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The Parable of the Ox
00:28:03
What does a 'guess the weight of the ox' competition tells us about a bloated and We...
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- [00:00]
Tim Harford
Thanks for downloading this edition of More Or Less. This is the version from BBC Radio 4. Here's Tim Harford.
- [00:08]
Hello and welcome to More Or Less. Following the Statistical Star to a numerical epiphany. This week we'll find out why one of our guests from this series brought a suitcase with him to the studio and wouldn't let it leave his side. And we'll try to decide which is the greatest racehorse of all time. But first, we're going to turn our attention to a parable about the financial markets. A parable about an ox. It's a story that starts with a trip that the British social scientist and statistician Francis Galton took to a country fair back in 1906. It's told by James Surowiecki, who recounts the story in his book the Wisdom of Crowds.
- [00:48]
James Surowiecki
As he was walking through the fair that day, he came across this contest. And the contest was that an ox had been placed on display and the crowd around the ox was basically placing wagers on the weight of the ox. So, as Galton described it, there was actually a huge crowd there that day. Something like 800 people actually tried their luck. And what's important about this crowd, at least from my perspective, is that it was a relatively diverse crowd. While many of the people in the crowd were butchers and farmers and probably had some skill in being able to guess the weight of something like an ox, the radio. There were also a lot of people in the crowd who were not, at least on the surface, experts at all. So Galton, as he was watching this contest, it struck him that this made an interesting natural experiment.
- [01:39]
Tim Harford
Galton took all the tickets and ran some statistical experiments on them. With his elitist background, he assumed the average of the guesses would be woefully wrong. But this wasn't the case.
- [01:49]
James Surowiecki
The crowd had guessed that the ox would weigh 1,197 pounds. And when all was said and done, the ox ended up weighing 1198 pounds. So, in other words, the crowd's judgment was essentially perfect. It was actually better than any one person in the crowd. And this is a phenomenon that you can actually see over and over again. You can do this with a jar full of jelly beans or, you know, pieces of candy or whatever. But the Galton example, I think, is a kind of perfect crystallization of this idea of the wisdom of crowds.
- [02:23]
Tim Harford
James Surwicky. Francis Galton's experiment at the country fair in Plymouth is famous and well documented. But not everyone has heard the rumours of what happened next. If you're sitting comfortably, we'll begin this tale.
- [02:41]
Narrator (John Kay's Parable of the Ox)
As the years went by, the competition continued to be a success. More and more people came to guess and the farmer sold more of his produce, which was the original aim of the competition. But the scales became old and seemed to become less and less reliable. Repairs were expensive, much too costly for the organisers of the fair. The competition looked to be in danger until they had a brilliant idea. Since the people who came to the fair were so good at guessing the weight of the ox, why weigh the beast at all? It wasn't necessary to repair the scales. They would simply ask everyone to guess the weight and take the average of their estimates. Newly invigorated and without the need for expensive equipment, weight guessing competitions became all the rage. But with popularity came high stakes. Some people tried to cheat. They even tried to get privileged information from the farmer who had bred the oxygen, offering presents and lavish dinners in return. The organizers became scared. If some people had an edge, others would be reluctant to enter. With few entrants, you couldn't rely on the wisdom of the crowd. The process of weight discovery would be damaged and that would be the end of that little game, and a very lucrative one at that. So strict rules were introduced to regulate the competition. The fear was calmed and the integrity of the weight guessing competition was upheld. But with regulation came innovation. Brighter analysts realised that understanding the nutrition and health of the ox wasn't that useful anyway. What mattered were the guesses of the bystanders. Since the beast was no longer being weighed, the key to success lay not in correctly assessing its weight, but rather in correctly assessing what other people would guess, or even what others would guess. Others would guess, and so on. As the money stacked up, the professional weight guessers and analysts congratulated themselves on how clever they were. A few lone voices tried to be heard over the roar of trading of the latest information. Some, such as old farmer Buffett, claimed that the results of this process were more and more divorced from the realities of ox rearing. Nothing sedates rationality like large doses of effortless money. He exclaimed, but his words went unheeded. True, Farmer Buffett's office oxen did appear healthy and well fed, and his finances were ever more prosperous. But he was a simple countryman who didn't really understand how markets work. One difficulty was that sometimes there were few or even no guesses of the oxen's weight. But that problem was soon overcome. Mathematicians from the University of Chicago developed models which estimated what would have happened if there had actually been many guesses as to the weight of the animal and what the average of these guesses would have been. No knowledge of animal husbandry was required, only a powerful computer. By this time, there was a large industry of professional weight guessers, organizers of weight guessing competitions, and advisors helping people to refine their guesses. Some people suggested that it might be cheaper to repair the scales, but they were derided. Why go back to relying on the judgment of a single auctioneer when you could benefit from the aggregated wisdom of so many clever people? And then the ox died. Among all this activity, no one had remembered to feed it.
