhaps most importantly of all, as Biden himself believed, it would take a 70-something year old white man to defeat a 70-something year old white man.
Consequently, I posed the following question to my Twitter followers:
With the exception of Mayweather v McGregor, which was a freak show, is Biden v Trump the biggest favourite-longshot bias in betting history?
I had in mind here both the size of the bias and the amount of money being put at risk. Some might rightly argue that Biden vs. Trump was a freak show as well; a one-off with no meaningful historical database with which to make any solid predictions. Nevertheless, if we accept the true price for Biden was 1.2 but the market quoted him at 1.5 close to market closing, surely this must represent an absurdly biased market. If correct, the expected value is around 25% and the Kelly Criterion strategy would advise a stake of 50% of your bankroll!
It’s not at all clear how such a bias could materialise. Trump was never such a huge longshot as to represent a lucky punt from entertainment seekers. Possible explanations might include a belief by more educated and turnover-heavy bettors that the polls would be wrong again, since they are ‘always wrong’, and that the demographic who backs Trump correlates with the one who tends to bet (and bet more). Of course, there is another explanation: both FiveThirtyEight and I were wrong.
A proxy model for the true odds: State betting
To investigate the true odds of the presidential election I could build my own forecasting model. Unfortunately, I’m not particularly good at building forecasting models. Nearly 25 years of trying to build them for a football betting market has taught me that it’s much easier to simply copy what the experts do and exploit others who do it slightly less well. That is the basis of my Wisdom of the Crowd betting system, which uses Pinnacle’s football match betting odds as the benchmark measure of the true odds in a football match. Pinnacle are literally at the pinnacle of setting the most accurate odds.
However, how do we investigate whether the odds for Biden and Trump were accurate? Clearly, we need a proxy measure. One method is to use the state betting market, using the probabilities for each of the 50 US states plus the District of Columbia (implied by the betting odds), and sum the expected Electoral College votes (xECV) which they imply. For example, Trump was considered to have a 61% chance of taking Florida. With 29 Electoral College votes up for grabs that is equivalent to 17.7 xECV (29 x 0.61) votes for Trump, with 11.3 for Biden (29 x 0.39).
Unfortunately, Pinnacle did not quote betting odds for all 51 state betting markets, so I had to use a betting exchange which did. In more traditional liquid betting markets, this betting exchange is arguably equally as efficient as Pinnacle. Taking the odds at 23:45 to 00:00 on Tuesday, November 3, Biden’s total xECV was 308, with trump collecting 230.
As of writing, there is a recount happening in Georgia, and another likely to take place in Wisconsin. In both, however, Biden is ahead, and his margin is sufficient for a flip to be highly unlikely. North Carolina and Alaska are yet to declare but look set to be holds for Trump. Should these projections stand the final tallies will be 306 for Biden and 232 for Trump. The betting exchange’s state betting market would appear to have forecast the result very closely indeed.
A Monte Carlo simulation
Of course, knowing the most likely outcome in terms of Electoral College votes doesn’t tell us what the odds were for Biden and Trump. For this it’s simplest to run a Monte Carlo simulation. By using a uniformly distributed random number to simulate the result of each US state, we can run the election many times and count how often Biden or Trump end up winning.
If the random number falls below the odds-defined win probability for a candidate, they take all the Electoral College votes; if above, they take none. For the purposes of this model I assumed that the two states, Maine and Nebraska, which split their Electoral College votes rather than awarding all to the winner, behaved as the other 49. They only contribute four and five votes respectively to the total of 538 and won’t make much meaningful difference to the model outcome.
The first chart below shows the distribution of Biden/Trump ECV tallies from 100,000 simulated elections. Biden won 89.9% of the simulated elections, which implies true odds of 1.125 - almost exactly the same as the figure predicted by FiveThirtyEight.
However, there is a problem with the model. FiveThirtyEight also predicted 348 Electoral College votes for Biden and 190 for Trump as the best estimate. The discrepancy arises because my model considers the votes in each state to be independent of all others. As a result, there is far less variance in the simulated Electoral College votes (standard deviation of 32 ECVs) than there would be in reality, meaning it’s much easier for Biden to win.
Unsurprisingly, that is a flawed assumption. Clearly there are common nation-level covariances at play – COVID-19 being just one of them - meaning that if one state votes in a particular way another is likely to do so too. Covariance is the reason bookmakers will not allow you to build accumulator (or parlay) bets from state betting markets.
