Election odds update (Biden still undervalued but not by so much)

Last week I wrote about the discrepancy between our election forecast and the betting odds:

Suppose I were to lay \$1000 on Biden right now. According to Betfair it seems that, if I win, I make a profit of \$840.

And our model gives Biden an 88% chance of winning. But we’re modeling Biden vs. Trump, whereas Betfair considers other possibilities, including replacements for the Democratic or Republican nominee. So let’s take our 88% down to 80% to account for those unmodeled outcomes.

My expected return from this \$1000 bet is then 0.80 * \$840 + 0.20 * (-\$1000) = \$472.

That’s pretty good—a 47% rate of return! That’s a pretty juicy investment.

I discussed this with Josh Miller and he pointed out that if you wanted to hedge this bet, you could just wait until Biden’s price goes up enough and then cover the bet in the opposite direction.

OK, how are things going today? Our forecast is now giving Biden an 87% probability—again, let’s round down to 80% to allow for possibilities not in our model.

And here’s Betfair:

So now \$1000 on Biden will give you \$670 if you win, and my expected return from that \$1000 bet is 0.80 * \$670 + 0.20 * (-\$1000) = \$336.

Only a 34% rate of return. But still pretty good!

Alternatively, had I bet last week and I wanted to cash out now, I could bet against Biden at the current odds and have a sure thing. But I wouldn’t do that, because I think that Biden is still way undervalued by the market.

As we’ve discussed, I think the implicit model of the bettors is relying too heavily on the experience of 2016. I guess things are changing now because of forecasts such as ours.

I’m not recommending you make this bet, or that you make any bet.

1. Phil K says:

Is it possible that bettors are accounting for additional uncertainty due to current events? I imagine your model takes into account the fact that June poll numbers aren’t perfect predictors of November poll numbers, based on past data, but one might argue that we are living in particularly volatile times. Maybe that’s what you mean by relying too heavily on 2016?

2. Carlos Ungil says:

> I guess things are changing now because of forecasts such as ours.

Have you considered the noise in your measurements? I don’t know about Betfair (I cannot even see their site) but there are other makets. Looking at PredictIt, Biden has been moving in the 56c-59c range (1.69-1.79 in Betfair terms) since June 11. The Democratic victory has ranged between 59c and 63c (1.59-1.69).

3. > Alternatively, had I bet last week and I wanted to cash out now, I could bet against Biden at the current odds and have a sure thing. But I wouldn’t do that, because I think that Biden is still way undervalued by the market.

If you want to succeed as a bookmaker (market maker), or even in your retirement planning, you need to hedge against risks, including the kind of catastrophic loss you get from going “all in” on a “sure thing”. Playing the spread (aka market-neutral or delta zero trading) isn’t just about cashing in early—it’s a hedging strategy. If bookies get bets all on one side, they move the odds until they have some coverage of the downside even if it implies they’re going to make a sure loss. They just can’t afford to be exposed to everyone in southeast Michigan betting U of M will beat the spread, nor can a bookie in Cleveland be exposed the other way.

Betfair’s simply giving you odds on Biden (1:1.62, or 63%) and Trump (2.8:1, 26%). Do you think that’s realistic (assuming it’s not all made up in the juice)? I have no idea, but they’re two old guys in the middle of a health pandemic that’s not been kind to the elderly. Do you think if one of them gets COVID or is hospitalized for another reason and drops out that it won’t affect the election outcome much?

• Andrew says:

Bob:

As I wrote, “Had I bet last week and I wanted to cash out now, I could bet against Biden at the current odds and have a sure thing.” This is literally a sure thing, a 100% probability of positive return. Except that, sure, Betfair could go out of business, we could have hyperinflation so that my winnings have no real value, etc. There is no sure thing.

If I were betting on this election (which I’m not) and if I could bet a lot of money on it (which I can’t), then (a) I would’ve placed my bet a week ago, before blogging on it, and (b) I would’ve bet a lot but not my entire life savings.

Betfair’s odds are not coming from Betfair. They’re coming from the people who place bets with Betfair. According to the bettors on the margin, yes, the Betfair odds are realistic. I don’t think they’re realistic. I agree that either candidate could become incapacitated or die; that’s why I took our 87% probability for Biden down to 80%. But, yeah, that’s just approximate. As a political scientist, I’m more interested in which party wins the election than which candidate wins. I’m really just using the betting market as an illustration.

• Carlos Ungil says:

> Except that, sure, Betfair could go out of business,

If I remember correctly you can close your bet and collect your profits when you enter the offsetting position so you can really cash out without waiting for the result. That’s as a sure thing as it gets.

• TBW says:

Catastrophic losses are bad, but so are opportunity costs. The correct thing to do is to use the Kelly Criterion and calculate the exact % of your bankroll to wager/invest. If you are uncertain about the accuracy of your model, you could apply a fudge factor like you did in your example(reducing your likelihood of Biden winning to 80%) and/or simply reduce your wager to a half or quarter Kelly. But, given the information specified above, I believe Kelly would recommend a large bet in the neighborhood of 2/3’s of your bankroll. .87 – ((1-.87)/.67)

• Andrew says:

Tbw:

Yes, I was thinking of Kelly when I wrote that I would’ve bet a lot but not my entire life savings.

