We now interrupt your normally scheduled viewing for this unimportant math lesson.
As has been mentioned previously, I spend a substantial amount of time playing World of Warcraft (WoW), Blizzard's MMORPG. More than anything else, I like playing with my friends. However, as is especially the case with friends who have a very limited amount of time they can play (or only use a single character), sometimes they play without me (I play on many chars, so it's rarely a problem the other way around). For catching up, I've developed a strategy, one that has left two of my friends with blank (uncomprehending) stares, thus far; so, I'll explain the math behind it, here.
First, let me give a brief summary of the relevant features of WoW, for those who haven't played it:
- Enemies near your level give experience (XP) when you kill them
- When in a party, XP for kills (only kills) is divided by the number of players in the party
- Quests come in many shapes and sizes; kill X number of Y, and collect X number of Y, where Y drops at some frequency from enemy Z are two examples
- Quests give XP when you complete them
- Each quest can generally only be completed once per character
- Thus, quest rewards are not a good way of playing catch-up, as the person you're playing with will have to do them in the future, and you won't have gained anything
- Grinding (killing enemies without any purpose other than to get XP) is boring
So, here's my strategy: when playing catch-up solo, do quests that require collection of items that drop off enemies. If you think about it, you can imagine the reasoning for my friends' skepticism: if you have to kill Y (the number of people in the party) times as many enemies, each giving 1/Y XP when in a party, shouldn't that mean that you get the same amount of XP doing the quest solo as when you do it in a group?
No. And here's why. While it's true that you will get the same amount of XP from the enemies when you do the quest, remember that the people you're playing with still need to do the quest. If you tag along with them, not only will you get the XP of when you did it solo, but you will also get a proportionate share of the XP from the party (100% * XP + 100%/Y XP). And by doing so, you decrease the amount of XP the other party members get, proportionally (100% * (Y - 1)/Y XP). This comes out, for example, to a 150%/50% (% of the amount of XP for doing the quest solo) or 3:1 split between you and your companion, if in a group of two (166%/66%/66%, 5:2:2, for three, etc.).
And on a completely unrelated note, there's a term in psychology called the hindsight bias. It describes the tendency of people who know the solution to a problem (especially in the case of nontrivial problems) to think that the answer was unavoidably obvious, even when the problem is difficult enough that it is likely that they themselves could not have solved it. Also known as the "I could have told you that" syndrome. A prime example of this is the media and others' response to the "intelligence failures" that prevented the 9/11 attacks on the World Trade Center from being stopped, despite the previously obtained evidence that the attack was coming.