13 Jul 2023

9 years worth of company foosball data analyzed

Nobody tell management

About 4 years ago I graduated from university and started my first job at a company. About two weeks into my employment I was asked to join a game of foosball (also known as table soccer or töggele if you care for some swiss german) by some colleagues. It was fun!

Anyway, so my career took off, I enjoyed the craft very much and developed some solid skills. I'd even say I made one or the other valuable contribution to the people around me and their success. So much so, that today I can proudly call myself Senior Foosball Player *cough* Software Engineer.

All jokes aside, I did spend most of my time writing software (sitting in meetings) and far too little playing foosball. Luckily a colleague built a web app that has been used to meticulously track every match played at work, so I could give you the exact time I spent playing foosball. But I won't without a lawyer in the room. Thinking about this now, you'd assume someone going through the trouble of building an app where people willingly record their slacking off would be out to blackmail you later. I'm reasonably certain that's not the case. Especially because the author is also the most prolific player.

So this is the deal: For the past nine years employees of my company have played foosball and tracked every match. The data includes timestamps of the start and end of every match, who played, in what constellation and who scored goals. The app also implements a ranking based on an Elo rating system. A typical pilgrimage to the foosball table would include 4 matches to 5 goals each. The players are arranged in a specific way and permutated between matches. For instance, among 4 players and 4 matches, everyone needs to play with someone twice. The app would ensure that the top and bottom rated players play together twice to even out the playing field.

Naturally, this treasure trove of company time embezzlement data deserves a thorough look. First, I want to run some analysis on the data and produce some nice visualizations. That's the note you're looking at right now. In the data and the plots you'll see below, I have anonymized the company-internal shortnames to protect the innocent (or rather the guilty). In a follow-up, I will compare different ranking algorithms and hopefully improve on the current implementation. Lastly, the goal is to implement V2 of this app as the old one is showing its age.

In total the data set contains around 25'000 matches spanning over 9 years! This works out to about 8 matches played per day (or over 10 per working day). I, for instance, was personally involved in 1'048 of them. There are a total of 254 players represented, scoring a collective 188'027 goals. No wonder the metal plates behind the goals are so banged up. The average duration of a game is approximately 4 and a half minutes (remember it's just 5 goals).

Let's see how these games are distributed over the years:

What's immediately evident is the general decline in eagerness to play over the years. When I joined at the end of 2019 the company was already in a pitiful state. And of course, COVID-19 has immortalized itself in yet another dataset. During mandatory home-office periods there is a disturbing lack of matches visible.

What's somewhat less obvious are the heroic actions of a single team (nay, single player) in reviving the foosball culture. In 2022, as the matches start trickling in again, you'll notice that most games are played on Thursdays. This happens to be the day where my team would come together in the office to socialize. And following my call, some people would reluctantly join for a match. And so it would begin.

There is still a long way to go of course, the golden age of ~60 games per day in 2014 and 2015 is long gone. But one day we shall ring in the days of bountiful matches again. When we look at the number of matches played by quarter we can see that we are at least at pre-COVID-19 levels.

Overall, the matches are distributed quite evenly across all weekdays. A few games have been played on Saturday, this might have been at some company events. And not a single game on Sunday, almost as if people consider foosball work and god-fearingly refuse to do it on that day. No, that can't be it.

If we plotted the day of week distribution over time we'd see that lately it has been very hard to find enough players on a Friday, as visible in Figure 1.

Most matches are played in the 2 hours around lunch. Maybe that's when people are unlikely to have meetings. Though some mad people have the nerve to show up to the office at 7 and go straight for the foosball table.

In a small personal detour, let's look at the distribution of matches I played. A fun fact about this is that of all games played in the last two years, I was involved in 78% of them. Did I already mention you shouldn't bring this to the attention of my companies management?

In the grand scheme of things I'm not that bad though. Let's see how many games other people have played:

Now, one does not play a game alone, that would be boring. But one also isn't equally likely to play a game with just anyone. A delicate process of inter-personal team dynamics (and meeting schedules) probably forms clusters of people that more often come together to worship play.

To see this, I've plotted a 2d grid where each axis are all players who played at least 1'000 matches. Each cell is colored according to how many matches the corresponding players have shared. In this case only matches where the two players are on the same team count.

The players are sorted (ascending towards top and left) by total number of matches played. I'm player #251 in this anonymized permutation. With my 1'048 matches I barely make the cut. Due to being a relatively new player - missing out during COVID, too - I haven't played a single game with the majority of these prolific players. Some people on here have surely already left the company.

How #39 and #161 managed to play with themselves is a mystery to me by the way. All I know is that they should get a room when they do.

There would probably be some correlation between higher density in ones row on this plot and seniority at the company. But I'm not about to enrich this already risky endeavour with personally identifiable data.

Let's turn our attention towards goals. We're playing to win, not just for fun, right?

The red line is a linear regression fitted to all the players. There is a surprising consistency to this. No extreme outliers at least among the more prolific players.

When we plot this more explicitly as goals per match vs matches played, we see that among rookie players there is a lot more spread than more seasoned ones:

I'm just glad I'm in the upper half.

Next, I wondered how consistent people are in scoring goals from different positions. There are some notorious players that can produce some real bangers from the defensive position, while others almost exclusively score goals in the offensive.

There is a lot more spread here. If we don't exclude players with less than 100 matches we even get some that score more in the defence than the offence. Some would say that makes them very balanced players, others that they suck in the offensive. It all depends on which team you're on.

Maybe some duos of players complement each others skills particularly well. To see this, I've plotted - similar to Figure 7 above - all combinations of players. The color of each cell indicates the win rate when the corresponding players join up. To exclude unrepresentative results, I'm not showing a color at all when the match-up has not played at least 10 games together.

The darker squares now indicate particularly well functioning teams. Neat!

Lastly, I leave you with a plot that looks kind of funny: The current win streak (consecutively won matches) at every match I played.

If this plot was really wide we would see a sawtooth pattern: With every won match, the streak would increase, only to drop down to zero instantly when I loose. The longer the win streak, the more rare of an occurrence it is. Clearly, the longest streak was 10 matches for me. The longest streak across all players is 23 by the way.

What's next?

There are of course many more interesting visualizations left untouched here. If you have a great idea make sure to let me know in the feedback box on the bottom right of the page.

The thing we're really interested in however, is who's the best. After all, at least half the enjoyment (according to me) of a competitive activity is being able to tell others they suck if you win. But how do we know who is the best? A simple measure like the ratio of wins to matches played has shortcomings. Luckily this is a well established problem with interesting solutions. In a follow up note we will compare different ranking algorithms by their ability to predict the outcome of future matches.