# FAQ

## The A/E Figure

What is this A/E figure that I constantly see within UK Horse Racing ratings and elsewhere?

A/E is, quite simply, a number which is derived from dividing the Actual number by the Expected number to see if one getting something is which more or less than can be expected.

### Basic Theory

Caution: Mathematics Ahead

For example, if I roll a fair die one hundred times and each time I roll a '6' I win at 5/1 and lose otherwise. I would expect to have broken even (more or less) at the end of the run and the A/E value should be 1.0.

The calculation is simple enough, get the number of winners and then divide that by the expected number of winners. And that's it.

So, if in this example I had fifteen 'sixes' over the course of the 100 rolls then my calculation would be:
15 / (100/6)

The numerator is simply the number from the number of winners and the denominator is the expected number of winners from those 100 rolls. This then works out to be:
15 x 6 / 100 = 0.9

This shows that my fifteen winners were not the expected number as I had ended up with 90% of the expected number of winners when, ideally, I would be expecting sixteen or seventeen successful throws.

That's the basic theory and all it gives us is an idea of 'value', i.e. is this worth it? The bigger the number it is over 1.0 then the more value that it is, the lower the number below 1.0 the less value it is.

### Application Within Horse Racing

Caution: Rant Ahead

The same principles apply; count the number of winners and divide that by the expected number of winners. Now, with horse racing we're not going to have such an easy way of calculating the expected number of winners. For the most part this is true; UK Horse Racing as a value figure which is derived directly from the probability of a horse's chances as determined by our Model.

However, in the Racing World it has been generally accepted, though certainly not by UK Horse Racing, that the price on offer is an accurate reflection of each of the horse's chances. Whilst this here that is considered to be utter balderdash we'll run with the hypothesis for the simple reason that this is the accepted measure and so for the purposes of this value we're going along with this flawed concept of markets being efficient.

So for this calculation we convert the SP for each of the horses involved into a probability figure (for example 3/1 is 25%, evens is 50% and so on) and then we sum all these up, divide the number of winners by this sum and there's the A/E figure.

As mentioned before it's a good guide line even if one doesn't believe in the theory of efficient markets. There is room, therefore, for another form of A/E indicator which is based upon the UK Horse Racing value figure which ought to give a more realistic figure but, of course, can't be compared with anyone else in the racing industry. This is the sole reason why we're using the A/E indicator in its current form.