## Freak Punts on Leicester Bet

I went over to the Freakonomics website and found this story about Leicester City’s unexpected championship.

Here’s Stephen Dubner:

At the start of this season, British betting houses put Leicester’s chances of winning the league at 5,000-to-1, which seemed, if anything, perhaps too generous. My [Dubner’s] son Solomon again:

SOLOMON DUBNER: What would you say if I told you the Cleveland Browns were going to win the Super Bowl next season?

STEPHEN J. DUBNER: I would say that you’ve started smoking marijuana.

SOLOMON DUBNER: Exactly, and that’s what you would have said if I said Leicester had won the league.

And yet: Leicester did win the league.

OK, so I looked up the odds for the Cleveland Browns winning the Super Bowl next year. I googled *betting odds cleveland browns super bowl*, and this came up:

In case you’re curious, the full table is here. The Browns are the biggest underdogs. Odds range from 7.5 to 1 (Patriots) to 200 to 1, with the top teams being Patriots, Seahawks, Steelers, Packers, Broncos, and Panthers, all of which have better than 15 to 1 odds.

If the Browns have 200-1 odds, I’d estimate their probability of winning the Super Bowl as being a bit less than 1/200, because of the well-known “longshot bias,” that people overbet longshots and as a results the odds on longshots aren’t as extreme as they usually are. The striking thing about Leicester City is that this seems to be one longshot where the odds were set too high.

Remember, the point about Leicester City was not that it had long odds, it was that the odds were sooooo long. If they’d had 200-1 odds, they’d be right where the Browns are, in the “smoking marijuana” realm. Even 500-1 and they’d be close to that. 5000-1, that’s another order of magnitude. I don’t know that anyone who’s studied this example would characterize those 5000-1 odds as “perhaps too generous.” The other part of the story was that, as the season went on, bookies were too slow to adjust the odds downward.

I have to admit to being a bit disappointed. Dubner might not believe me here, but in all sincerity I have no desire to find fault with Freakonomics. I clicked over to that page with the hope that they’d done this story right, that they’d’ve dug into the fascinating story of how the oddsmakers got this one wrong, how they went against the traditional longshot bias. I’d bet that Nick Goff, the bookmaker who wrote a couple posts on this topic (see link just above), would be a great radio interview.

I hope the Freakonomics team can do better next time. As I’ve written many times, I respect and admire the outreach that is done by the Freakonomics franchise and I’d like them to live up to their potential. Especially in an example such as betting odds which would seem to be right in their wheelhouse.

P.S. Some commenters argue that the 5000-1 odds were, a priori, fair. I’m doubtful but I’m also open to the possibility that I’m wrong on this one. My key point, I suppose, is that the odds are not necessarily fair, and in writing about Leicester’s surprising success, one should at least consider that the odds were, even prospectively, off.

1. fraac says:

I don’t know why you keep writing about Leicester when you don’t follow football. Leicester City winning the Premier League is the most outrageous sporting result in my lifetime of following many sports. 200-1 winners happen every day.

• Andrew says:

Fraac:

Take it up with Dubner. He’s the one who placed Leicester’s and Cleveland’s chances on the same footing, even though Leicester was 5000-1 and Cleveland is 200-1. That’s a factor of 25 we’re talking about here!

2. Phil says:

I wasn’t under the impression that the odds placed on teams winning a championship were based on the bookmakers’ assessment of the probability of that team winning. I thought they place their odds based on the patterns of bets that people make on the various teams. At the end of the day, bookmakers don’t care about who wins, they just care about making a profit, and minimizing risk to ensure they don’t end up at a loss after payout.

So regarding Leicester, it’s wrong to criticize bookmakers for being too slow to change their odds of Leicester winning. Rather, it reflects that bettors still did not believe that Leicester could maintain their pace.

• Christian Hennig says:

“So regarding Leicester, it’s wrong to criticize bookmakers for being too slow to change their odds of Leicester winning. Rather, it reflects that bettors still did not believe that Leicester could maintain their pace.”
Actually bookmakers were too slow to change their odds means that bettors were faster. Bookmakers lost quite a bit in this thing but as far as I know, this wasn’t so much because of 5000-1 pre-season but rather because bookmakers’ odds were still too high when bigger numbers of bettors started to bet on Leicester.

