Let's get a baseline by looking at the conditions that are the most favorable to hopping. Let's assume a hopper has his choice of an infinite number of pools that have no defenses against pool hopping. And we'll assume no pool fees.

Now the ideal hopping strategy would be to get the first share after a block has been found for a pool that divides the block reward among those who have contributed shares towards that block. With an infinite number of pools, he can always find a pool that has had no shares contributed since it last found a block. (This is, of course, an unrealistic assumption. The point is to show the best a hopper can do.)

Note that if he finds a block in his hash, he gets the *full* reward! Since he is submitting the first share to a pool after it has found a block, if a block is solved, he is the only one who gets any shares. Hence he gets the full reward.

Now, consider this -- if the next share submitted finds a block, the hopper gets half the block reward. So for every share he finds, he not only gets the full solo reward, he gets an additional, equal chance at 50% extra. The next share submitted to that pool also has the same chance of solving the block, and he would get 33% of the reward.

You can't simply add these percentages though, because each event is not a certainty. However, under realistic conditions, the first share submitted to a proportional pool after it has found a block is worth several times the average share.

Of course, in reality, there are not an infinite number of pools and pools do have a fee. Also, a hopper has to choose a work unit to process and then won't have a share for some amount of time later -- during that time, the picture can change. And in general, a pool won't tell you exactly how many shares it has, so you have to estimate based on its estimated total hashing power and its announced blocks.

It's hard to make a model that tracks the complex real-world interplay of pool fees, fixed numbers of pools, and different pool payouts. However, hoppers I've spoken to have reported incomes 20%-35% above baseline. The best mathematical models we have predict 25%-30%. See this article on pool cheating.