Grand National 2007

The 2007 GN was won by the Irish entry Silver Birch. A maximum field of 40 started out of which out of which 12 finished.

Fence 1: One fell and one unseated rider

Fence 6: One fell and two unseated rider

Before Fence 7: One refused and one pulled up

Fence 8: One fell and one unseated rider

Fence 9: One fell

Before Fence 15: One refused

Before Fence 19: One pulled up

Fence 19: Two fell

Before Fence 20: One pulled up

Before Fence 22: Three pulled up

Fence 22: Two fell

Before Fence 23: One pulled up

Fence 24: One unseated rider

Fence 25: One fell

Before Fence 27: One pulled up

Before both Fence 29 and Fence 30 two pulled up

Your task is to analyse the non-finishers of the race – how many fell, how many unseated rider, how many refused and how many were pulled up?

From this and the information above, work out how many successful jumps there were during the race and express this as a percentage of the theoretical maximum.

The Grand National is the most famous steeplechase in the world raced over 30 fences, 14 to a circuit with The Chair (No.15) and The Water (No.16) jumped just once. Additional puzzles based on the famous race will occasionally be updated here.

Note that prior to 2009 horses could be remounted; all puzzles are provided purely for educational purposes only and on the basis that any horse that finished jumped all 30 fences cleanly unless otherwise stated. Therefore the question might not be entirely historically accurate.

An understanding of the mathematics in forming betting odds for any sporting activity will help with understanding of the use of Ratios in everyday life.

Suppose we have an eight runner handicap hurdle race. Every horse has an official rating, which will then be translated into an actual weight according to the conditions of the race which may set an upper and/or lower limit.

The best horse in the race (No.1) and therefore carrying the top weight of 11st 7lbs has already won two handicaps this season from two starts and the First Show makes him Even money favourite. Numerically this is 1/1 expressing the ratio of reward to win; he wins £1 is won for every £1 staked and the stake is returned.

To reflect the contribution to the overround, add the numerator to the denominator then divide the numerator by this sum. So 1/2 = 0.50 which is this horse's contribution to the overround. The bookmaker might expect to take slightly less than half the money wagered on the race to be bet on this horse so he can anticipate a small profit should it win.

Another way of looking at it is to consider an analogy with "The Cake" which may be found on the **Educational Downloads** page. The Cake is our Round (100% or 1.0) so if it is halved the ratio is 0.5:0.5 or 50:50. Now if we imagine one half is our stake at Even money, then it follows the contribution to the (Over)round is 0.5 or 50.

The horse carrying bottom weight (No.8) of 10st is actually 4lbs out of the handicap but coming back fit after a long lay-off and is quietly fancied by connections to upset the favourite. The bookmaker might adjust the odds quite significantly to closely reflect the bets so if it wins he just about breaks even. Let's say 3 to 1 against is offered; close to a quarter of the money wagered is actually bet on this horse. Because it is odds against, the numerator is the smaller number, so this, divided by the sum of the numerator and denominator is 1/(3+1) = 1/4 or 0.25 (As an aside if the horse had been 3 to 1 on rather than against, the numerator is now the larger number so 3/(3+1) is 3/4 giving an overround of 0.75)

The third horse in the handicap (No.3) has been quite good in the past but is now on the downgrade. However the horse still has a keen following and because of it, is identified as a possible source of profit should it (almost certainly) lose. So the bookmaker offers 9/1 (overround 0.10) knowing this will attract more than 10% of the total bet pool and should he take a bigger bet in the lead-up, then he will offset part of the risk elsewhere.