• Phil says:

Christian:
“Bookmakers lost quite a bit in this thing but as far as I know”

• Christian Hennig says:

I think that somebody posted a few links toward the end of the Comment Section when Leicester last came up on this blog.

• fraac says:

Most of the big companies combine a calculation of their exposure with a dollop of intuition. Markets like Betfair track the actual demand but the precision depends on liquidity, so longshot bets could still be just a few guys with a funny idea.

As expected, the rank outsider odds for next season’s Premier League are 1000-1, for Bournemouth, West Brom, Watford and Burnley. For people saying Leicester should have been 200-1, in what ways would we have expected them to be better than those teams?

• Andrew says:

Phil:

What Christian said. Yes, bookies aim to set the odds so that the bets on various sides are balanced and thus they are guaranteed to win money. But it doesn’t always happen that way.

• Phil says:

I just want to clarify that the Phil who has been posting on this is not Phil Price, the Original Phil of this blog. I think I will have to change my monicker to Phil OG or something.

–Phil Price

• There’s this thing called the “risk neutral probability measure” in finance. The basic assumption is that the price of the asset today is its expected discounted future price at any future time under the probability measure. However, although this probability measure can’t possibly be a Frequency measure, it also isn’t any one person’s Bayesian probability. As near as I can tell it is a mixture of all the different investors “tilted” Bayesian probabilities. When I say “tilted” I mean adjusted so that people are willing to pay the expected value under this measure, whereas when things are risky, people actually prefer to pay less than the expected value under their *actual* Bayesian probabilities.

All of that is to say that there exists some probability measure by which you can take expectations and get market prices. What that probability measure is over N assets is itself a complex thing to try to calculate. As the last sentence of the Wikipedia intro says: “The method of risk-neutral pricing should be considered as many other useful computational tools—convenient and powerful, even if seemingly artificial.”

I think you’re talking about the same thing basically. Bookies are acting as go-betweens, they’re reflecting the probability measure that’s some kind of mixture of what all their client’s think. What they want is to win some, lose some, and on average make a little. When they win bet A and lose bet B they essentially transfer money from person A to person B, plus or minus their “fee”. They’re looking for that fee to be as large as possible, but generally are satisfied with a smallish margin, because if it’s too large their competitors will attract the bettors.

So, the question is, what should an informed Bayesian investor do in a market where most people are using risk-neutral pricing? In this case, bet on Leicester

• Anon says:

>I wasn’t under the impression that the odds placed on teams winning a championship were based on the bookmakers’ assessment of the >probability of that team winning.

There are exchanges for gamblers these days as well, where you can trade assets that pay if an event occurs or doesn’t occur directly with other gamblers. Competition forces bookmakers to offer a similar deal to those exchanges.

As far as I know, when you take the bookmaker odds for the premier league and compare how they match up with actual results, they outperform any (public) statistical model to predict football matches that has been developed so far.

• If they were probabilities, then they should sum to one, right?

• Chris G says:

>> In case you’re curious, the full table is here.

>If they were probabilities, then they should sum to one, right?

If I did the math right, 120% chance that somebody wins the 2017 Super Bowl.

3. Jonathan says:

Those Leicester odds were rooted, as I’ve noted before, in a wrong model of the Premiership that only contemplated a handful of big money clubs as possible champions. It didn’t understand the influence of huge TV money spread across the league or that an average salary of over \$2M US means every club should now have, if run reasonably well, an entire roster of capable players. That Mahrez and Vardy emerged as stars and that Leicester implemented a radical attacking style of play is the kind of unknowable that would be more appropriately 200:1 or less. In terms of money, consider Spain: the money gap has been as much as 12 or perhaps 15 to 1 between the top few clubs – was 2 and now 3 – and the rest. But that is now down to under 4 to 1 so the Spanish league will also become more competitive. The Premiership passed that point with the last TV contract.

• fraac says:

Any new model still has to deal with a finite talent pool. The best twenty players still get the top twenty wages at the top four clubs. I think this means that without real minnows any club can finish 8th but I’m not sure it gives the field a better chance against the top four.

• jrc says:

The top 4? You mean Leicester, Arsenal, Spurs and Man City? Oh wait, you mean Arsenal, Man City, Man Utd (5th) and Chelsea (10th).

