# Why do betting odds give Michael Bloomberg 10% chance of winning the Democratic nomination?

Currently https://www.electionbettingodds.com/ give Michael Bloomberg a bit over 10% chance of winning the Democratic nomination.

Since he is polling single digits(not even close to double digits) 4th or 5th nationally this seems weird to me.

Is there something obvious I am missing or it is just the way the betting markets work? Only thing I can think of is that Bloomberg is rich.

• update: now it is at 35% :) Commented Feb 14, 2020 at 17:44
• Update: now it as 14% - Seems that money isn't everything. Commented Feb 28, 2020 at 23:13
• Update: Now it's zero percent. (Okay, not zero percent. If Biden and Sanders both drop out of the race, Bloomberg might have a chance again...) Commented Mar 6, 2020 at 3:47

The important thing to understand is that betting odds are not a prediction of an outcome.

They are a simply a balancing act that aims to ensure the bookmaker will make a profit - no matter what the outcome is.

It can be implied that the betting odds reflect the crowd-wisdom, of what people think the probability of the event is - but in no way is the system designed to be a predictor.

When a bookies takes bets, it is trying to ensure that no matter what happens - they will never pay out more to either side, than they have taken in total. They do this by constantly balancing the odds they are offering, to entice people to put money on the unbalanced side. Given enough bettors, this works well.

long example incoming

As an example, say we're betting on an unbiased flip of a coin. We know the probability is 0.5 for each side, guaranteed.
The bookie in this case, for simplicity, is going to take no margin - that is, they are for some reason, an unrealistic charity case who simply wants to avoid losing money - in real life, the odds will not add up to 1.0 at any point and that part is the margin the bookie will take profit from.

So for the starting odds, the bookie will set the bet at what they expect people to go for, in this case they expect everybody to split their bet evenly. So we get the odds:

1:1 tails

People come along, and they start betting. You'd expect it to spread evenly (like the bookie did - hence the initial odds), especially since you actually know the exact probability of winning in this case.

However, a TV psychic recently explained the importance of "always betting on heads" to the masses - as such, the bets that come in are actually:

\$10 tails (@1:1)

So now, despite us knowing the true probability is 0.5 tails, 0.5 heads, we've now got the following liabilities.

If heads, we lose \$90 (\$10 kept from tails bettors - \$100 paid to heads bettors).
If tails, we win \$90 (\$100 kept from heads bettors - \$10 paid to tails bettors).

Clearly, we want to balance this, so that no matter what happens, we do not lose money.

Let's say we go back in time, as we're seeing the first few bets come in (we'll ignore these, in real life we would still pay out at that rate) - we want to start balancing the odds. As we're seeing 10x more bets on heads than on tails, we might for example adjust our odds to be:

1:10 heads (bet \$10 to win \$1)
10:1 tails (win \$10 for every \$1 bet)

Even though we know they actually have the same probability of being true

As such, when we get the same bets in:

\$10 tails (@10:1)

So now our liabilities are:

If heads, we get \$0, (\$10 kept from tails losers - \$10 lost to heads winners (\$1 paid out for each \$10 bet))
If tails, we get \$0, (\$100 kept from heads losers - \$100 lost to tails winners (\$10 paid out for each \$1 bet))

So now we have balanced our liabilities, no matter what happens - we're guaranteed not to win or lose money. How does a bookie then actually make a profit? They add a margin on each bet, so rather than 10:1 vs 1:10, you'll see something like 11:1 vs 1:9. But the key thing is the same: the odds are set against the spread of bets, not against the actual outcome of the event - even if there is a correlation between those two things.

And hopefully clearly from this, just because the bookie here was giving 10:1 on heads - does not affect the fact that the unbiased coin flip, still has a real probability of 50% heads, 50% tails.

The only information it gives, is that for some reason - the bettors put more money behind heads than they did tails. (and there is no indication if that was a single super-rich bettor, or an even spread of small ones - you do not even get that information)

Of course, the reality of deciding how to adjust the odds isn't simple, and there's a lot that goes into it.

• Great answer. Another example is when a particular outcome has an effect on the market (e.g. if X happens the stock market goes down), then a stock investor could bet on X happening to reduce risk in their overall portfolio. Commented Jan 20, 2020 at 16:07
• Fantastic answer! Commented Jan 20, 2020 at 18:25
• Of course the accumulated bets are a form of prediction: Betting is a prediction market, sourcing "the wisdom of crowds". Alas, "it’s Difficult to Make Predictions, Especially About the Future." Commented Jan 21, 2020 at 10:02
• In your example you're assuming everyone behaves irrationally. A rational actor would disregard the psychic and could make an enormous amount of money betting on tails. Given enough rational actors, that should reset the odds back to 1:1, or in general, makes the dominant strategy for the bookmaker to give odds that agree with the their idea of the probability. Given the amount of money involved in political betting, your answer should either explain why Bloomberg does in fact have such a high chance, or explicitly state you think the bettors are behaving irrationally. Commented Jan 21, 2020 at 13:43
• @Kasper Actually it assumes that there are more irrational people than rational people (who are good at math), or at least that such irrational people have at least as much money to burn, irrationally, on gambling. Commented Jan 21, 2020 at 21:13

Betting markets are not necessarily more accurate than polls. For example, during the Brexit referendum:

The political betting markets were far less equivocal, showing a wide lead for remain. In the end, the polling proved more accurate than the political bettors. [...]