- [07:04]
Tim Harford
This imaginary tale. The Parable of the Ox was written by John Kay, and it first appeared in the Financial Times. And John's here to tell us what it means.
- [07:13]
John Kay
Well, what it's about, of course, is the development of financial markets and the relationship between financial markets and companies. And there are two or three aspects of the parable, I think, that are central. One is the idea that the sideshow, the competition actually takes over and overwhelms the underlying object of the fair, which is actually to enable farmers to breed and sell their livestock and get money to invest in new livestock. And of course, that's really what we want the financial system to do. Second point is that in the kind of overdeveloped financial system we now have, what people are doing is not so much focusing on the underlying reality, but on what other people, like themselves, think about the underlying reality. So that people are not trying to guess what the truth is, they're trying to guess what each other is guessing.
- [08:11]
Interviewer (likely Tim Harford)
So this happens, for instance, if people are trading bonds or trading shares, if they stop caring about the credit worthiness of the bond or they stop caring about the profitability of the company that the shares are issued by, and they just start caring about, well, can I sell this thing to some other idiot later?
- [08:29]
John Kay
That's right. It was exemplified for me by a fund manager I talked to who said, I don't want to know this stuff about the competitive advantage of companies. I just want to know what shares are going to go up.
- [08:41]
Interviewer (likely Tim Harford)
Now, is this a particularly British problem, this excessive financialization, or is it a feature of all developed economies?
- [08:49]
John Kay
I think it's a feature of all developed economies, but it's reached its most extreme form in Britain and the United States. And it's exemplified for me, by the way, in which, for example, the amount of the volume of trading we have in foreign exchange is 50 to 100 times the actual volume of trading international trade in goods and services. We're Saying for every transaction in which an importer needs foreign currency to buy some goods, there are 50 transactions in which people round about this real phenomenon of trade in goods and services are dealing with each other. And of course, now, as you know, we have in London and New York, possibly a majority of trades in shares being conducted between high frequency traders, who are not really traders, they're computers, because actually real people can't react quickly enough to engage in this process.
- [09:50]
Interviewer (likely Tim Harford)
One thing that interested me is this question of the ox dies at the end. Implicitly, you think this is very damaging for somebody or for something.
- [10:00]
Tim Harford
So what is being damaged?
- [10:02]
Interviewer (likely Tim Harford)
The economy or corporate profitability? You and me?
- [10:06]
John Kay
Yes. So what prompted me to write this actually was doing work in this government review of how equity markets in the UK were performing and realizing that there was now almost no trade in what people call primary markets. That means British companies using the stock market to raise funds for new investment. All the trade now is in secondary markets where people are buying and selling claims on companies that already exist and that don't need any further funding. And the paradox of that, I came to realize at the end, is that the stock market now isn't a way you raise money for business, it's a way you get money out of business.
- [10:49]
Tim Harford
But does this matter?