When only 1 of the “Top 4” are guaranteed Champions League group stage play, I think we have to seriously update our priors about what the PL will look like in the coming years. Other than the usual suspects above, West Ham (7th) move to a 65k stadium; Spurs (3rd -hah!) and Liverpool (8th) apparently aspire to things with their new coaches. I mean, 1/3 of Stoke is now players who were marginal at Barcelona.

So I agree with Jonathan to some degree. What I think we may have learned this season is that the difference between the most skillful player in their position, compared to a player 1-step down, is small, and the quality difference can be negated by overall team tactics, spirit, work rate and luck. And since the premier league can basically afford 20 of the 25 best players in their positions, the other factors start to come more into play.

That said, I do disagree with Jonathan’s description of Leicester as having a “radical attacking style of play”. Maybe in the first half of the season, but by April they won 5 out of 6 by the good old (champion-defining) 1-0 scoreline. Over the season, they kept 15 clean sheets (out of 38) and conceded 0.95 goals per game. Some of that may be due to a change in incentive structure after the early part of the season*.

• fraac says:

It’s the first time in the 24 year history of the Premier League that a non-top4 club has won (not counting Blackburn who were biggest spenders for a while), so I’d be very wary of ‘learning’ too much from it. Far more likely it’s a freaky one-off.

• jrc says:

I wasn’t implying that teams outside the top 4 are likely to start winning the league regularly. What I meant was I think the era when we just assume ex ante that Arsenal, Chelsea and the Manchester Clubs will take all the Champions League spots every year is probably over. Increased parity between clubs and increased variance in final standings is what I meant.

And I think partly that’s because the talent pool that Europe pulls from is going to be more concentrated in the PL in the future. Before the last few seasons, the 20 best left-backs in the world were scattered around 5 or so different leagues, but soon 17 of them will be in England – same from the goalkeepers to the strikers. So whereas it used to be that a team like West Brom would have the 100th best left-midfielder in the world, now they’ll have the 30th best. That means there is more room for other margins (tactics, team spirit) to overcome the (smaller) quality difference.

That was my point. I think you are right that one of the big four teams is likely to win in most of the upcoming seasons, if not all of them. But I don’t think they’ll take all 4 top stops every season anymore.

• Jonathan says:

Yes, it could be a 1 off but that would still not be the same model as of old; it would need to be a new model that explains why the old top clubs still run the league even though all the teams are relatively rich and can buy talent from all over the world. I don’t know what that model might be. A tradition of better management?

As for Leicester’s style, while I focused on the offense – their trying deep passes and crosses at every chance without much of the traditional possession style of attack – they certainly coupled that with a very disciplined defense, often a full 8 man box that maintained spacing and forced attackers to work the edges, and of course revolving around Huth’s strength.

• jrc says:

Note to Wenger: next time you buy a Big F***ing German, get the one with a square head.

4. Dzhaughn says:

The NFL is a oligopoly that enforces parity. The value of the Browns is 1.5 billion, vs. 4 Billion for the most valuable NFL franchise that shall not be named. There are only 3 teams worth twice what the Browns are.

In 2015, Manchester United was worth 1.8 Billion pounds; Leicester City was 130 million, almost 1/14 the value. There are 6 Premiere League teams worth 5 times more.

http://www.sportingintelligence.com/2015/08/21/from-man-utd-at-1-8bn-to-cherries-at-104m-whats-your-club-worth-210803/

I see the Cubs are favorites to win the world series; thanks Leicester

• Tuckfield says:

This was my thought exactly. In addition to the values of the teams being similar, many US sports including (I believe) NFL football have salary caps that force teams to spend roughly the same amount on players to avoid rich teams becoming too dominant. I believe that European soccer leagues don’t have salary caps and so a mismatch much greater than that between the Browns and the best teams could certainly occur.

Another thought: in graduate school I was taught to judge a decision by its process and not by its outcome. If you don’t wear your seatbelt, and then you’re in a car accident where some freak set of circumstances means that not wearing your seatbelt actually saved your life, that doesn’t mean that it was wiser to not wear your seatbelt. It still had a worse expected value than wearing your seatbelt, but you just got extremely lucky. If we’re discussing the bookmaker’s wisdom, we should do it based on something other than the fact that they turned out to be wrong. If they were unwise, we should be able to see it using only information that they knew when they set the odds. If we can’t do that, then we can’t say they were unwise, only unlucky.