• Ben says:

> I believe Kelly would recommend

Oh I like the move from ‘Kelly criterion’ as a name for an algorithm to personification of this algorithm as Kelly.

‘Using a Kalman filter’ -> ‘Rudy says’

I always think of Stan as a program, not a person. But if you think of it like a person it’s like every time you go to do an inference you’re yelling at this little unfortunate fellow named Stan. (“Stan! Data EQUALS mydata, cores EQUALS four — Didn’t you hear me the first time?”)

An Andrew program would be cool. It wouldn’t give you your results back until 4PM ET.

• Chris Wilson says:

wow, this illustrates really nicely how badly the expected utility paradigm fails! Betting 2/3 of one’s bankroll on the outcome of this election would be madness, even if we think that Andrew’s model is totally reasonable and approximately correct. The trouble is it’s a rule for maximizing a quantity that applies to an ensemble, not to an individual over time (i.e. non-ergodicity). See Ole Peters, or anything from the “Ergodicity Economics” folks to learn more.

4. oncodoc says:

I think you’re highlighting the difference between predictions and bookmaking. A predictor makes a forecast, and his credibility is at stake. A bookie doesn’t care who wins; a bookie wants lots of players on both sides of the proposition with a nice middle to generate juice. Michigan+3/Ohio State is not a reflection of the bookie’s sympathies. For us regular folks a big bet against our preferred candidate would be distasteful even if probably profitable.

• Andrew says:

Oncodoc,

Betfair is not a bookmaker; it’s a betting market. In this case I’m focusing not on bookmakers but on the individual bettors who are betting (small amounts of) money at bad odds. I guess the dollar values are small enough that we shouldn’t take these bettors seriously—but it’s my impression that lots of people do take these betting markets seriously, which is why I brought up this example.

• Michael Nelson says:

As you say, small bets are a huge reason to be skeptical of election betting markets as predictive tools. Other reasons include:

*Ideology–people who have a huge emotional investment in an outcome may bet on it despite or even because it’s unlikely

*Constrained participation–Americans can’t bet legally on US elections, removing the (arguably) most informed bettors

*Ulterior motives–since people take betting markets seriously, change in the markets can shape the political conversation, which incentivizes bets as political instruments

5. Ethan says:

Andrew, can you comment at all on how your likely voter models are taking the pandemic into account? It seems like the pandemic is really changing who votes in terms of increased vote by mail penetration, fears of going to the polls, etc. This is made increasingly complex due the uncertainty in election practitioner changes. For example, we still don’t know if vote by mail will be allowed in many states.

6. Ethan says:

Andrew, can you comment at all on how your likely voter models are taking the pandemic into account? It seems like the pandemic is really changing who votes in terms of increased vote by mail penetration, fears of going to the polls, etc. This is made increasingly complex due the uncertainty in election law changes. For example, we still don’t know if vote by mail will be allowed in many states.

• Michael Nelson says:

You’re right that the pandemic and related factors should impact things like voter preferences, enthusiasm and participation–all of which are reflected in poll responses. If Andrew’s model were to try to account for these factors separately, he’d be double-dipping, in effect over-weighting the pandemic’s impact. It’s the same fallacy as when people claim under-representation of Republicans in polls skews the results and therefore we should change the model to “unskew” them–but party self-identification mainly reflects respondents’ candidate preference and enthusiasm, which are already built into the responses.

7. Joseph Candelora says:

Regarding last week’s post, I’d be interested in Mr. Madeka’s response to the criticism of the 538/rigorous updating chart he posted — that its apparent result came from a simple math error.
John on the prior thread pointed to this summary:

I emailed Mr. Madeka last week, but haven’t heard back.

• Dhruv says:

Oops! Ill make sure to find and respond! – I sent all to Spam after the fourth accusation of being a trump hack :)
Who knew elections were contentious!

• Dhruv says:

Sorry Joseph – I dont see it. Would it be possible to resend it?

• Joseph Candelora says:

Hi Dhruv,

Note that I sent it to the email address you get when you click on the little envelope icon at http://www.dhruvmadeka.com/index.html#
(it has an @bu.edu domain). Let me know if that’s not still current.

Thanks.

8. Alex Lamb says:

Just speculating, but reason to make the odds more tilted towards Trump is that incumbent presidents historically have some advantage. I guess: Obama, Bush JR, Clinton, and Reagan won re-election. Bush SR lost reelection. So there’s not a lot of data but there does seem to be a difference.

One practical reason why an incumbent might have an advantage is that they can use their office in a way that influences the election. For example, Trump could do internal polling and find an issue where most people support him, and issue a bunch of EOs to capitalize on it.

Unfortunately I suspect that will mean more China-bashing in practice.

• Joshua says:

Alex –

Seems to me the question would be whether incumbents outperform the polls in consistent way – otherwise what you speak of would be baked into the polling, no?

• Andrew says:

Alex:

Incumbency is in the model; see the linked description.