- [10:50]
John Kay
I think it matters a lot because we need to ask two questions, really. What value does this activity add? And why is it so profitable? Or apparently profitable, because if we have a group of people sitting in a room exchanging bits of paper with each other, then at the end of the day, the value of the bits of paper which they've exchanged with each other will be much the same as what they had at the beginning of the day. And yet what this activity seems to be doing is attracting a lot of resource, both financial resource and people who might be doing more useful things in the real economy. And the other thing we need to worry about, and this is very much the theme of the parable of the Oxford, is whether this process is actually generating any real information about the underlying performance of companies, which is what we care about, rather than other people's guesses.
- [11:46]
Interviewer (likely Tim Harford)
Because the original idea with the ox is you weigh the ox, and then in the parable of it, it's an
- [11:51]
John Kay
amusing game to guess what the true weight will be. But if we stop measuring the true weight and just look at other people's guesses of the true weight, then we can end up with a world, and we often do end up with a world. Look at the new economy bubble, for example, where there's no relationship between people's guesses and the true underlying weight of the ox.
- [12:14]
Tim Harford
John Kay I put John's points to James Surowiecki and asked him when this wisdom of crowds idea does work.
- [12:22]
James Surowiecki
I should say I still think many financial markets do still work reasonably well in terms of assessing values. But I do think that the process over the last, say 15 or 20 years has been a process of sort of getting more and more distant from hard reality that the market in theory is trying to assess. There are some concrete ways in which this is true. For instance, the fact that companies stopped paying dividends as much as they once did a dividend is a kind of hard reality. In other words, if you're trying to decide whether or not to invest in a company, if that company is essentially paying you on a regular basis for your investment, that gives you a kind of concrete incentive to try to assess the true value of that company. As dividends have become less common and less lucrative, that I think has encouraged more of a speculative bent. I think that the spread of momentum trading and the kind of trading where people are really just trying to ride trends rather than actually in a sense being interested at all in the underlying asset has obviously played a major role in this. I think that there is a circular thing that gets going. The more people do this, the more incentive there is for people to do it. Because if everyone is trading in this way, in theory, it starts to seem like, well, this is the way to make money or alternatively to lose money. If you're not paying attention, I do think you get that kind of mirror chamber effect. And I think that that does have a big impact.
- [13:50]
Interviewer (likely Tim Harford)
Do you think that this process of self reference, of financialization, sucking of more and more talent into Wall street and the city of London, is it genuinely damaging for the rest of the economy? Because at the end of the fable, the ox dies.
- [14:07]
James Surowiecki
Yeah, I thought the end of the fable was maybe a slight exaggeration in the sense that. Well, I guess it sort of depends on what you think the ox is. Because if the ox is corporations, the stock market at least is supposed to be doing is gauging and assessing the value of corporations. You'd be a little hard pressed to argue that corporations are in bad shape these days. There are certainly problems with them. And you could argue that they're excessively focused on the short term perhaps and the like, but certainly in terms of their bottom line performance, which in theory is what the stock market is supposed to be evaluating, their bottom line performance has been pretty good. There is an argument to be made, and I think there's something to it, that the quality of stock market trading these days, let's say financial market trading generally is not a good thing for corporate America or corporate Europe in the sense that it encourages CEOs to spend too much time worrying about what investors think and the like. I think there's something to that. On the other hand, I also think that if you actually look at the concrete performance of these companies, they're doing a reasonably good job of what they're supposed to be doing.
- [15:16]
Tim Harford
James Surowiecki of the New Yorker, you're listening to More or Less with me, Tim Harford, in association with the Open University. Now, you might remember that a few weeks ago we spoke to James Grime, a mathematician at Cambridge University, about whether zero is an odd or an even number. What you wouldn't have known is that he came to our studio clutching a large black suitcase from which he refused to be parted. So I asked him, James, what's in the suitcase?
- [15:44]
Interviewer (likely Tim Harford)
What?
- [15:44]
Dr. James Grime
This suitcase here?
- [15:45]
Tim Harford
This one?
- [15:46]
Interviewer (likely Tim Harford)
Oh, that's nothing.
