Three Icons

This post links three icons.

Icon 1: Erling Haaland

Basic facts: Age: 22 years

Sport: Football

Team: Manchester City

Achievements: Too many to list – here’s a link to 26 individual records.

Icon 2: Giannis Antetokounmpo

Basic facts: Age: 28 years

Sport: Basketball

Team: Milwaukee Bucks

Achievements: Again, too many to mention: check here.

Icon 3: The Normal Linear Model

Age: Approximately 218 years.

Achievements: 99% (fact!) of all statistical analyses start here.

The link

One way of writing the normal linear model is this:

Y = f(X) + 𝜖

The details don’t matter here. The important thing is the separation of Y, which might, for example,  be some measure of a team’s performance on the day, into two terms:

• f(X) which is non-random, and depends on the stuff contained in X (which might be team lineups, weather, referee and so on).
• 𝜖 is a random draw from a Normal distribution.

It’s literally signal plus noise.

Now, back to Erling Haaland. There’s been a lot written lately about the effect he has had on Manchester City and whether, right in this moment, City are unbeatable. (Unbeatable when Haaland is playing, I mean).  For example, as I’ve mentioned before, Jonathan Liew is a brilliant football journalist who integrates statistics in his writing. In this piece about Haaland, written towards the end of the season, he mentions:

All but one [of Haaland’s goals] have come from inside the penalty area. The vast majority of his goals have come with his left foot, and the vast majority of those have gone to the goalkeeper’s right.

In other words there’s an extraordinary simplicity to Haaland’s exceptionalism. But whatever it is, his successful integration into the side  has led to a considerable positive shift in the f(X) bit of Manchester City’s linear model.

However, there’s a saying in Italy…

La palla è rotonda

It translates literally as ‘the ball is round’, and is used to imply that in a game ‘anything might happen’. In statistical terms what it means is that you might have brilliant players like Erling Haaland in your team, ensuring that your value of f(X) is as big as possible, but you could still lose on the day if you’re unlucky enough to get a very large negative value of 𝜖. 

Which brings us to Giannis Antetokounmpo. Milwaukee Bucks qualified top in the NBA Eastern Conference this season, and therefore played the lowest qualifying team, Miami Heat, in the playoffs. Their respective win percentages over the regular season were 70.7% and 53.7% respectively. In both statistical and basketball terms, those are very different win rates, and the Bucks were very strong favourites to win the playoff series. But Miami won the series very comfortably, 4-1.

Shortly after, in interview, Giannis was asked if the Bucks’ season was a failure. If you have two minutes to spare, watch the video of his reply.

It’s not just the words, but the body language too. The words are great though. Here’s a section:

There’s good days, bad days. Some days you’re able to be successful. Some days you’re not. Some days it’s your turn. Some days it’s not your turn. That’s what sports is about. You don’t always win. Other people are going to win. And this year, somebody else is going to win. Simple as that.

Which is to say, you can do as much as you like to improve the f(X) contribution towards your team strength – buy Haaland and all the rest – but there’s still a contribution from 𝜖 that you can’t do anything about.

The ball is round and sport is signal plus noise.