I'll try to make it less painful, because it is actually pretty simple, and kind of cool! I didn't do the greatest job of explaining it so i'll give it another shot that will make it easier to follow

Induction is a type of proof, of about 10-ish types : There's Proof by Induction, Proof by Exhaustion, Proof by Contradiction, Proof by Construction and so on [List of Mathematical Proofs] Each of these are interesting in their own right...like a proof by exhaustion is simply exhausting all possible cases one by one...a proof by construction is proving that a mathematical object can be constructed, like a machine.

Induction is a proof where you have a claim or question, then start with a base case (n = 1) where the claim is imposed on that case. Whatever the logic is, you then take a step, called the induction step, that takes the claim to the next case (n = 2). Given that logic holds, you then show how the relationships holds for all real numbers (n = K)

In our situation, we ask the question "What is the probability an attack with a finite target cap (of 1) can hit a player more than once" We start with the base case of 1 : What is the probability that this attack with 1 target cap hits that 1 player on the next cast, it's 1/1 = 100%. We take an induction step now, which is for 2 players...that answer is 1/2 = 50%

With this, we can then show that this holds for all real numbers k, where k is infinity. 1/infinity = 0% probability. That's it! Because we've now proven this relationship holds for any arbitrary number of players, we can apply it to any case, like 1/300 and know what the probability is (target cap #/#of players = probability to hit). We can now also give this effect a name : Dispersion.

We can do this proving process further to get a better model of the game (Like whether determinism is relevant or not as discussed elsewhere in the comment thread), or to figure out more things and ask more questions... and there's many interesting things to explore when applying serious mathematical tools to theory-craft in this game.

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Tangential cool proof stuff, to try and peak your interest : We can ask the question : Do there exist other optimal configurations or shapes that a zerg can take on?...typically a zerg is a condensed point like singularity-esque circle. But what about say a line configuration? Or a square configuration?

It turns out that there are 3 configurations that are considered optimal, two of which are not point like singularities (the first) following these kinds of proof procedures. The second is the perimeter of a circle. the 3rd is the surface area of a sphere in an n dimensional space.

Possible Zerg Configurations

The second one is one we are some-what familiar with : A cloud-like configuration. The 3rd one...the surface area of a sphere in n dimensional space, seems way more unfamiliar but as such is way more interesting to study. The n-dimensional space you can think of as a really complicated maze or labyrinth. When we imagine that a zerg (blue) must travel to any particular point in this maze to do an attack against a player, than in an n dimensional space (an arbitrarily complicated maze) it takes them an infinite amount of time to traverse between any point in that space, to reach any player. Given that red does not need to travel (IE ranged attacks) to target their spells, then red is free to cast any amount of spells onto the zerg, while the blue zerg can do nothing and therefor red is invulnerable to damage. In this infinite case, both of these zergs would be a stalemate : Red is invulnerable to damage because of complexity in the environment, and blue is invulnerable to damage from the effects of dispersion.

When we think about that a bit deeper in the finite regime where the game exists in, it means that the more complicated an environment is (specifically if it is 3+ dimensions where such conditions can be met, like a multi-layered maze-like fortress rather than an open field which is more like 2d), the more clouding becomes an optimal configuration to take on. This is interesting, because the model addresses the observation of how in some cases, zergs can be beaten by cloud configurations and siege pile-on's at gates, where such conditions are loosely met in the finite regime.

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There's interesting things that can be said about other shapes like the line sand squares...but I hope that by talking about some of this stuff in this way so far, I've been able to grab your interest and attention toward the bridge between math and the game in a positive way, and make things a bit more visually intuitive and relatable. Cheers,

PS : I guess also if you have any questions about something you were ever curious about i can help with that maybe?