Quote:

**Makbeth**:

Okay. Here is a brief explanation, but the most I am willing to type out without explaining it on the telephone. I'm not being paid, after all.

You may look at balancing in two different mathematical ways, as an arithmetic selection process or as a geometric one. An arithmetic process assumes that each pick is of equal value; i.e. the fourth pick is as important as the 7th pick. A geometric one assumes that each pick becomes increasingly more important than the last. This selection process is somewhat geometric because of the knowledge each player gains as a choice is made. Should team 1 choose five physical DPS players, team 2's last player would likely choose someone with the most armor. This is what we call a "real life" version of an exponential advantage. Lucky for us, both schools of thought (arithmetic and geometric) have the same outcome here.

Quote:

**Makbeth**:

You *must*, in any game theory model, assume each pick's quality is equal. That is to say, each champion is exactly balanced. I'm doubtful that a mathematician is proofing your balancing, but nonetheless we will assume it to be as true as humanly possible. As such, the first pick *is not an advantage*. Any player selecting a champion randomly will be as equally successful as a person who really really really really wants to play a jungling warwick (something I hate Riot for, by the way!). The last pick, therefore, has the absolute most value.

I think there are several logical flaws in how you are thinking about the draft that lead your game theory premise being incorrect.

The first is that you are trying to apply game theory to the real world. While game theory can be illustrative it comes with some inherent weaknesses. The prime of which you summarize quite well saying 'You

*must*, in any game theory model, assume each pick's quality is equal.' While that may be true (I disagree though, unbalanced options appear in

**many** forms of game theory) it assumes that simply because game theory says so that the real world will conform to those rules as well. Which brings me to the second flaw.

The second is that you are not treating the champions as having inherent differences, or to be more precise 'Champions are not fungible'. Even in a perfectly balanced game (which is an impossibility in this genre) the capacities of individual champions will suit them more to different roles. Thus unlike rock, paper, scissors there is an intrinsic reason to value one balanced champion over another. Which in turn leads to the ultimate failure in your theory.

The third is that you are only considering the draft in terms of countering the opposing team. However you will also be choosing picks for the strategy your team is pursuing, balanced composition, and player talents and preferences. This gives 4 different basis for making selections and if your team focus' on one it will be detrimental to your success.

First pick strongly benefits from being able to serve those alternate reasons to select a champion. Additionally it can potentially grant the team the ability to prevent the opposing team from accessing three champions, rather than just their two bans, due to the exclusivity (assuming you want that 3rd champion yourself).