This is a critical point, and while I think your statement that bookies "offer odds below what they calculate to be the probability" is absolutely true most of the time, they are actually so busy trying to do this for the well-known and consequently well-backed teams, that they often leave value on the other side of the book.Take bookmakers for example. They make money because they offer odds below what they calculate to be the probability. Those odds are only moved by changing probability ( in-play ) or weight of money ( again, the numbers ). Winners are easy to find. Winners where the odds are more generous than the probability, are not.
The reason they do this, in my view, is because they would rather be exposed on the underdog than on the favourite. I used to believe that the bookmaking industry was a purely probability based business, but since I've been pricing up games myself using my own statistical tools, I can see that the market is distorted by the mob especially when it comes to certain teams.
As an example, and without getting into too much self-congratulation, I tipped Setubal on the +1.25 Asian Handicap against Benfica last weekend. Benfica, one of the most famous clubs in Europe, and probably a favourite of the accumulator coupon because of the name and the (usually very) short prices. They were priced at 4/11 to win away at Setubal despite the fact that they couldn't beat Setubal in the home head to head earlier in the season (despite being priced at 2/11 to do so). Setubal won 1-0.
Arsenal last night were priced at 2/9 for the win and Watford could be backed on the +1.5 handicap at 5/4. Like most other people, I expected Arsenal to win, but I had them at 2/5 for the win, and would never have had them odds on to clear the -1.5 handicap. Arsenal have won 33% of their home league games this season by more than 1 goal, yet there was an implied probability of 60% in terms of the market's estimation that they were going to beat Watford by more than one.
There is a similar issue in the prices for Man Utd tonight. I make them 4/11 favourites for the win; the market has them at 2/11, and unbelievably, they've actually shortened from the opening price of 1/5, and the famous Old Trafford outfit are at 1/2 to win by 2 or more, and only a shade odds against at 13/10 to win by 3 or more.
Man Utd have won 3 of their 11 home league games this season by more than one goal, a 27% ratio, yet the market has them at a 66% probability to do so tonight. United have won just one of their home league games this season by 3 goals or more, a ratio of 9%, yet the market gives them a probability of 43% to do so tonight.
Those prices are designed to ensure that Man Utd don't cost bookies money, and yet incredibly, the market is happy to back them into an even shorter price. After all, everybody loves a 'sure thing'.