What you're asking is related to probability theory. It's easiest to work with one reel, and then extend it to multiple reels once you understand how it works.
Consider if you had a reel you have some symbols which you want to assign to the stops. More symbols on a reel will lead to greater control over the final results, but will feel more random to the player. The goal is to balance the number of symbols and stops so the machine feels less random to the player, and like they have more of a chance.
If you had 10 symbols and 10 stops, each symbol would have a 1 in 10 chance of appearing. It doesn't matter what order the symbols are in (in theory, in practice the randomness of the game is only as good as your random number generator). In other words, you might expect to see 10 different symbols in 10 spins, or a different symbol on every spin. The chance of getting one particular symbol is 1 in 10. So for every 10 spins, you can expect to see each individual symbol once. If you picked 1 symbol to be the "winning" symbol, the player would have to play 10 times before they won. With this information it's quite straight-forward to work out the payout. If you charge them $1 for each spin, they will have to spend $10 before they land on a win. If your expected rating is 95%, the calculation is $10 x 95% = $9.50. In other words, the prize for landing on the "winning" symbol must be $9.50 to have an expected payout of 95%. Now remember that this is all based on average. There's no guarantee that the symbol will appear in exactly 10 spins, it may take 100 or 1000 spins, or even just 1 spin to appear. Taken over a long enough time the machine will pay the correct amount on on average.
To getting this to work on multiple reels you need to multiply the winning probability of each reel. Consider an example of 3 reels with 10 symbols on each reel, and 1 winning symbol on each reel as in the previous example. Lets say you wanted the player to win only when all three reels show the winning symbol at the same time. To do this, you need to work out the probability for each reel, and then multiply the probabilities together. We know from the previous example that the probability is 1 in 10. This can also be written as 1/10, or 0.1. The probability of all three reels landing on the winning symbol at the same time is 1/10 x 1/10 x 1/10, or 0.1 x 0.1 x 0.1, or 0.001, or 1 in 1000. We see that there is a much lower probability of the winning symbol appearing on all three reels at the same time. The player would need to spin 1000 times on average before they win. If each spin was $1 they would need to spend $1000 to win. The calculation for the winning percentage then is: $1000 x 95%** = $950.00.
That's the theory in a nutshell. The rest is balancing balancing the different probabilities to make the game appear more interesting.
In your case, if you have 22 stops and 16 symbols. This means you will have 6 symbols which are the same as at least one other symbol. The exact probability of any particular symbol appearing depends on the total number of occurrences of that symbol on the reel. How many of each symbol is on each reel is really up to you.
As an example lets say you have 15 unique symbols, and 7 which are all duplicates. The chance of any one of the duplicates appearing is 7 in 22, or 7/22, or 32%. If you had 1 reel, at $1 a spin, the player would land on one of the duplicates 32 times in 100 spins. The payout is calculated as (1 / (32/100)) x 95% x $cost. So if it cost $1 per spin, you would pay the player $2.97 every time one of the duplicates appeared.
As another example, if you had 3 reels and it cost $2 per spin, you would work out the pay out as follows: (1 / (32/100 x 32/100 x 32/100)) x 0.95 x $cost = 30.5 x 95% x $2 = $57.95 payout. You can calculate the probabilities of the other non-duplicates as follows: (1 / (1/22 x 1/22 x 1/22)) x 0.95 x $cost = 10648 x 0.95 x $2 = $20231.20. That's quite a large number, but then the probability of any of the winning sequences appearing is quite low (it's roughly 9x10^-5).
In the last examples the differences are quite extreme, the player either wins $58 very often, or $20231 almost never, with no variation in between. The art of making the game engaging is in creating more opportunities to win with varying amounts. This is often accomplished by mixing reels with different probabilities. So instead of each reel having
the same number of each symbol, one reel might have more symbols, or more of one type of symbol, and so on. The formula for calculating the probability is the same as before, just remember to use the correct ratios for each reel. For example, if you have reel A with 22 stops and 3 occurrences of a symbol, reel B with 26 stops and 2 occurrences of the symbol, and reel C with 20 stops and 5 occurrences of the symbol, the formula would look like this: (1 / (3/22 x 2/26 x 5/20)) x 95% x $cost.
And that's all there is to it. Hopefully I didn't make too many mistakes in the examples so you'll still be able to find it useful :P
** A note on notation, 95% is identical to 0.95. 32/100 is identical to 0.32, 7/22 is identical to 0.31818.. etc.