Intro

In this post, we break from the conventional realism and consider a fictional alien planet called “USA” (pronounced “Oosaa”). Their culture is heavily influenced by an appreciation of probability through wagering on sports outcomes. The sport in question has been called “gridiron”. It is magistered by the “NFL” (pronounced Nifel), and consists of transporting a ball (a prolate spheroid object) to a region, while an opposing team tries to accomplish a similar task. During a critical maneuver called the “downfield pass”, the ball is airborne, and players arrange themselves so as to maximize strategic advantage.

This post focuses on predicting the future positions of players during the course of a downfield pass, utilizing player data.

Motivation

Jokes aside, sports betting is becoming ubiquitous in our lives, and as such, warrants some consideration. Even if you refuse to participate, you may find yourself working for a casino/betting house/market-maker. Alternatively, you could be working in a trendy start-up where app features are gamified (random reinforcement, see B.F. Skinner) to increase user satisfaction (stimulus addiction). Regardless, sports offer a controlled environment with clear rules, copious data, and rapid feedback, unlike business, where tax laws, KPIs, and incentives are opaque and dynamic. As a result, industry “specialists” often fail to establish clear links between operational metrics and business outcomes (If you don’t set clear targets, your boss can’t fire you for clearly failing to reach them.).

I hope this convinces the reader to play along with our aleatoric antics.

Method

In a bid to post more often, I am shrinking the scope of my posts; as such, there is no prediction in this one. Instead, I foreshadow two approaches. The first is based on classical mechanics, using only player position and movement data to extrapolate future movement. The second is blind pattern finding, by means of some gradient boosted learner (I have yet to decide). The former is solidly supported by well-established physical laws, but ignores the strategic nature of player actions. The latter hinges heavily on data and carries the potential to capture complex movement patterns.

Here is an animation of a single play (without proper axis labels or legend):

Conclusion

Sport betting and gambling in general receive widespread condemnation for draining resources and ruining lives. This moral grandstanding obfuscates the actual problem: unbridled human passions and statistical incompetence. It is easy to stand on the sidelines and cast insults at those in the arena, but ultimately, we are all subject to probability. Every choice we make is a wager based on our expectation of the future. Whether it is wealth, health, or happiness, nothing but death and taxes is guaranteed.

If the probabilities are keeping you up at night, consider hiring the MathMerc.