ESPN's Luck Index smashes cliche that luck evens out over time

I can't believe the ref gave that decision?

The league are biased against us. We could have won the title if not for so many bad calls.

If we didn't have bad luck, we'd have no luck at all!

Sound familiar? It's the refrain of every single football fan at some time or other.

Oh, and you can forget that silly cliché that decisions even themselves out over the course of a season. We know that's not the case. In fact, you can work it out for yourself by simply flipping a coin: the more times you flip, the less likely it is that you will get an equal number of heads and tails.

Likewise, on the pitch, every time there is an error it can be in your favour or against you. (Of course, football supporters usually only see the bad luck that goes against them -- sort of the opposite of rose-tinted glasses. Goes for the managers, too.)

But how much does luck -- good and bad -- really play a part? To find out, we devised and created a study, along with our friends at the University of Bath, to find out the degree to which luck and refereeing decisions impacted the 2017-18 Premier League season. After the numbers were crunched (check out our page for more on the results, alternative table and methodology) the Luck Index was born, along with an alternative Premier League table.

The headline result? Manchester United were the most fortunate side, gaining six additional points, while Liverpool were the unluckiest: strip out the effects of luck and Jurgen Klopp's crew would have had an extra 12 points, enough to finish second ... and above arch-rival United. Arsenal, too, were somewhat hard done by as the Luck Index suggests they should have had an additional eight points.

Luck was also evident at the other end of the food chain. In real life, Huddersfield Town avoided relegation, finishing four points above the drop zone. Factor in the Luck Index and David Wagner's men would have been relegated, albeit on goal difference, while Stoke City would have stayed up. Interestingly, it's not so much a function of Huddersfield having been lucky as much as it is other sides (like Stoke) experiencing bad luck.

The ESPN Luck Index

- The Luck Index: The findings and methodology
- Top 10 Premier League games where luck played a part
- Man United luckiest, Liverpool unluckiest

How do you go about creating the Luck Index and quantifying something -- luck -- that can be like catching smoke with your bare hands? First step was to identify incidents that were impacted by luck. Many were down to refereeing errors. These included incorrectly awarded and disallowed goals (whether due to offside, or a foul in the build-up), penalties that should have been awarded but were not and red cards, both those that were incorrectly given and those that should have been given, but were not. A refereeing decision was deemed to be "an error" when at least two of the three trained coders who reviewed it agreed that it was incorrect.

(For further accuracy, former Premier League referee Peter Walton reviewed a sample of 20 incidents.)

Another category involved goals that were "scored outside the allotted time" -- in other words, goals that arrive after the referee's whistle should have blown at the end of the half. Finally, there were deflected goals: goal-bound shots that hit off an opponent and beat the keeper.

Each time a team was deemed to be "unlucky" based on the above criteria, the Luck Index judged the likely impact of the incident on the final outcome of the game. To do this, we used a mathematical model that gives you the likeliest outcome based on a series of factors. These include the time of the incident, the type of incident, the relative strength of the team, whether it was home or away and so on. Once the data is inputted, about 100,000 simulations are run to ascertain the most common outcome.

Remember how Chelsea hosted Burnley on opening day last season and lost 3-2? According to the Luck Index, the home side were unlucky to have Gary Cahill sent off after 14 minutes and because the red card came early with the game tied at 0-0, it had an out-sized effect. If that incorrect decision were not made, Chelsea would have won 1-0; therefore, the Luck Index awarded three points to the home side.

Or take the Manchester derby in April. A victory for City would have mathematically given them the title. Instead, they dominated the first half, going two goals up but then suffered a 3-2 defeat as United, marshaled by a brilliant Paul Pogba, roared back. There were a number of contentious calls but the Luck Index noted only one that was clearly incorrect. That was after five minutes when Ashley Young handled David Silva's cross as it was bound for Raheem Sterling. Referee Martin Atkinson waved play on (either he didn't see it or he felt Young, who appeared to slip, had handled the ball unintentionally).

According to the Luck Index, it was a clear refereeing error: City should have been awarded a penalty. Fire up the Luck Index (and the usual 100,000 simulations, which would have also taken into account City's penalty conversation rate) and the match should have finished 3-1 to City.

It's pretty easy to know what Pep Guardiola and Jose Mourinho would have to say about that.

Of course, we expect some healthy debate around the Luck Index. For a start, you may take exception with, including goals scored "outside the allotted time." We've all heard the jokes about "Fergie Time" but when a referee determines the number of minutes of time added on, it's always a minimum. Incidents during the time added on (like an injury, a goal or a substitution) can mean the referee is entitled (in fact, obligated) to tack on extra minutes to those shown on the fourth officials board.

Including deflected goals is another one for debate. Again, we've all seen goals where the ball hits a defender's backside and balloons over the keeper; we talk about what a stroke of bad luck that was. Quantifying the effects of deflections -- could they have been saved? -- is subjective.

And that's the point. There's simply no definitive way to measure luck, its impact or indeed forecast out events in a match thereafter. But these conversations -- and the ESPN Luck Index -- are the lifeblood of postmatch analysis among fans and pundits alike. This project takes us a step forward in understanding the impact of luck against the backdrop of VAR's impending adoption across the sport, and how differently things might have turned out.

At its core, the Luck Index is a fascinating tool that taps into this, reinforcing the absurdity of the old trope "mistakes even themselves out in the long run." If it's 50/50 whether luck and bad calls go for you or against you, it's highly unlikely that they will "even themselves out" over such a 38-game season in a sport with such fine margins for victory and defeat.

Luck is simply a part of football.