The Taxman Cometh

Introduction

Anyone who uses exchanges - and if you're reading this, you are almost certainly in this group - will be familiar with the concept of commission - the money that the exchange operators charge you in return for providing you with the platform to bet directly with other users. Of course, what this commission amounts to, even though we don't normally think of it like this, is a tax on our winnings. And it isn't 1%, or 5% either - at least not usually!

"Andy's wife allows him to bet £20 per week. For Andy, his betting is an adjunct to his enjoyment of televised football."

Some Sample Punters

Let's look at some notional punters to examine the impact of commission on our betting. First in our group is Andy Amateur. Andy's wife allows him to bet £20 per week. For Andy, his betting is an adjunct to his enjoyment of televised football. He likes to have some money riding on the result, and anything he wins is a bonus. In a completely fair market (i.e. 0% commission), Andy would make a 5% loss on his betting.

Next in our group is Barry Beginner, a guy who knows his football well, and figures he might be able to make some money by betting on it. Barry has a good job and can afford bigger stakes - in part because he makes a 1% profit (against a fair market) - he bets £200 per week.

Charlie Cleverclogs is a shrewd racing punter from the north of England who has decided to try and enter the world of professional betting. He is testing the water and bets £500 a week. Charlie makes a profit of 2%.

Dave Disciplined is a canny racing punter, residing in Scotland. He has been betting for many years and can make a profit of 3% in our market. His careful management of his money means that he has a betting bank sufficient to allow him bet £1000 per week.

"Thanks to a succesful spell of ambulance-chasing in the 80's, he has a tidy sum as a betting bank."

Ernie Eke-Outaliving is a crafty cockney who is a full time pro. Thanks to a succesful spell of ambulance-chasing in the 80's, he has a tidy sum as a betting bank. Ernie bets £20,000 a week and makes a 5% profit in our notional market.

Frankie Fancyhouseandcar is our next member of the group. Frankie is a shrewd pro, specialising in American sports and tennis betting. He makes 7% profit and bets £50,000 per week.

The last member of our group is Glenn Godcomplex, a crafty punter from the north-east of England. His background is in racing, but while still active there, he makes a very healthy profit from football betting - specialising in long-term markets. Glenn bets £100,000 per week and makes a very impressive 10% profit in our notional market.

We can easily calculate the weekly incomes of our select group in a 0% commission market, shown in the table below:

Punter	Weekly Stakes	Yield	Income
Andy Amateur	£20	-5%	(£1)
Barry Beginner	£100	1%	£2
Charlie Cleverclogs	£500	2%	£10
Dave Disciplined	£1,000	3%	£30
Ernie Eke-Outaliving	£20,000	5%	£1,000
Frankie Fancyhouseandcar	£50,000	7%	£3,500
Glenn Godcomplex	£100,000	10%	£10,000

Of course in the real world, they have to pay commission, so they don't realise this amount of profit. To calculate their net profit, we need to look at how commission is calculated. We only pay commission on our winnings, so we need to look at how much winnings we have in each case. This will depend on the odds at which we bet. At short odds we will expect more winners, on each of which we will pay commission. If, on the other hand, we are betting at longer odds we would expect fewer wins.

If we take the generic case, we can assume we have X% winners, which means we have (1-X)% losers. If are betting at decimal odds of Y, our returns, pre-commision are given by:

Returns(no commission)= (X)(Y-1)-(1-X) = (XY-X-1+X)=XY-1

When we add commission, we have to pay commission of Z% (the commision rate) on our winnings. The equation above becomes:

Returns(with commision)= (1-Z)(X)(Y-1)-(1-X) =XY-1-ZXY+ZX

Let A = Returns with no commision, and B = Returns with commision

Our effective tax rate = 1-B/A = 1-(XY-1-ZXY+ZX)/(XY-1) = 1-1+(ZXY-ZX)/(XY-1)

= ZX(Y-1)/(XY-1)

This means that our effective 'tax rate' will depend linearly on the commission rate - i.e. double the commission rate means we pay double the tax. You might be thinking - "so what - I already knew that!".

"He is in fact paying 17.2% tax on his profits at a 1% commision rate, when betting at evens."

Well, maybe you did - maybe you didn't, but it is instructive to see just what that tax rate is. Lets take our example of Dave Disciplined above. He is in fact paying 17.2% tax on his profits at a 1% commision rate, when betting at evens. Were he to go t0 long odds, e.g. 10/1, he would be paying 31.2% tax. The implication is that if he was to transfer his business to a higher commission exchange (e.g. 3%) he would be making hardly any profit at all - he'd be paying 93.6% of his gross profit in taxes (i.e. commission) to the exchange operator!

The graph below shows the effective tax rates for EACH 1% commission, at various values of edge (the edge being calculated in a 'fair', i.e. 0% commission, market):

Conclusions

The above graph has a logarithmic scale, so values at the high end (i.e. above 10% are more compressed, e.g. the value for the effective tax rate when betting at 10-1, with 5% yield is approximately 20% FOR EACH percentage of commision paid. Thus, betting at Betfairs current maximum rate on most markets (5%), would result in almost no profit!

It looks like Ernie Eke-Outaliving might have to do more of his business at BackAndLay if he wants to stay afloat! Even Glenn will think twice about betting his long-shots at Betfair if he realises he is paying about 45% tax!