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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.

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