A term I haven’t seen in the Leicester discussions on this blog yet is “hindsight bias” – I think judging the bookmakers based on the observed outcome is an example of this.

• Andrew says:

Tuckfield:

There’s been much discussion of the possibility of hindsight bias. But one must also beware of Panglossianism: the assumption that all decisions were made correctly. The argument that many people have made, and I find it convincing, is that the 5000-1 odds were too high prospectively; that is, that the bookies were making a mistake at the time. Or maybe it was not a mistake in a larger sense (extreme odds serve as a form of advertising, or maybe it just wasn’t worth their while to bother to think hard about this particular extreme case. Some people who know more about British betting than I do made the case that a sort of competitive pressure pushed all the bookies to raise the odds to this high level together.

Bookies are just people. People make mistakes, so can bookies. Organizations can make mistakes too; for example Bill James made a convincing case that certain baseball players (those with low “secondary averages”) were overrated.

In this discussion, we’re well aware of the distinction between prospective and retrospective evaluations of decisions. The argument that the 5000-1 odds were overstated does not rely solely on the fact that Leicester won; follow the links for some specifics.

• Tuckfield says:

Thanks for the reply. I suppose in light of the many sports, gambling, social, and philosophical issues at hand in judging the wisdom of the 5000-1 odds, we have to use a phrase common among academics: “further study is required.”

• ASV says:

Sure, but the 76ers are probably just as good a comparison as the Browns are. They had similar odds before this season to win the NBA championship, when they were a) playing in a league with no parity at all, and b) openly tanking.

5. Eric Loken says:

It’s true the article didn’t address the poor setting of odds, but it was still a decent read. I liked the flip-flop contrast comparing European and American sports economies, and then their broader economies.

But all in all the piece did have a feel of “isn’t it nice to see something magical occur?” The apparent magic is only relative to a false threshold. Leicester didn’t overcome a 5000:1 barrier – those odds came from models that underestimated tail area probabilities. The story is much more about poor prediction than magical success. Maybe we should replace the slogans: “If Leicester can win the Premier, then you can do anything!” to something like: “If they were wrong about Leicester’s chances, they could be wrong about yours.” (Substitute anyone for the second “they” – teachers, recruiters, pundits, mean relatives etc.)

6. Jojo says:

I make no judgement of the veracity of the statements, but here https://twitter.com/nntaleb/status/729730570146725888?s=09

NN Taleb seems to make the claim that long shots are generally _under_ priced due to uncertainty in coming up with accurate estimate of Pr(rare event).

• Andrew says:

Jojo:

It was my impression (without actually seeing the data) that, in horse racing, favorites win more often, and longshots win less often, than you’d expect based on the odds (adjusted for the vig). But people bet on lots of other things besides horse races.

• TBW says:

The longshot bias in horse racing is a little more nuanced. Longshots are overbet not to win, but to show(finish 3rd), and as a result favorites are underbet for show. You can still see this if you spend a few minutes monitoring the betting pools at tracks. You’ll see a favorite that has 33% of the win pool bet on him, but just 15% of the show pool, and longshots that have 3% of the win pool, but 10% of the show pool. Most of the time these discrepancies are erased in the last minute or two of wagering, so it is very difficult to exploit the inefficiency. A bet that has a very nice positive expected return 5 minutes before post could turn negative by the time the race is actually run. It’s my understanding that there are people out there akin to high-frequency traders who are tied directly into the pari-mutuel systems that are able to take advantage of whatever market inefficiency is left.

7. Joe says:

I don’t understand the point you’re trying make about this. How on earth are we supposed to know what the pre-season odds of Leicester winning were? The bookies, who do this for a living and had money on the line, settled on a value that appeared to be reasonable to them. Why write a story about “how the oddsmakers got this one wrong” given that we don’t know if that is true or not.

Given that there are at least a few dozen high profile professional sports competitions out there every year, it shouldn’t surprise us that occasionally, outcomes with a genuine 5000-to-1 chance occur. I would expect Andrew to be as aware of this as anyone. The failure of the bookies to adjust the odds sufficiently quickly over the course of the season is quite a different thing than where the initial odds were set.