FiveThirtyEight naturally make it their business to develop a highly sophisticated covariance model that attempts to take into account these state-by-state voting correlations. By contrast, I applied a very crude tweak which would probably fail any statistical modelling course. Using a second normally distributed random number, a positive or negative deviation was then applied to the original 51 random numbers so that all deviations were correlated. The output from the ‘covariance’ model is shown below.
This time we can see a lot more variance in the simulated ECVs, and a much greater overlap between Biden and Trump. Now Biden wins 71.7% of the elections, implying true odds of 1.39. Encouragingly, despite the crudeness of my second model, the variance in ECVs (standard deviation = 63 ECVs) is broadly similar to FiveThirtyEight’s forecast model (59 ECVs).
Was the 2020 US Election winner a biased market?
We are now in a position to attempt an answer to the question I posed on Twitter. At the time I collected the betting exchange’s state betting odds they were quoting 1.68 for Biden to win. If my model implies the true price was 1.39, then this still represents an expected value of 21%. In the final few days leading up to November 3 both the betting exchange and Pinnacle had been trading Biden at around 1.50, and this is where the majority of the late pre-in-play money was taken. I myself took 1.51. Nevertheless, this would still seem to represent value (8%) implying a strong favourite–longshot bias.
Granted, I might still have not factored in enough state covariance, or that the way I did it was flawed. Nevertheless, playing with FiveThirtyEight’s election simulator, there are scenarios which give Biden odds of 1.33 and 299 xECVs, or odds of 1.52 and 282 xECVs respectively. Those figures would seem to be broadly consistent with mine. The point, then, is that odds of 1.5, and certainly 1.68, are far too long if the number of projected Electoral College votes for Biden is 308. On this basis I’m happy to stick my neck out and call it: yes, the winner market was biased, but perhaps not quite as biased as I had initially thought.
Given the much smaller size of the state betting markets compared to the winner market in terms of turnover, it is all the more puzzling that the latter appears to have been far less efficient. Typically, market turnover correlates with market efficiency. The more money, the more opinions, the more random errors cancel, the more wisdom of crowds, the more paradox of skill and so on. And in this case the winner market became Pinnacle’s biggest market of all time.
Yes, my model could be wrong, and it could actually have been the state betting markets which contained the biases. Interestingly, however, if we just look at the odds for the 51 betting markets, just one, Georgia, saw the favourite (Trump) lose. In all the other closely fought states – North Carolina, Florida, Ohio, Arizona, Wisconsin, Minnesota, Pennsylvania, Texas, and Michigan – the betting exchange state betting market called the most likely outcome correctly.
A closer look at the in-play betting
What seems to me to be far less doubtful is the massive inefficiency that arose as the winner market went in-play. Within a couple of hours, Florida was called for Trump and panic set it. Traders started to believe that 2016 was going to repeat itself. Four years ago, Hillary Clinton had been a much bigger favourite than Biden, but as the early state results came it, the market swung massively towards Trump and it never flipped back.
2020 was a completely different ball game. Firstly, Biden had a bigger poll lead than Clinton, both overall and in some swing states. Secondly, Biden never needed Florida to find a path to the White House, whereas Trump almost certainly did.
Finally, and perhaps most importantly of all, many traders seemed to have forgotten about the later counting of absentee and postal ballots, which unsurprisingly were heavily biased in favour of Biden, given he had encouraged his supporters to vote in such a manner as a means of protection against the COVID-19 pandemic.
By contrast, Trump had downplayed the pandemic – after all, he is now immune and has a ‘protective glow’ – and furthermore reiterated the belief that large scale postal voting could prove to be fraudulent and a massive embarrassment to the USA.
The extent of the panic reached a zenith when Trump shortened to as little as 1.24. However, by the early hours of Wednesday, November 4 it started to become clear that the early leads he had built in some of the swing states key for a Biden victory were diminishing on account of the late postal ballot counting, and that those leads were easily retrievable given the exit polls for those absentee ballots.
And so, over the following few days, it has proved to be. Those smart enough and disciplined enough to always believe Biden would win, and was probably always quite a strong favourite to win, will have made a good return from arbitraging the market.
Those who weren’t, and in particular those who always believed that lightning would strike twice, and that the pollsters are always idiots, will have to pay for them. Of course, pollsters sometimes are wrong; they appear to have been again this time but not catastrophically so and not beyond typical confidence limits, and certainly not in who they predicted to be the winner. Very occasionally, like this time, major betting markets are wrong too. But the smaller state betting markets seemed to have provided the clue as to what was really going on.
To coin a phrase: all markets are efficient, but some are more efficient than others.
P.S. Why isn't Donald Trump allowed back into the White House? Because it's forBiden. Thank you and goodnight.