Andrew Gelman, a Columbia University statistics and political science professor, said political betting markets provide information that should not be ignored, but he added that the low volume of trading on some bets is one among many issues they face.

Gelman also said that part of the betting markets’ resilience to budging from the Brexit “remain” vote may have been “circular reasoning,” whereby the markets were self-reinforcing.

Another issue that may have contributed to the miss is the relatively similar mindset among bettors generally, according to Joe Crilly, a press officer for bookmaker William Hill.

“They’re all of a very small niche,” Crilly said of political bettors.

So basically betting markets are more like "expert opinion".

There's an older (2012) comparison paper using past US elections:

This paper assesses the accuracy of US presidential election betting markets in years before and after opinion polling was introduced. Our results are provocative. First, we find that market prices are far better predictors in the period without polls than when polls were available. Second, we find that market prices of the pre-poll era predicted elections almost on par with polls following the introduction of scientific polling. Finally, when we have both market prices and polls, prices add nothing to election prediction beyond polls. To be sure, early election markets were (surprisingly) good at extracting campaign information without scientific polling to guide them. For more recent markets, candidate prices largely follow the polls.

It's usually impossible to explain individual departures (like your question on Bloomberg specifically); individual polls can be pretty far from each other too. (See this provocative question for an example.) Bloomberg, of course, even has the money to manipulate some of the betting markets, which not I'm saying he's actually doing...

• It's always worth noting that betting markets are moved by smart people taking money away from the stupid. Unless a candidate has a policy platform of kicking puppies and stealing candy from babies, you'll always find someone who thinks that they're going to win and is willing to bet that it'll happen, rapidly followed by the smart money piling in to take that bet Commented Jan 19, 2020 at 18:11
• The outcome of an event has got nothing to do with the accuracy of the prediction. If I predict that event X has a 60% probability of occurring and instead event Y happens, that doesn't make me wrong. To establish that my prediction was inaccurate you have to establish that 60% was the wrong probability, regardless of the actual outcome (e.g. by analysing a larger sample of my predictions). This is a very basic misunderstanding of how probability works, which unfortunately seems to be quite a common error in the media (when talking about polls / betting markets "getting it wrong") Commented Jan 19, 2020 at 21:44
• @JBentley Further, polls and betting markets seem to measure a completely differnt thing. Polls measure the percentage of people that will vote a certain way. Or at least the expected value. Betting markets measure the probability of winning. Polls are just one metric one may use to determine a probability of winning. Commented Jan 20, 2020 at 18:09

What you are seeing are probabilities implied by people placing bets on a particular result, and reflects how much people who place bets expect to receive if they win.

On BetFair exchange, if you want to place a bet on Mr. Bloomberg winning the primary, you stand to receive \$9.40 for every dollar you bet if he does win. This implies, if the bet makers are to break even on this particular market, there is a 10.6% probability of him winning (1/9.4=0.106).

For comparison, people placing bets on this market think that Tom Steyer is the least likely to win the nomination. Betters are demanding \$240 for every dollar bet to reflect how unlikely a Steyer win is perceived. On the other hand, people betting for Joe Biden are prepared to accept less in the event of his win (\$3.20 for every dollar bet), as they deem this to be more likely.

• I think the implied question is, why do people believe he has this much of a chance of winning.
– D M
Commented Jan 18, 2020 at 16:37
• The implied question is all but unanswerable. The only correct answer is this: people are willing to put real money on the line at these odds. The 10% is not the actual probablity of Bloomberg winning, it is the what the wisdom of crowds thinks is the probability. If you think they are wrong you can pick up the bet and win some cash. Commented Jan 18, 2020 at 18:20
• People who place bets are bettors, not betters. (One could even argue that habitual bettors are worsers :-)) Commented Jan 19, 2020 at 18:24
• Pollsters also try to do random sampling (and adjust for the biases they can predict). Betting exchanges are self-selected groups, not a fair representation. Commented Jan 20, 2020 at 2:37

Bloomberg is a late entry, makes the possibility of growth of support more likely; with someone like Biden, if you don't already support him by now, you're probably not going to change your mind in the future. Bloomberg is, AFAIK, also the richest candidate, which gives him more opportunities to increase his support. Also, as a billionaire, he's more of an outlier, which is going to increase the odds for long shots.

Looking at the chart might help us guess

The 10% figure for Bloomberg appears to be a recent development. On January 2, his odds were at 5.1%. On the same day, Elizabeth Warren had a 15.4% chance to win. Since that day, Warren's odds have decreased and Bloomberg's odds have increased, such that they are now each within less than 1 percentage point of each other at 10%.

https://www.electionbettingodds.com/DemPrimary2020.html#chart

Maybe it's not a story of Bloomberg being likely to win, but of Warren being more likely to lose and lots of other candidates quitting

The probabilities need to add up to 100%. You may not think Bloomberg is a winner for all the reasons you cited in the question, but I think it is uncontroversial to say that during the past month Warren has looked to be less likely to win the primary. So, if you thought Warren is not going to win, and you think Biden, Buttigieg and Sanders aren't going to win either (the three other "front runners") then who do you have left to bet on?

Looking at the list on that site, not very many people:

• Clinton, who isn't even running
• Andrew Yang
• Amy Klobuchar
• Michelle Obama, who is also not running
• Tom Steyer
• Tulsi Gabbard
• 4 people who have dropped out
• "Other"

None of these other people are exactly likely winners either. So, Bloomberg might actually be the most likely of the subset of candidates not currently identified as front runners to win.