"Entropy" in Fantasy Football League Compare playoff structures of two leagues. One (League A) in which we add divisions (where the top finishers in a division move on to the playoffs based on overall-record) and the other (League B) where the playoffs are determined by overall-record compared to the entire pool of teams.  Does League A have more entropy (randomness) of the final outcomes relative to League B?
My intuition says "yes" because it brings more parity to the league, but I'm not sure if I'm understanding parity/randomness/"entropy" correctly (i.e., does this actually flatten everyone's chances of winning to look more like a uniform / max-entropy distribution, or are there points that I'm missing).
Maybe "entropy" is the wrong word, and if so, could someone explain my misuse?
 A: League A does have more entropy.
In the Boltzmann equation for entropy: 
$$S=k \ln W$$
$W$ is defined as the "ways" or complete set of possible configurations of a system. While Boltzmann used this for the kinetic theory of gases we can make the natural extension to the configuration for both of the leagues.
For League A, we have to configure the league into different divisions. The "ways" to do this is a fundamental combinatorial problem. We have $N$ total players in the league, $k$ players in each division and $m$ total divisions:
$$W_{LA} = \frac{N!}{(k!)^m}$$
Where $W_{LA}$ is the ways to arrange league $A$. Determining the number of playoff teams is simple. The top $j$ players from each division are given a playoff spot then the total number of playoff combinations is:
$$W_{PA} = {{k}\choose{j}}^m$$
The total "ways" the league can end the regular season is then the product of the two:
$$W_A = \frac{N!}{(k!)^m}{{k}\choose{j}}^m = \frac{N!}{(j!(k-j)!)^m}$$
For League B if there are $N$ players and $j$ playoff spots, the total possible regular season endings are:
$$W_B = { N \choose j}$$
Clearly there are more configurations for League A.
I've also created a qualitative picture to show you how many "ways" there are to configure both leagues.

I used a natural fantasy football setup where I tried to keep division size greater than 3 teams and the same number of playoff teams in both leagues.
In a Maximum Entropy sense, because this is an unconstrained problem and have no more information, this problem would match the Laplace "Principle of Indifference" which simplifies into the uniform distribution.
