It’s a question that is becoming increasingly pertinent in modern football: how do we measure success? Football, in the beginning, was just a game. And success in a game is only achieved by victory. There may be other reasons for playing, but there’s only one way to succeed; and that is to win.

Football is no longer just a game, it’s much more important than that. Football is a business. People depend on the game not for exercise or enjoyment but for income.

With the introduction of money into football the game became distorted. Winning was no longer about chance. People don’t like chance when it comes to their money. Chance suggests they might lose some of it.

Elite football now finds itself divided into two strata: those that can win and those that cannot. Arsenal have been criticized in recent years for falling too meekly into this second category; for accepting they won’t win the league and contenting themselves with Champions League qualification.

Whether you believe this to be an acceptable goal for a football club or not is a question of principle. However, given their relative resources, fourth place is about right for Arsenal and around where many people would have expected them to finish at the start of the season.

As it transpired, Arsenal have performed well above expectations for most of the season and mounted an unlikely title challenge. Their constant quality performances caused many fans to adjust their expectations, and see the title as a realistic possibility.

On current form, the most likely finish for Arsenal would now be fourth place. For many, this can only now be seen as a failure given how close they were for so much of the season. But is this really the right way to assess Arsenal’s season?

Imagine Arsenal had started the season poorly. Maybe Ramsey’s incredible development over the summer never happens and the team find themselves 15 points off the league leaders at Christmas.

Suppose now, in this hypothetical campaign, that Arsenal kicked-on from here and finished the season strongly, in a similar fashion to last year. Let’s say they end up safely in the Champions League places and lift the FA Cup.

In this counterfactual, the mood around the Emirates would be much more positive then we currently find it. And yet given the points differential to Tottenham and Arsenal’s draw in the FA Cup, the results in these two scenarios are very likely to be the same.

What’s different in these two situations is the order in which the events happen. But if we always expected Arsenal to finish fourth, how can we call this season a failure?

Bayesian reasoning is a way of thinking about probability in which we update our predictions as we gain new information. So According to Thomas Bayes, people were right to change their expectations when Arsenal continued to win match after match as they did in the early part of the campaign.

However, in order to update our expectations we must have first made a prediction, or prior, before the event happens – in this case the league season. This Bayesian prior plays an important role as it essentially stops us from getting too carried away in light of new evidence.

Given that Arsenal finished either third or fourth in the last eight Premier League seasons, it’s likely we would have given a high probability to this happening again this season. So while we would have adjusted our expectations as Arsenal continued to clock up wins throughout October and November, they would not have shifted too wildly given the strength we attached to the prior.

Similarly, in the hypothetical scenario in which Arsenal started the season quite badly, we would still have been reasonably confident that they’d still finish fourth.

So just because Arsenal exceeded expectations at the start of the season does mean that finishing fourth would now constitute some kind of failure. They’ve merely met expectations. Whether consistently aiming to just qualify for the Champions League is deemed as a success or not is a matter of principle.

However, we cannot call Arsenal a failure for achieving what we expected of them.

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