• Andrew says:

Joe:

Please follow the links, which include much discussion on this point (including from some people who seem to know a lot about bookmaking and aren’t so sure that this was, even prospectively, “a genuine 5000-to-1 chance”). Following the links, you’ll also see how Nate Silver made up his 2% chance of Donald Trump winning the Republican nomination. Short story: bookies are people, and people can make mistakes, or people can even rationally choose not to devote the resources to setting good prices. Even people who do things for a living and have money on the line can make mistakes. We can’t “know” the correct pre-season odds but we can assess the process that led to the 5000-1 odds, and we can look at precursor events and comparable events. There are ways of assessing probabilities; we do not need to resort to blind trust in whatever numbers a group of bookies happens to converge on.

• Joe says:

I’ve read your other stuff on this and followed the links. It’s incredibly disingenuous to compare Leicester and Trump. Those assigning long odds to Trump did so by deliberately ignoring the polling and the mistake is incredibly obvious in hindsight (far too much weight was placed on the “party decides” theory). So far as it goes, I believe that you’re competent to identify a process failure here because you’re an expert in the area.

But Leicester wasn’t like that. You linked to the Nick Goff posts, which do come from someone capable of assessing process failure, but he’s very careful to draw a distinction between the pre-season odds and the odds after Leicester started winning (and these are really quite different things). You seem to want to blur these together. But the “It’s only Leicester. They’ll drop away soon. It’s only Leicester, they’ll drop away soon.” fallacy identified by Nick Goff simply does NOT imply any faults in the initial 5000-to-1 assessment.

And I think the point is that people familiar with the process think that was a reasonable assessment. The imbalances are so much greater than in the North American Leagues that that kind of imbalance is plausible and Leicester clearly had some instances of very good luck that we can specifically identify.

You haven’t cited, and I haven’t seen, any bookies coming forward to say that there was a process failure. The only person you appear to have cited to this effect in any of your posts was Paul Campos, whose post you quote opens with the remark: “I’m only a casual follower of the big Euro soccer leagues.” His reasoning, like yours, seems to be based on a false equivalence between the relatively balanced talent levels in North America and a case like Leicester City which was, literally, almost a minor league team. This is not like Minnesota Twins winning the World Series this year. This is like a AA team winning the World Series.

• Eric Loken says:

It’s not like a AA team winning the World Series because that has 0% chance. They were one of 20 teams in a league where they played everyone twice. They had won 7 out 9 of the final games the previous season. Goff does point out that if he opened up the variance a bit in his models, his estimates would have gone from 5000:1 to something like 300:1. I think the point here is that the achievement of Leicester was phenomenal, entailed a good degree of luck, and may even be the greatest underdog story in modern sports. But is it really that they overcame 5000:1 odds? Did they flip more than 12 heads in a row? Or do something more exceptional than dealing 4 of a kind in 5 card draw? I think that part of the story here is that 5000:1 was not well calibrated.

• Andrew says:

Joe:

You write that I was being disingenuous. Here’s the definition of “disingenuous”: “not candid or sincere, typically by pretending that one knows less about something than one really does.” Everything I have posted on this topic is candid and sincere. Of course, if you really think I’m not being candid or sincere, you might not believe me on this one either! Really there’s no way of responding to such a statement.

• Joe says:

Moreover, if you’re right that there was a process failure, then why haven’t we seen some dramatic change in the way the bookies change their odds. They got burned on this one, so if this is because their decisions were prospectively wrong, then shouldn’t they change something? Again, you agreed with Paul Campos that Leicester, by consensus one of the weakest teams in the League, should have been put at “50-1 or maybe even 100-1 odds”. If this is true, then why are there currently NINE teams in the Premier League offering odds of 750-1 or worse?

• Andrew says:

Joe:

1. Regarding the odds for Leicester, see Eric’s post above. Again, these odds were not well calibrated which explains how they could be off.

2. I found Campos’s arguments convincing—certainly more convincing than the default, “Wow, a 5000-1 shot won! What a miracle!” story—but, sure, maybe 50-1 or 100-1 is going to far.

3. There’s a big difference between 750-1 and 5000-1.

8. Paul says:

What I would like to see (has anyone done it?) is an analysis of the performance of EPL teams that had similar pre-season odds to Leicester over the last 15-20 years or so. Even just a plot of the season points behind the champion for that year would give a better idea of just how much of an outlier Leicester was.

