Recently there has been a good deal of discussion about how gear will be handed out in 10-player and 25-player raids in Cataclysm. Blizzard representatives have waffled on the issue a little bit, which is natural since they are still in the alpha and things could change dramatically between now and release. We know that 10- and 25-player raids will give the same loot, but the goal is that 25-player raids will be more efficient in gearing up the raiders to reward the extra effort of organizing a larger raid.
How can this be accomplished? One suggestion is to have 25-player bosses drop more "badges" to buy gear with, another is to have 25-player bosses drop slightly more loot per person but with the same loot table.
What is ignored in this discussion is that 25-player is more efficient than 10-player at gearing up the raiders with precisely the same loot per boss. Intuitively this is actually pretty easy to understand. Suppose you live in a simple raiding world where a boss can drop five different items, you want one of those items, and you can fight the boss by yourself. Each week you have a one in five chance of gearing up. Suppose instead you have to fight the boss with four friends to defeat it, but the boss drops five items, rolling on its loot table five times. Assuming that your friends want different items (or that some of your want different items at the very least) you can now hand the loot out to the people who need it. If the boss drops item 4 and you want item 2 then at least someone gets item 4. And when you go back next week you know that you have five chances at item 2 and if it drops you get it because the other four people don't want it.
That's a very simple example, but it shows the principle. If we got a roll on the loot table for everyone on the server and then handed out loot to people who need it, almost everyone would get what they wanted, and those who didn't would be virtually guaranteed of getting it the next week.
How does this work in practice? Well, raid loot is pretty easy to simulate. Here is the gearing progress for 10- and 25-player raids fighting bosses that drop 1 item per 5 participants, 12 bosses a week. Tanks are selected randomly from all tank specs, same with healers and dps. 10-player raids are 2 tanks, 3 healers, 5 dps and 25-player raids are 3 tanks, 6 healers, 15 dps. There is one of each type of item in the mix (1 mail shoulder with intellect and another with agility, for example) and the chance of each item dropping is proportional to the number of people who can use it (there is five times as much plate itemized for dps than there is for intellect, for example). Finally, I assume there is only one useful trinket available to each raider despite having two trinket slots (this is how things seem to always work). These assumptions are not what the reality would look like, but they work to show how the curves look. Here is 8 weeks of raiding:
For reference, the bars show the number of shards per raider. Of course because the 10-player raids have less useful loot they have more shards per person. The percentage shows the total percentage of slots filled in the raid. Each person has either 14 or 15 slots, depending on whether they use items in both hands or use a single two-handed weapon.
So after 8 weeks, 70% of 10-player slots are filled. That means the typical 10-player raider has 10 or 11 pieces of gear, leaving 3 to 5 upgrades left in that raiding tier. After the same amount of time a 25-player raider will have 12-ish pieces of gear, meaning they need 2 or 3 more upgrades.
Here's the same chart for 15 weeks of raiding:
You see that both 10-player and 25-player raids are plateauing at this point. Extended infinitely both would tend towards 100%. But for realistic length of time, 25-players raids will tend to gear out their raiders about 95% of the way while 10-player raids will only tend to gear out raiders about 90% of the way.
So 25-player raids don't need more "badges" or more drops in order to gear up more efficiently. They gear up more efficiently by just rotting less loot. In fact, even if 25-player raids get less loot per person, they can still come out on top. This is 15-weeks of raiding with only 4 drops from 25-player bosses:
On this chart we see that while the 25-player raid starts out pretty even, it pulls ahead as time goes on.
What we have here, then, is really a problem with innumeracy. People want there to be an incentive to raid 25-player because it is harder to raid 25-player. Finding nine friends you like to play with or nine people who are really pretty good is not nearly as hard as doing the same thing when nine becomes twenty-four. It turns out, though, that if we actually understand how the math works out, that incentive exists with the same rewards per person for both raid sizes.
What should the developers do with this information? In a perfect world I'd say set the drops per boss and "badge" rewards to the same per person for 10- and 25-player raids. In reality, the amount of time they would spend explaining why this makes 25-player raids more efficient is probably pretty prohibitive, and their current plans of giving more rewards to 25-player raiders is probably the better one from their perspective, even if it is a tragedy from mine.