# Mathematical Connections to Wrestling

March 12, 2009*Preface: I have been working on this article for some time now and have put a lot of thought and effort into it, so I hope it makes for enjoyable reading.*

*If anyone reading this has any mathematical understanding, feel free to comment on whether you think what I have written makes sense. If you don't know too much about mathematics then don't worry, I hope you will follow anyway.*

*Following the relative success of this article I began a series, next examining Biology and Philosophy. So if you enjoyed this, I have created links so you can find the others.*

I have studied mathematics for quite some time now, and wondered if I could blend my knowledge of it with my passion for wrestling and discover some mechanical undertones embedded in the wrestling world.

I remain undecided on whether or not this article will work, as most will see no direct link between mathematics and wrestling, but I hope you find my connections interesting.

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**Surviving the fall**

*I will start off easy, with hopefully something a few of you may have noticed already.*

Ever wondered how a wrestler falls from such great heights and remains comparatively unharmed? The answer lies in mathematics.

Two key tactics are employed by a wrestler when falling to ensure that they keep the impact sustained by their body to a minimum:

The first is to equally distribute as much impact over their body, without risking injury to vital areas.

When a wrestler lands from a high-impact move, they try to make their arms, legs, and entire back hit the mat at the same time, reducing the force exerted on one area.

Think of what would happen if you applied a certain force to your skin using a pin. The pin has a small surface area on its head, and could easily break the skin.

Apply the same force but using a bottle top and there is seemingly no affect. Due to the comparatively large surface area, it can easily dissipate the force.

This stems from the definition of pressure: **P = F / A** (P = pressure, F = force, A = area.)

For a given force of an impact it is reasonably easy to see that as the area increases, the pressure decreases (as the denominator in the equation is increasing, it would be like going from a half to a third, for example.)

The second tactic is to increase the amount of time the wrestler has force applied to their body, to reduce the force applied at a given time. This can either apply when falling onto another wrestler, or going through an object.

When a wrestler falls from a high height, they gain momentum due to gravity, and this unavoidably is going to be stopped by something.

The equation **F x t = Δp **directly applies in this instance (F = force, t = time, Δ = change, p = momentum.)

For changing a given momentum (e.g. the momentum of a wrestler falling), the force applied is inversely proportional to the time it is applied. Ergo, increase the time, reduce the force.

Examples of this are the receiving wrestler putting his arms up/down to cushion the impact, or even being put through a table. Yes, you heard me right, a table.

Contrary to what the professional wrestling world will have you believe, a table actually lessens the impact received by wrestler. Tables are designed to break, and thus absorb some force without doing damage. In all notable respects, they are effectively crash mats.

Wrestlers spend a lot of time practicing, making sure they can effectively use techniques like these to keep as safe and injury free as possible. This is why it is advised never to try it at home.

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**How the brand extension affected possible feuds**

*This next segment has a pretty sound connection with mathematics, and applies relatively justly. However, due to the nature of some wrestlers (e.g. some may have reason not to feud) there may be some potentially negligible in-built error.*

Before the brand extension there were roughly 60 superstars all completely within one large roster. Following the 2002 draft there became two completely separate brands, across which no wrestlers could seemingly feud.

I have often noticed people within the Internet wrestling community discussing whether or not unifying the brands would open up more possibilities for feuds, so thought I would answer the question.

There is a function known in mathematics as the ‘**choose function**’ or ‘**nCr function**’, which has roots in binomial coefficients, which can effectively solve this problem.

The choose function in this instance can, for a given n-element set (n being the number of elements, in this case wrestlers on a roster), find how many ways we can uniquely select two different wrestlers.

In establishing this number we can then see that each of these pairings resembles a feud, and my goal is to establish which of the two roster configurations (pre or post draft) yields the most possible feuds.

Pre draft, we had 60 wrestlers in one roster, which according to the choose function leaves **1770** (60C2) possible feuds.

Post draft there became two brands, each with 30 superstars. Again, the function can be used to determine that on each brand there can be **435** (30C2) possible feuds. As there are two brands the total number of feuds will be **870**.

So by splitting the roster the WWE more than halved the possible feuds they could have.

The same result applies in reverse, meaning that if the WWE did merge the rosters they would increase the number of possible feuds by a factor of approximately two.

Although this seems to imply that unifying the brands would create more feuds, in essence it doesn’t. A wrestler can only feud with so many people a year, and with the almost yearly draft things are always being shaken up.

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**Popularity**

*This next one doesn’t really have a direct link to mathematics, but some areas in mathematics do have similarities in terms of growth, or in this instance for popularity.*

No matter how hard some promotions try to push some wrestlers it never seems to work. Then other wrestlers become instant successes without much effort at all, but why?

For the past few days, I have pondered many different models from population mathematics in biology, dynamical systems, and other areas to find the best way to describe the quantitative popularity of a wrestler.

After much deliberation, I picked out some elements that could explain popularity of a wrestler, which I hope you can follow.

One system used in modeling, is that of many predators, vying for some either limited or dynamic food source. In this instance I consider the predator to be a wrestler, vying for popularity.

This comparison may seem unrealistic, but essentially works on the same basic principals. The main element of this model is that if another predator’s population increases, there are fewer resources for you acquire, and hence your population decreases.

This applies to the wrestling world as well; if there are no popular wrestlers, odds are that some recognition will come your way, whereas if there are many liked wrestlers on a show, it will be harder to gain a reputation.

The other key contributing factor that helps a population grow is time. Given the right conditions a population will flourish, but it won’t happen overnight.

In the wrestling world it may take someone years to become accredited at what they do, and to receive the adoration of the fans. Either way, the longer a wrestler is around, the better chance they have at achieving success.

These two variables aside, there is one other consideration that usually occurs in most models. These are certain parameters, which usually rely solely on the individual predator, which affects growth proportional to population and time.

In wrestling terms, these can be characteristics like skill, appearance, association with other popular wrestlers, championships held, and several other factors.

Similarly to the population or predators, some wrestler can be given the perfect conditions to thrive. But good conditions alone won’t garner you popularity, it’s usually down to the wrestler themselves if they are to make it or not.

There is not a lot of point in explaining the equations behind these results, but the same conclusions apply. It is hard to make an effective comparison like this, but I hope you understood it.

Mathematics may not be a subject that most consider on a daily basis, let alone in wrestling, but it does affect almost everything we do. So for me to discuss these connections has been fun, but challenging, and I hope you have enjoyed reading and thinking about wrestling from a slightly different perspective.

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