This is related to a comment Andrew made previously asking how many “near-misses” there have been in comparable situations.

• Andrew says:

Paul:

Yes, exactly. I’d be interested in seeing such an analysis.

• fraac says:

Just thinking about it in my head, either two or three presumed bottom six teams in twenty years have qualified for the UEFA/Europa Cup by finishing in the top six (or seven). None finished in the top four.

9. fraac says:

My problem with this topic whenever it comes up is it *seems* like you’re saying “My gut tells me it can’t have been 5000-1 because it happened”. But as a professional statistician you can’t possibly be saying that. So why does it feel like you are?

Goff looked at it and his first model spat out 5000-1. I’ve followed tens of thousands of sporting events, betting on many of them, and my gut says at least 1000-1.

It’s perhaps impossible to convey to non-football fans how unlikely this event feels. It blows everything else out of the water. John Daly was 250-1 to win the 1991 PGA Championship, but he hit the ball longer than anyone else and the course suited him. When Leicester appointed Claudio Ranieri as manager, Gary Lineker, the BBC’s top football guy and legendary Leicester City player, tweeted “Ranieri? Really?” They were a bad team and they were about to get worse. Leicester fans knew this better than anyone.

They retained the least possession of the ball of any team in the league. Spain and Barcelona of recent years are argued to be the greatest teams of all time – they’re so religious about keeping possession that Spain won a major tournament without needing a striker. Leicester’s squad of one-dimensional players used a simple counterattacking style with ballwinning midfielders and pace up front, and had good team spirit. IS THAT IT? IS THAT ALL YOU HAVE TO DO TO WIN THE LEAGUE???

It’s like a game of Football Manager 2016 and Leicester found the bullshit formula that beats the game. Like reality is a simulation and Jamie Vardy is Neo.

Consider this: football fans find it inconceivable that Leicester won the league. It makes no sense. You find it inconceivable that the league winner was a genuine 5000-1 chance. Perhaps the fault isn’t in the bookies’ methods but in humans’ post hoc perception of very unlikely events.

• Andrew says:

Fraac:

You could be right. It’s a possibility. As I said in one of my posts, I think the way to make progress on this one is to increase N by looking at precursor data. I still think that any serious look into the Leicester story should at least consider the probability that the odds were a priori poorly set.

• Joe says:

What does it mean for the odds to be poorly set, though?

The bookies looked at the available information, made some (largely implicit) assumptions and arrived at a figure of 5000-1 that, so far as I’m aware, everyone thought was reasonable at the time. So why was it unreasonable?

1) I think we can all agree that, on the basis of information we know have, the bookies underrated Leicester’s chances because they did not realize, for example, how talented some of the Leicester players were or the fact that Ranieri was a more competent manager than everyone thought. If you revised that information, the bookies would have come up with a different figure, but that doesn’t mean that the odds were poorly set. The bookies were in that case, just decent Bayesians working off of iffy information. I mean, for Christ’s sake, it doesn’t seem unreasonable, even in retrospect, to infer that a manager coming off a loss to the Faroe Islands is incomponent.

2) Maybe the bookies used some faulty assumptions about the way football works. But if this were true, we’d expect to see more of a rethinking of the way we evaluate football teams, and we haven’t. This is the big difference between Trump and Leicester. Trump has forced observers to rethink the way the process is assumed to work. But even if those assumptions do turn out to have been iffy, they appear to have been widely shared by everyone with relevant expertise. Can we really call this mis-setting the odds?

3) I think it’s only fair to say the odds were poorly set if the bookies, working from the information and assumptions that everyone held at the time, delivered odds that diverged from what a rational observer should have set. I haven’t seen any evidence that this was the case.

• Andrew says:

Joe:

As noted in an earlier comment, just as we need to beware of the hindsight fallacy, we also should watch out for the Panglossian fallacy. There are various reasons that the odds for Leicester could have been set wrong, including the very simple idea that not many people were betting on Leicester to win the championship so there was not much of a mechanism to keep prices honest. Again, people do make mistakes, even prospectively.

If you want to argue that the bookies were doing their best, sure, I don’t disagree with that. But that’s the point, that maybe they were working off a flawed model, or maybe they just didn’t bother to try to get the odds right because the loss was such a low-probability event.

