Shake It Up — Monte Carlo Simulation in Sports

In my last article of the “Shake It Up” series, I will apply the statistical approach to a different domain: the world of track and field.

TL;DR — In the Shake It Up series I have explored implementing Monte Carlo simulators using standard Google Sheet functions. My attention was mostly given to project delivery, but Monte Carlo simulation is more than that, and so in this article I am using it to help me predict the best formation of a 4x100m relay team.

1. I start by introducing the relay selection problem in track and field
2. I explain how Monte Carlo simulation can help
3. I explore the various profiles of interruptions that will impact the overall relay performance
4. I devise a question which can be partially answered by the simulations generated

If you want to catch up with the Shake It Up series, here are the articles:

1. An introduction to Monte Carlo simulation
2. A first attempt at building a Monte Carlo simulator using Google Sheets for project burn-downs
3. An improvement by simulating things that can go wrong to the simulations
4. A prototype for boosting the number of permutations generated that feed into the Monte Carlo simulator

The journey we took in this series was one that exposed us to the various mechanics that can make a Monte Carlo simulator an effective tool for forecasting and decision making.

One article at a time we saw how we can build a simulator that creates a forecast for project delivery, an application important in contexts I attend as a coach in the software engineering world. Consistently along the way, my approach was to decompose the event being simulated, i.e. the trajectory of a project, into variables that we can then shake up with random values based on the understanding of those variables’ behaviors.

A few simulators into the experience I was left with a question that kept knocking on my mind:

Was this an adventure into appreciating the geek side of Monte Carlo simulation, or was it a challenge to unlock the value of a statistical approach to forecasting?

Hand on heart I feel that I wanted to satisfy both 😅, though I know that in my efforts to explain the mechanics of the simulator I might have gone into some serious technicalities.

To put my conscience at rest, I wanted to dedicate this last article towards reusing some of the concepts I introduced along this series to build another simulator that does not pertain to the world of project or product management.

Sprint Relays — Simulating Teamwork

While typically an individual sport, track and field also has its team-oriented variations, the most popular of which are the relays.

Relays come in various shapes and formats, but the most common ones are the 4 x 100m and the 4 x 400m relays. The basic premise in relay events is that all members of the team participate in covering a distance in the fastest time possible. One athlete at a time, the athletes cover a portion of the distance (in 4x100, it’s 100m, in 4x400 it’s 400m) passing on the baton to the next athlete when they finish their part.

The 4 x 100m and the 4x400m relays have one major thing in common, that is the way the baton is passed on between the athletes (an activity referred to as changeover). While in my experience as athlete, coach and sport enthusiast I have seen 4x400m changeovers failing badly, it is typically in the 4x100m relays that coaches seek for the lowest risk and highest reliability of the changeovers when selecting the team.

As counter intuitive as it might sound, it is not always the fastest 4 that, combined, can make up the strongest relay team.

Why Monte Carlo?

In this article I will keep my focus on the 4x100m relay, although I am pretty sure that with minor alterations the outcome can also be a good tool for other kinds of relays.

The challenge for coaches selecting a 4x100m team is to find the combination of athletes that provides the highest confidence in running a desired time.

Typically, coaches would have the following data at hand:

1. A history of timings for the individual athletes over the distance.
2. An observation of consistency of changeovers between the different permutations of the athletes.

The first is very straight forward. Whether in personal journals or official results repositories, historical data is available nowadays more than ever.

As for the second, my next question was: How can I translate an observation of consistency into tangible data?

Perfect, and Less Perfect

I briefly researched the topic, and found this article by Jimson Lee. Basically, Lee gives a formula that alters the individual timings into a potential time for the relay. One key detail, however, is that Lee assumes perfect changeovers. Perfect changeovers, in Lee’s assumption, will only cost 0.1s to the team.

I trust Lee’s experience in the topic knowing that if I had to build a tool for myself and fellow coaches who work with lower tiers of the sport perfection cannot be the obvious case. At times, not even top-most teams manage to execute perfect changeovers. Somehow I needed to model less perfect changeovers.

My changeover losses profiles depending on the confidence observed

I therefore decided to create four levels of confidence:

• Perfect
• High
• Fair
• Low

Each of these confidence levels were backed by a numerical distribution. Ideally, this is a smooth probabilistic distribution but in my prototype I decided to model the shapes of the distributions myself. I looked at some recent performances in my local circle of athletics and listed down some numbers and patterns. The numbers I ultimately chose are to an extent arbitrary, but these can be improved.

In an attempt to make it even more adaptable, I even created a variable for team experience (Pro, Advanced, Low) that would shift all numbers to slower or faster levels. The variant here is not changeover proficiency but experience in the sport.

Making the Dream Work

I liked the simplicity and elegance of Jimson Lee’s approach. In essence, assuming a 1 second gain for those runners not starting from the starting blocks (and therefore not running a conventional 100m, but what is called a flying 100m) and adding a minor penalty for the changeover (which I have explained in the previous section).

This was the formula that would sum up all the random numbers, i.e.:

SUM(individual times) — 3s + changeover losses = Simulated Time

The Golden Question

With all the setup ready, my next step was to make use of the numbers.

I could have taken 2 approaches. The first approach would be to give an 85% confidence timing, like I did with projects. The problem with this was that in this case we don’t want safe confidence. In other words, if I’m coaching a world-class team I would not be interested to see whether the team can run a middle-school standard time. Competitive teams would be goal driven.

My real question, and the second approach, would be:

What are the confidence levels for this team, in this order, to run a given time or faster?

The big question...

Coaches and technical directors typically would know the competition level and the usual podium times. With this approach they can test how likely their current selection would make the cut (whether with the top 8, top 3 or even top 1).

I decided to take this approach.

Coaches using my simulator would just need to enter a time, and the simulator would quote the confidence of that team hitting the given time based on the generated simulations. All of this would be done preventively, allowing coaches to test multiple scenarios and focus on improving those changeovers that can really make a difference on the end result.

Conclusion

In this article I have shared my building of a 4x100m relay time simulator using Monte Carlo simulation concepts and Google Sheets. The ideas of my approach were inspired by the ideas I explored in the series on the topic of simulation which I named Shake It Up.

This article also brings to an end the series. If I had to condense all the lessons learnt into a single sentence, whether using Monte Carlo simulations for projects, cycle times, investment portfolios or relay times, the biggest lesson would be the following:

Think of ways how your prediction can go wrong, model the behaviour, and randomly shake it up.

Let me know in the comments 💬 if you enjoyed this series or would like to learn more.

Matthew Croker is a Team Process and Data Coach, specialized in the software development industry. Through his work he helps teams within companies focus on learning how to work best together by analyzing their data, simplifying the setup of processes and creating habits that boost their productivity.