How unlikely were The Invincibles?

This summer marked the 10-year anniversary of Arsenal completing their Invincibles season; a team remembered not only as a ruthless winning machine but also for being totally unlike anything previously seen in English football.

There has been plenty of good writing on The Invincibles – indeed this post was inspired by Dennis Bergkamp’s recent autobiography – and this blog won’t attempt to compete with these pieces. Instead, 5 Added Minutes is more concerned by the question: how unlikely were The Invincibles?

To answer this, we can turn to a couple of sources. First, the excellent Club Elo website, which allows you to compare teams across all eras. On 1 July 2003, Arsenal were some 58 Elo points off the best team in the country, Manchester United. This about the same distance Liverpool are off Manchester City at the time of writing; it’s difficult if not impossible to imagine the Reds eclipsing City this season.

Of course, Chelsea were bought by Russian oligarch Roman Abramovich in the summer of 2003, and simulations of the 2003-04 season based on bookmakers’ odds suggests that Arsenal, Chelsea and Man United were all rated to finish in the 73-76 points range*.

But this merely indicates how probable or improbable an Arsenal title win would have been, and doesn’t reflect the unlikeliness of an entire season undefeated.

Turning back to our simulations, we can estimate in how many seasons that particular Arsenal team would have not lost a single game, based on the pre-match odds expectation. The answer was just 6 in 10,000 seasons, or 0.06%*:

In other words, Arsenal would have been expected to have gone that season undefeated in roughly 1-in-1600 attempts**. A much more likely outcome was somewhere in the range of 5-8 losses, which is generally the number of games a title winner loses in a season. Through a combination of luck (think of Ruud van Nistelrooy’s missed penalty), fabulous skill and possibly a bit of underestimation on the bookmakers’ part, the Gunners achieved a truly improbable feat.

To put the feat into perspective, Greece were 150-1 to win Euro 2004 – even if this is a conservative estimate, it pales in comparison to Arsenal’s achievement.

The Invincibles – a joy to watch and a remarkable statistical outsider.

* Note that these odds used were updated through the season, so it’s not a true reflection of the pre-season expectations.

** Given the rarity of unbeaten seasons in the 10,000 simulations, this is only a very rough estimate. Nevertheless, the odds were long.

Al odds data from football-data.co.uk.