This gives an overround so far of 0.5 + 0.25 + 0.1 = 0.85 and only three of the eight horse so far accounted for in the betting. The other five only win very occasionally in their turn so are offered at an average of just over 13/1 or or 1/14.3 or 100/7 therefore giving a contribution each of 0.07

0.07 x 5 is 0.35 so the total overround for our handicap is 0.85 + 0.35 = 1.20 which seems rather in favour of the bookmaker overall, but in fact both bookmakers and most savvy punters are totally discounting horse No.3 from winning the race. The large overround is essentially an insurance for the bookmaker, even taking into account any offset bet, as both he and the punters are largely discounting the chances of No.3 - both odds and bets are framed on the basis and the true overround may actually be about 1.13

One more point that needs to be made, and is immediately obvious from the downloadable chart, is that although we talk about an event being 2/1 against or 1/3 on, for example, what we are really expressing for odds against is the stake required to win a £100 and therefore contribution to the overround , so whilst 14/1 literally converts to 1/15 or 0.0667 in practice it may be reflected as 100/7 or 0.07 ; the slight rounding error is less significant than the variance of the amount wagered at the odds and with a bigger field of runners could be compensated elsewhere.

This is perhaps not a particularly good example as a 14/1 shot would probably be staked in units of seven for a total return including stake of 105 (14 x 7 = 98 + 7 =105) but reinforces the point that for framing a book on an event, the overround can only ever be a guide.

You may have heard of "overround" and wondered what on earth it means. The actual numbers obviously depend whether you are working on a basis of the round being 100 percent or as decimal percentage of 1.0 but what it means in practice is that an overround of, say, 127 or 1.27, means that assuming the level of wagers is reasonably close in proportion to the the odds on offer, a bookmaker might reasonably expect a return of 27% or 0.27 on turnover.

In practice, market forces exert a strong influence on the framing of a book. This means the bets actually laid deviate from the odds on offer and a bookmaker will react to betting patterns by lengthening or shortening the odds as circumstances dictate.

A small bookmaker is unlikely to take enough money on every race to obtain a balanced book so he will offset a potential large loss by placing a bet with a larger or national organisation. This will minimise his exposure if the original punt is landed but reduce his profits in the event of a more favourable result.

The overrround will also vary according to the amount of money taken; a large turnover means a small percentage profit is acceptable whereas a small turnover will need a larger overround to have a chance of making anything.

A bookmaker, at whatever level and depending on the market, will often "bet" - that is, place odds say on a horse race, where one horse will be a guaranteed loser (but perhaps covered to some extent by a side bet), one might make a loss - that is the odds are very close to the wagers - whilst the other six are guaranteed profit.

So if betting is a mug's game, why to people bother to bet? Kept to manageable levels, betting should be regarded as a form of entertainment and you should never, never lose more than you might spend on some other source of entertainment. But even this needs some qualification. Firstly, if you go to a race meeting there is absolutely no point betting on every single race on the card. Secondly, racing is all about opinion and the skill element, rather than say roulette or a fixed-odds betting machine is trying to pin-point something someone else has missed; albeit an almost impossible task today when every statistic you could ever want is almost freely available.

No system under the sun is ever guaranteed to make a profit, but betting is a lot more fun (i.e. entertaining) even when you lose if you can evolve a system that might tip the odds slightly in your favour; and after all the bookmakers are doing exactly the same thing! For very occasionally it is possible to bet where the bookmakers cannot shorten sufficiently to reflect the weight of wagers so whatever any literal overround states, money previously placed at longer odds are a disproportionate liability. The all time classic was the day it poured with rain on the morning of the 1998 Grand National; the punters piled onto Earth Summit, a proven mud-lark, the odds collapsed and the horse duly obliged that afternoon.

Another option is to look out for the exact opposite of this where popular support shortens up a favourite far too much where the conditions of the race weights and/or track and/or going do not justify. Such a scenario has often affected the Epsom Derby; at one time it was a particularly profitable scheme to stick with the second-favourite.

Have you ever wondered how bookmakers make a profit...?

In the "old" days it was easier to get a grasp as essentially betting was limited to On Course betting on the horses or greyhounds whereas in today's market you can bet on almost anything via many methods, plus there is the complication of the Exchanges where the facilitator takes a percentage from the winner of a matched bet between individuals; a bit like a service charge.