- [15:47]
Dr. James Grime
That's just a World War II Enigma machine. Let's open up this serious looking case.
- [15:52]
Interviewer (likely Tim Harford)
That is actually amazing. I just touched an Enigma machine and it looks a bit like a typewriter. It's got the normal keys. It's got what look like a duplicate copy of keys. I don't know if you could actually press them. And it's got three wheels or wheel shaped bumps and a dial. And James, talk me through what this thing actually is and what it did.
- [16:13]
Dr. James Grime
This is what Nazi Germany were using in World War II to send their secret messages to each other. Now this machine that I'm showing you is an original Enigma machine. So this is currently 76 years old.
- [16:24]
Interviewer (likely Tim Harford)
Talk me through how it would have been used.
- [16:27]
Dr. James Grime
The machine itself didn't transmit. So what you had to do was if you had a message to send, you would type it into this machine and your code would light up. So we've got two sets of letters. We've got the keyboard where you type and the second set of letters above it light up, up and they give you the code. So you would have to write down that code and then you would give that piece of paper to the radio operator and it was his job to transmit it. And he would transmit it by Morse code.
- [16:52]
Tim Harford
It would travel by radio and just
- [16:54]
Interviewer (likely Tim Harford)
explain what was so difficult to break about this code because it was different every time in some way.
- [16:58]
Dr. James Grime
That's right. So the machine inside has moving parts. So an old fashioned Code, if you had a double letter, it becomes a double letter.
- [17:06]
Interviewer (likely Tim Harford)
So I type S twice and S becomes Q and Q, and every time there's an S, there's another Q, and people can pretty quickly figure out the code.
- [17:14]
Dr. James Grime
Yeah, exactly. So this has moving parts inside, which means the code is always changing. So if I press the letter S first time, I might get a Q, but if I type S again later on, I'm going to get probably a completely different letter.
- [17:29]
Tim Harford
And how does the receiver of the
- [17:31]
Interviewer (likely Tim Harford)
coded message understand what on earth's going on?
- [17:34]
Dr. James Grime
So these two machines, they have to be set the same. We've got some dials here at the top of the machine. Now, that setting is written down for you on a piece of paper for every day of the month. It told you how to set that machine.
- [17:46]
Interviewer (likely Tim Harford)
So if the British could get hold of both the sheet of paper and an Enigma machine, they could presumably break the code. But I guess neither of those things were terribly easy. And how did the Bletchley park team go about trying to crack the Enigma code?
- [17:58]
Dr. James Grime
There is a flaw in the machine. So we talked about pressing S repeatedly and it would keep changing. And if I keep doing that, every letter on the machine will light up eventually, except the letter S itself. And this was your clue. What you do is you imagine an Enigma code and you try and guess a phrase that might be in that message. Maybe it ends with Heil Hitler. So you think, if it's Heil Hitler near the end, I also know that H can't be H and E can't be E. So if Heil Hitler fits, I know that letters can't match up, so that must be true. And then maybe, if it does work, maybe that's Heil Hitler at the end of the message. That's your starting point for breaking the code.
- [18:41]
Interviewer (likely Tim Harford)
And why is this a mathematical problem? Because that seems like common sense. I mean, it's very clever, but it's common sense. Where does the maths come in?
- [18:48]
Dr. James Grime
Before World War II, code breakers tended to be linguists. And at this point, we were able to mechanize our code making. That's what the Germans did with the Enigma machine, and so it needed a technological solution as well. So that's when they started to get in the mathematicians, and they gradually took over the world of code breaking.
