## The First Bookie

Posted in Football, mathematics, Sport with tags , , , , , , on April 24, 2019 by telescoper

I read an interesting piece in Sunday’s Observer which is mainly about the challenges facing the modern sports betting industry but which also included some interesting historical snippets about the history of gambling.

One thing that I didn’t know before reading this article was that it is generally accepted that the first ever bookmaker was a chap called Harry Ogden who started business in the late 18th century on Newmarket Heath. Organized horse-racing had been going on for over a century by then, and gambling had co-existed with it, not always legally. Before Harry Ogden, however, the types of wager were very different from what we have nowadays. For one thing bets would generally be offered on one particular horse (the Favourite), against the field. There being only two outcomes these were generally even-money bets, and the wagers were made between individuals rather than being administered by a `turf accountant’.

Then up stepped Harry Ogden, who introduced the innovation of laying odds on every horse in a race. He set the odds based on his knowledge of the form of the different horses (i.e. on their results in previous races), using this data to estimate probabilities of success for each one. This kind of `book’, listing odds for all the runners in a race, rapidly became very popular and is still with us today. The way of specifying odds as fractions (e.g. 6/1 against, 7/1 on) derives from this period.

Ogden wasn’t interested in merely facilitating other people’s wagers: he wanted to make a profit out of this process and the system he put in place to achieve this survives to this day. In particular he introduced a version of the overround, which works as follows. I’ll use a simple example from football rather than horse-racing because I was thinking about it the other day while I was looking at the bookies odds on relegation from the Premiership.

Suppose there is a football match, which can result either in a HOME win, an AWAY win or a DRAW. Suppose the bookmaker’s expert analysts – modern bookmakers employ huge teams of these – judge the odds of these three outcomes to be: 1-1 (evens) on a HOME win, 2-1 against the DRAW and 5-1 against the AWAY win. The corresponding probabilities are: 1/2 for the HOME win, 1/3 for the DRAW and 1/6 for the AWAY win. Note that these add up to 100%, as they are meant to be probabilities and these are the only three possible outcomes. These are `true odds’.

Offering these probabilities as odds to punters would not guarantee a return for the bookie, who would instead change the odds so they add up to more than 100%. In the case above the bookie’s odds might be: 4-6 for the HOME win; 6-4 for the DRAW and 4-1 against the AWAY win. The implied probabilities here are 3/5, 2/5 and 1/5 respectively, which adds up to 120%, not 100%. The excess is the overround or `bookmaker’s margin’ – in this case 20%.

This is quite the opposite to the Dutch Book case I discussed here.

Harry Ogden applied his method to horse races with many more possible outcomes, but the principle is the same: work out your best estimate of the true odds then apply your margin to calculate the odds offered to the punter.

One thing this means is that you have to be careful f you want to estimate the probability of an event from a bookie’s odds. If they offer you even money then that does not mean they you have a 50-50 chance!

## The Arithmetic of Relegation

Posted in Biographical, Sport with tags , , , on April 30, 2018 by telescoper

When I got back home after yesterday’s concert, I ate some dinner and settled down to have a look through the Sunday papers. Most of the news was as grim as expected, especially the ongoing fiasco of Brexit, and the scandal engulfing Home Secretary former Home Secretary Amber Rudd who obviously lied to Parliament on at least one occasion. Anyway, turning my attention to the Sports pages there was a write-up of Saturday’s disappointing home defeat for Newcastle United against bottom club West Bromwich Albion. I was gloomy enough to wonder whether Newcastle might actually still get relegated, so looked at the Premiership Table:

Neither West Brom (28 points) nor Stoke (30) can catch Newcastle with only two games to play, but Southampton can in principle get 41 points from here if they win all three games. It’s true that they have a worse goal difference but if Newcastle lost all their three remaining games, and Southampton won all theirs that would change. It therefore looks mathematically possible for Newcastle to be relegated.

However, I then glanced at the fixture list and found that Southampton have to play Swansea in one of their remaining matches. If Southampton win that fixture then the maximum number of points Swansea can get by the end of the competition is 39, so Newcastle can’t be relegated. If Southampton lose or it’s a draw then they can’t catch Newcastle.

I conclude, therefore, that Newcastle United are mathematically safe from relegation. Hooray!

