The proposed changes to the UK National Lottery

Camelot, the operators of the UK National Lottery, have announced that the price of a national lottery ticket in the UK is set to double from £1 to £2 in the autumn (2013). The prizes are also changing. Currently the prizes for the Saturday draw are approximately as follows:

 

Match 3 balls = £10 (could be less but only under truly exceptional circumstances).
Match 4 balls = £60 (average)
Match 5 balls = £1,500 (average)
Match 5 balls + bonus = £100,000 (average)
Match all 6 balls = £4,100,000 (estimated)

Come the autumn these prizes will be:

Match 3 balls = £25 (could be less but only under truly exceptional circumstances).
Match 4 balls = £100 (average)
Match 5 balls = £1,000 (average)
Match 5 balls + bonus = £50,000 (average)
Match all 6 balls = £5,000,000 (estimated)

However a meaningful comparison of these figures has to take into account the fact that the stake has doubled. It is more useful therefore to compare the prizes as a ratio of the stake. So we have:

Match 3 balls current ratio = 10 new ratio = 12.5
Match 4 balls current ratio = 60 new ratio = 50
Match 5 balls current ratio = 1500 new ratio = 500
Match 5 balls + bonus current ratio = 100,000 new ratio = 25,000
Match all 6 balls current ratio = 4,100,000 new ratio = 2,500,000
 
Let's make it clear what this means by looking at matching 3 balls. Currently the stake is £1, the winnings are £10, hence the winnings are 10 * the stake, or a ratio of 10. In the autumn the stake will be £2, the winnings will be £25, hence the winnings are 12.5 * the stake, or a ratio of 12.5.

The important thing here which should concern people is how these ratios are going to change. We get the figures by dividing the new ratio by the old ratio. So we get the following figures:

Match 3 balls = 12.5/10 = 1.25
Match 4 balls = 50/60 = 0.83
Match 5 balls = 500/1500 = 0.33
Match 5 balls + bonus 25,000/1000,000 = 0.25
Match all 6 balls = 2,500,000/4,100,000 = 0.61
 
What this means is that for the number of balls matched other than 3, the prize money proportionate to the stake is going to go significantly down. Proportionate to the stake the jackpot prize will only be 61% of what it is now . The match 5 balls + bonus will only be a quarter (25%) proportionate to the stake of what it is now!

I assume that the 1.25 proportionate increase in the prize money for 3 balls will precisely offset the relative decrease in the prizes for 4 balls or more (since 3 ball prizes vastly exceed all other prizes combined). That is to say that I suspect that as a percentage the amount devoted to prizes will remain the same.

It seems to me that people predominantly play the lottery, not at the prospect of matching 3 balls and winning £10 (strictly £9 once the £1 stake is taking into account), but rather for that very small possibility of winning the jackpot, or at least matching 5 balls + bonus and winning a life changing ~£100,000. And given that lottery players tend to disproportionately come from those with lower incomes, one imagines that they want this small possibility for as small a stake as possible. If I am correct in this supposition then Camelot's proposals seem, if anything, largely diametrically opposed to these wishes.

I have therefore taken the liberty of emailing Camelot in order to express my dissatisfaction with their proposals. Within their response they state:

We know that players still love Lotto, but through extensive consumer research, they have told us that they want more ways to win more money. This is exactly what we will be introducing with the following changes to Lotto later in the year:

• More than doubling the bottom prize tier which is what players have said they want, from £10 to £25. This creates by far the most winners on Lotto on each draw.
• Increasing jackpots. £2.5 million on a Wednesday (£2.2m) and £5 million on Saturday (£4.1m).

I have no doubt that people have expressed the wish that the prize for 3 balls should be significantly increased. I also find it likely they expressed the wish to be able to win more money. Although peoples' motivation for playing is to win a life changing sum of money, in reality they realise that they most probably will only ever match 3 balls. So clearly they will express a desire for the £10 prize money to be increased. But I also strongly suspect that if it had been made clear by Camelot that such an increase in the smallest prize will be accompanied by a doubling of the price of a ticket, in addition to a relative decrease in the value of the Jackpot, and an absolute decrease in the value of the 5 balls + bonus and 5 balls prizes, then I'm sure peoples' reactions would have been somewhat less favourable.

But we shall see. Perhaps most people will welcome these changes with cries of delight. However I doubt it. Once it has sunk in that not only is the price of a ticket doubling, but that the relative amounts won relative to the stake for matching 4 or more balls is undergoing a substantial decrease, then I cannot imagine most people being happy.