- [19:10]
Tim Harford
Dr. James Grime, how do you tell which is the best racehorse of all time on the flat? This year, Frankel, who apparently is some kind of horse, has staked his claim to the top spot with 14 wins out of 14 races. But officially, he's not the best. As the BBC's racing correspondent Cornelius Lysert
- [19:30]
Cornelius Lysert
explains, for many people, Frankel is the best horse that they've seen. However, we await the official ratings because at the moment, technically speaking, he's marginally, marginally, marginally behind Dancing Brave, an iconic horse from the 1980s. Now, that's on an official basis. Obviously, Dancing Brave and Frankel will never take each other on and both will have fans and lots of people will have views. However, the official ratings are, to some people, the be all and end all, because they are official, if you like. At the moment, he's marginally behind Dancing Brave, but he will be reassessed, having been considered by every assessor, every handicapper in the big racing world, and a decision will be unveiled in January.
- [20:14]
Tim Harford
Currently, Frankel is rated 140 and Dancing Brave is rated 141. But what do these ratings mean? If I have two horses, one rated 120 and one rated 140, what do we conclude other than that the horse with 140 is better? Phil Smith is the head of handicapping at the British Horse Racing Authority, and he says the numbers are expressions of weight.
- [20:36]
Phil Smith
These horses, if they were running over a mile and it were a handicap, the 140 horse would have to give 20 pound to the 120 horse and that would be a difference of around about 10 lengths. So we would expect, if they ran against each other on level weights, we'd expect the 140 horse over a mile to beat the 120 horse by 10 lengths.
- [20:55]
Interviewer (likely Tim Harford)
How do you calculate these rankings? Is it a purely objective formula that you just plug in the race results and out comes the ranking? Or is there an element of judgment as well?
- [21:06]
Phil Smith
It's probably 80% judgement and 20% arithmetical.
- [21:10]
Interviewer (likely Tim Harford)
What you're saying is there's a huge amount of judgment. This is really subjective.
- [21:14]
Tim Harford
Is there another way to do it? Is there an objective way to do it?
- [21:17]
Phil Smith
Well, you could get a computer to do it, but the problem with getting a computer to do it, all it could do is calculate pounds per length. Looking at some of Frankel's races, when he won at York, for example, he won by seven lengths there. That's a long way. That's over a second. And yet, when I was assessing that race, I didn't call the winning distance 7 lengths because I looked at how Frankel was finishing compared with how the second horse far was finishing, and I judged the winning distance to be actually nine and a quarter lengths because Frankel won The race easily the jockey was not hard on the horse at the end, whereas every other jockey was hard at work on the horse and they were trying absolutely their best and they couldn't have got any closer to Frankel.
- [21:57]
Interviewer (likely Tim Harford)
This element of subjective judgment, does it apply only at the level of the races? You use your judgment to decide what the margin of victory really was after adjusting for effort and so on. Or is there further subjective judgment? At the end of the year, everyone gets together and says, come on, he's a bit better than that, give him an extra point.
- [22:15]
Phil Smith
That's very similar to what happens. And we had a debate in Hong Kong where we showed a number of Frankel's races and I have to justify my addition of a couple of lengths in the race at York. And we watch the video of the race, they're in there, there are 20 other experienced international handicappers and they may well turn around and say, well, actually, no, we disagree. We think he's only value for length and a half more, or perhaps he's better than that. Maybe he's value for three and a quarter lengths, in which case, obviously you'd get him higher and eventually it comes to a vote.
- [22:46]
Tim Harford
So if the World Ranking Conference reassessed Frankel's rating and this puts him ahead of Dancing Brave, does this mean that Frankel is indeed the greatest flat racing horse of all?
- [22:56]
Phil Smith
Well, it's very difficult certainly, to compare the ranking given in 1982. The system started in 1977, but there were only three countries involved Britain, France and Ireland. By the mid-1980s, the Germans and the Italians joined, so it was a sort of pan European rankings then. It's now pretty much a worldwide classification. So how do you compare Frankel with years gone by? Well, if you wanted to compare them with the horses in 1977, you could only compare him with the best horses in Britain, France and Ireland at that time. It's mighty difficult because you're not actually comparing like with like. The whole system has changed. The number of countries has changed as well.
- [23:35]
Tim Harford
So perhaps we'll never know who's the best. But the British Horse Racing Authority aren't the only ones to rank racehorses. Jamie lynch is from timeform, a company which also produces ratings, and he thinks you can make comparisons using Timeform's ratings.