But who will go down? I think West Brom and Stoke will probably get relegated, but I’m not sure about the third team. Huddersfield must be very nervous because their recent form has been poor and they have a very bad goal difference. The betting odds are interesting: BetFred are offering 200/1 on West Brom not being relegated and most bookies are about 8/1 on Stoke to stay up. PaddyPower are quoting 4/9 on Huddersfield and even money on Southampton to go down. If you want to bet on Brighton to get relegated your best odds are with BetVictor who are offering 50-1. Few bookies are quoting odds on West Brom to get relegated, so they obviously think that’s the likely outcome.

I expect these odds to change a lot after the next round of matches.

## On the West Indies Winning

Posted in Cricket with tags , , , , , on August 30, 2017 by telescoper

Back in the office after a rather chaotic Bank Holiday Weekend during which, among other things, I managed to mislay my phone, I couldn’t resist a short post about yesterday’s victory by the West Indies over England at Headingley. I don’t often write about sporting events that I haven’t attended in person, but I thought I’d make an exception in this case for the reasons I’ll outline below.

The first is that, although England will be hurting after losing a game many expected them to win comfortably, I think this result is great for cricket.  Before this game I was gearing up to write a post wondering why there seem to be so few close Test matches these days, the previous series and the first one in this series having been quite one-sided. Although the West Indies won this one fairly comfortably in the end – by five wickets with several overs to spare, it still counts as `close’ in my book because the final day started with any result possible. That doesn’t happen very often, but when it does it makes for a marvellous experience. I wish I had been there. Long may five-day Test matches endure!

Shai Hope, whose beardpower led the West Indies to victory  (Photo credit: JEWEL SAMAD/AFP/Getty Images)

Secondly, I am not as critical as some of Joe Root’s decision to declare on 490-8 on Monday evening, leaving the visitors 322 to win. He obviously hoped to knock over a  couple of West Indian wickets in the six overs left to play that evening, but that didn’t happen. However, as long as no significant time was lost to the weather (which it wasn’t), that decision meant took the draw out of the equation. If the Windies batted all day on the last day – a big `’if’ – they would comfortably score the runs as only a shade over three an over was required. It’s one of the fascinating curiosities of cricket that maximising the chance of winning by declaring  can also maximise the chance of losing.

In the end, England’s bowlers didn’t perform to their best on the last day and, while many expected the batsmen to feel the pressure, it was England that seemed to crack, losing their cool in the field and dropping a couple of important catches. Crucially, Jimmy Anderson just didn’t get the ball to swing enough to be the threat that he can be. The other likely match-winner, Moeen Ali, did not bowl well either. But let that take nothing away from the excellent performance by the West Indies batsmen, especially Shai Hope (above), who looks a super player. Well played to him, and the rest of his team!

Incidentally, England’s 2nd innings score of 490 for 8 (declared) is the largest Test innings ever in which no batsmen has scored a century. Not a lot of people know that.

I have to admit that I was a bit saddened by the manner of the West Indies defeat in the First Test at Edgbaston because they looked so outclassed. So many of my boyhood sporting heroes were from the West Indies (including such illustrious names as Clive Lloyd, Viv Richards, Gordon Greenidge, Michael Holding, Joel Garner, and Malcom Marshall to name but a few) that it was painful to think of the team fading so badly as a force in Test cricket. They seem to have been in decline for some years, but perhaps the comeback starts now. I certainly hope so. The game is richer for having the West Indies as a force.

Finally, on the result. As regularly readers of this blog will know, I’m not averse to placing the odd bet now and then. When Joe Root declared I had a look at the website of Mr William Hill and noticed that the West Indies were 12/1 against to win the match. Largely based on England’s lacklustre bowling in  the first innings (with the exception of James Anderson), the strong batting performance by the West Indies in their first innings,  and the draw having been eliminated from consideration, I decided to put a pony (£25) on a West Indies win.  I had a look at the betting markets along with the score now and then throughout the day yesterday. The available odds changed throughout the day: at 84 for 2 the price was 8-1, at 101 for 2 it was 5-1, at 169 for 2 it was 13/10 and by the time they passed 200 the West Indies were favourites at 11/10 on (England 4/1 against).

At one game apiece with the West Indies on a high,  it’s all set up nicely for the deciding match of the series at Lord’s next week!