Estimating quantities for redemption prizes
Estimating quantities for redemption prizes is a little tougher, but it's worth it! Again, I have an Excel spreadsheet I use, email me if you would like a copy. Here is an example of the basic steps I go through:
Estimate how many players will play each game. If your carnival is 180 minutes long, and you have a player every 30 seconds, you could have 360 players per game. The play time may differ by game, some may take longer or shorter. Do a reality check here  if you are only expecting 50 kids at your carnival, you will not have this many players!
Estimate how many total players you will have for all your redemption games. Multiply the number of players times the number of redemption games. If you have 10 redemption games and each game has 360 players, you will have a total of 3600 total players at these games.
Estimate the average number of tickets you will award to each player. This is a bit of a guess, but say if you give 13 tickets per play, your average will be around 2 per player.
Estimate the total number of tickets that you will give out. Multiply the number of total players times the average tickets they will win. In our example, that is 3600 players times 2 tickets to get 7200 total tickets.
Estimate how much money your redemption games will take in. Multiply the cost to play times the total number of players. For example, 25 cents per play times 3600 players means you will take in a maximum of $900. You now know that you want to spend less than $900 on the games and prizes.
Estimate the total number of prizes to order. Because you'll never come out even with the number of tickets and the number of prizes (the last person in line won't want the last item you have), you have to overorder on the prizes. I plan to be able to redeem about 1.5 times the number of tickets I give out. In our example, that is 1.5 times 7200 times to equal 10,800.
Estimate how many tickets total the average player will win. If an average player plays 10 of my redemption games and wins 2 tickets at each game, they would win 20 tickets total. Now this is the average player  a young player might only win half that, and an aggressive "ticket centric" player might win three times that. But now I know that most of my players will want prizes for around 20 tickets.
Estimate how much each redemption ticket should be worth in prizes. I know I need around 10,800 ticket's worth of prizes, so I can make a chart like this:
If I order 10,800 ticket's worth, 

And my prizes are worth this much per ticket,  Then I will spend: 
3 cents 
10,800*0.03=$324 
5 cents 
$540 
8 cents 
$864 
In our example, I know I need to spend less than $900 to make any money at all,
so I would make my prizes worth around 34 cents each. If you are ordering by
mail, don't forget to include the cost of shipping in your estimates.
Set your prize levels. In my example, I know that my players will win around 10 to 40 tickets each. I may want to have prize levels of 1, 5, 10, 20, 30, and possibly 40 tickets. Don't have too many levels or it makes it too hard for the players to choose a prize.
Decide how many prize choices to offer per level. I would suggest no more than three choices per level. Again, it cuts down on the decision time. At the higher prize levels, consider offering only one or two choices. Another benefit is that you can often get a discount by buying a single item in larger quantities.
Estimate how many of each prize to order. The general rule is to order the most in the lowest category and then decrease the amount for each level. I use my spreadsheet here, but this chart shows the basic idea:
If I need 10,800 ticket's worth of prizes, 

For this prize level,  I will order this many prizes,  To redeem this number of tickets: 
1 Ticket 
600 
1*600=600 
5 Tickets 
400 
5*400=2000 
10 Tickets 
300 
10*300=3000 
20 Tickets  200  20*200=4000 
30 Tickets  50  30*50=1500 
This would give me 11,100 ticket's worth of prizes, which is pretty close to my goal. 
Choose your prizes. This is the fun part! Go through catalogs and look for prizes that are close to your prize levels in cost. For my example, since I'm trying to stay around 4 cents per ticket, I would look for prizes that cost around 4 cents, 20 cents, 40 cents, 80 cents, and $1.20. Remember that you just have to average these amounts, you can go over and under as long as you come close. Have a few choices, your first choice may be sold out.
Check your work. After your carnival, take an inventory of your leftover prizes. Did you run out of too many items? Did you have tons left over? Write it all down for next year's carnival. This will help tremendously in the future.