- [23:50]
Jamie Lynch
We have been doing this since 1948. Timeform was established, and over that time we've used exactly the same methods and crucially, exactly the same scale, which we feel makes us best placed to judge one horse against another in generational Terms as well. What we are saying, why 2012 was such a momentous year for horse racing was that in our opinion, Frankel achieved a higher rating in 2012 than any other horse has in time forms, history.
- [24:18]
Interviewer (likely Tim Harford)
How can you say that Frankel is a better horse than, say, dancing brave from 25 years ago, 30 years ago?
- [24:26]
Jamie Lynch
Well, at the end of each racing season, the whole ratings from that year are standardised. That is, what does it normally take to win a Group 1 race? What does it normally take to win a listed race or a Group 3 race? And therefore you are able to set how good the generation as a whole is compared to previous historical terms.
- [24:46]
Interviewer (likely Tim Harford)
And this rankings conference, the World Thoroughbred
- [24:49]
Tim Harford
Rankings Conference, do you think after the
- [24:50]
Interviewer (likely Tim Harford)
conference we'll be able to say they have decided and we have discovered the best horse of all time?
- [24:56]
Jamie Lynch
Well, to be honest, Tim, it's up to the BHA and the World Thoroughbred Rankings themselves to discuss in more detail how comfortable they are with the ratings. But it is an issue, I think, in the wider scheme of horse racing, that we feel that the BHA and therefore the World Thoroughbred rankings, potentially undersold Frankel, that is, in putting him behind Dancing Brave. We feel a time form that that is not doing Frankel justice in terms of what he's capable of. It'll be interesting to see what they do in reaction to that because there is a bit of a public outcry in terms of people thinking, of course, Frankel is the best horse of all time. Why isn't he rated as such? My personal belief is that they may well revisit that Dancing Brave rating and say, actually, looking back, that horse possibly wasn't worth the figure that we put on him at the time and therefore will reduce his rating. And that will leave Frankel at the top of the rankings.
- [25:50]
Tim Harford
So Jamie lynch is sure. But we'll have to wait until later in the month before we find out what the World Ranking Conference has decided. No matter what they say, I suspect there's just enough uncertainty for the debate to continue. Last week we asked you for your numbers of the year. This one's my favourite.
- [26:08]
This is a number from listener Michael Fletcher. My number of the year is 3/4. 3/4 of all convicted rioters had a criminal record, was the headline in newspapers earlier this year. Kenneth Clark, the then Justice Secretary, used this to back up his assertion that the criminal justice system was failing. This number, however, doesn't back up the Justice Secretary's concern. If three quarters of all people with criminal records had been convicted of rioting it would be a cause for great concern. The fact that 3/4 of rioters had criminal records is not the same thing. Actually, the statistic in question is worryingly small. Only 12 in every 10,000 people with a criminal record were involved in the recent riots. But what about the 400 people who did not have any previous convictions? It may be that some of these people had committed crimes before but just never been caught. Even so, it seems reasonable to conclude that hundreds of people, for the first time in their lives took part in criminal activity. The shocking statistic we should be worried about is not 3/4, but the 1/4 who previously did not have a criminal record.
- [27:11]
This is the last in the current series of More or less on Radio 4, but if you subscribe to our podcast, you can keep yourself going with the version we do for the BBC World Service until we return in the spring. Thank you to the BBC's legendary Radiophonic Workshop for providing the composition that went with the retelling and of the Parable of the Ox. Thanks also to its writer John Kay, and the narrator Sarah Tom. And as always, for more information on the program, go to BBC.co.uk more or less if you have any numerical conundrums you want us to look into for the next series, please email more or lessbc.co.uk. for now, though, goodbye.
- [27:52]
More or Less was presented by Tim Harford, the Financial Times undercover economist. The producer was Wesley Stevenson and the editor was Richard Varden. The programme is made in association with the Open University.