Everyone has their own fantasy, I suppose. And I shouldn’t tread on someone else’s dream. But I have to admit that very few of my feverish imaginings feature Carlos Tévez.

And there’s another thing. Even if creating fake teams on paper and entering them into competitions is your thing, I strongly advise against employing reverie to select your side. Instead, as you would expect, the Fink Tank advises the use of statistical techniques and a computer.

The new Times game, PlayTheGame, has been designed to be as close as possible to a realistic football management exercise. In particular, each player can belong to only one team. This makes the game much closer to the real thing. It also makes it harder to crack.

Other, more straightforward fantasy games rely on two things. The first is a formula that it is possible to hack with a computer. The second is luck. Our statistical work suggests that these components are about half and half.

Anyway, Dr Henry Stott, Dr Ian Graham and Richard Berriman have been taking a look at The Sun’s Dream Team game because it has big prizes and is well put together.

The first step was to look at the player data for 2007-08 and the value given to each player for the game at the beginning of the 2008-09 season. We wanted to know the relationship between this data and the number of points these players added last season. If we could work that out, we would get a formula relating all these variables to outcomes, which could be used to select an optimal team for this year.

As you might expect, the value given to each player at the beginning of last season was strongly related to their performance during the 2008-09 campaign. These people knew what they were doing. But if there weren’t weaknesses to exploit, the game would hardly be worth playing.

The main thing to look out for is something I have warned you about before — reversion to the mean. If a player does particularly well at, say, scoring goals in one season, there might be one of two reasons for it.

The first is that the player really was better than you thought; the second is that the player had some luck, scored more than their real skill dictated and in the next season will revert. In other words, go closer to or even underperform in relation to their real long-term average.

So The Sun values overestimate goals scored and clean sheets kept. Among other things, our model adjusted for that.

Once the formula was in place, predicting the points from each player for the coming season, the next step is to look at value for money. We looked at each player in turn and got a “value for money 11”, the players who we expected to gain the greatest number of points per pound. Ricardo Fuller, Nick Barmby, Dave Kitson and Titus Bramble all featured.

This led to the final stage. To go through each player in turn, replacing them with players in their position who would add more points and were next best in terms of value for money. This was done until the optimal team was reached costing £50 million. England fans might like to note that Frank Lampard and Steven Gerrard make the cut.

You are not stuck with this team, of course. If you do an exercise of this sort and find that some players are, say, injured, you can do a little manual adjustment. The graphic below gives an example. Once you have done that, you have an optimal team. The rest is luck.