Again, I think the best way to adjudicate these claims would be to look at calibration of this and other historical odds using precursor data such as point totals and goal differentials (as the N is not large enough to calibrate based on counting championships).

• TBW says:

If not many people were betting on Leicester then how did the bookies lose so much money ? Someone earlier mentioned the notion that bookmakers simply try to balance their books so that no matter what happens they walk away with the vig. But what if they don’t ? What if sometimes they actually take positions in order to enhance their returns ? What if they believed that since Leicester couldn’t possibly win, any money bet on Leicester was ‘free money’ ? In that scenario wouldn’t you jack the odds up to something ridiculous to attract more bettors to Leicester and get more free money ? Then when Leicester actually wins, you’re screwed because you purposely didn’t balance your books, but instead intentionally overloaded them with Leicester bets.

The idea that the bookies don’t balance their books does a much better job of explaining why they lost so much money. If their business is balancing the betting action in order to collect the vig, then how could they be so slow to adjust the odds in season ? Adjusting the odds to balance the betting action is their ENTIRE business according to that model. Instead, they acted like Leicester was a gift from the sporting gods and kept the odds so high so they could collect all of the free money.

• Eric Loken says:

I hear your objection fraac. Seems to me though that there are two issues here:

1) Converting the expert pre-season appraisals of “unthinkable” “unprecedented” “impossible” etc into a quantified probability for betting purposes is imprecise and vague. I think that 5000:1 in a 20 team league underestimates tail-area probabilities, and it does seem from the Goff discussion etc that the quoted odds might have more to do with drawing in customers and an underestimation of system variance because the bookies themselves use those same narrative terms for likelihood and they have the same priors on how the league works.

2) In the post-mortem, taking the pre-season odds as a quantified representation of the remarkable achievement of Leicester misses the opportunity to reflect on the accuracy of those odds. It’s not just about a post-hoc finger wagging that because it happened it must have been likely. We’re running back and forth here between subjective priors articulated in words, and articulated in concrete numbers. And just because it feels outrageously unlikely, it doesn’t follow that 5000:1 is the properly calibrated number for the risk function. For human, variable systems “could never happen” and “that would be impossible to conceive” are difficult to quantify, and very easy to underestimate.

10. Ney says:

Does the 5000:1 mean that a team like Leicester would be expected to win the English championship only once within 5000 years? Or, to put it another way, that from 5000 high profile sports tournaments, only 1 would be won by an extreme underdog? “Once in 200 years” or “one out of 200 events” sounds a lot more plausible IMHO.

• Ney says:

By the way, what happened to Leicester isn’t as extremely rare as one would maybe expect. E.g. in 1998, the German football championship was won by a team which had just ascended from the 2nd league (1. FC Kaiserslautern). According to later accounts, the odds were 2000:1 to 5000:1 then. No football fan would ever had expected the event.

• No. 5000:1 means more or less that among the various scenarios people could come up with for what might happen in the future of this season, at the time those odds were set, for every one where Leicester won there were about 5000 ways they could lose. In other words, it’s closer to an accounting of how the future would have played out in that one season than it is an accounting across 5000 different imaginary future seasons.

You could imagine a markov model… first there’s the first week of play, and various matchups happen, and the outcomes of those matches determine who plays whom in the next set of matches and that determines what happens in the next set and so-on. Each full path through the season winds up with some plausibility associated with it. After you’ve looked at every path through that whole mess of future matches for the season, you could roughly imagine 5000 units of plausibility that go to paths where Leicester loses for every unit of plausibility that goes to one where they win.

11. londenio says:

The Euro Cup starts soon. Albania and Northern Ireland have 300-1 odds to win the tournament. They are about 500 Elo points below Germany and France (which means that Germany wins 19 out of 20 times in a match against Albania). Anyone with enough time in their hand to simulate the Euro Cup using the Elo Ratings and see if Albania wins 1 in 300 times? Sadly the group and knockout system is more annoying to code in R o Python than coding something like the Premier League.

By the way, I think this football Elo system is a bit off. In chess, a 2700 player would never lose against at 2200 player. Or is the system a different?

12. Iggy says:

In case anyone is interested, this morning at 5dimes.eu and sportsbetting.com the Atlanta Braves, with 2/3s of the season left to play (108 games),can be had at 3000:1 to win the World Series. They were 250:1 on the first day of the season.

The windows are open.