There was a ripple of excitement on Twitter last night when Ivory Coast beat Japan 2-1, meaning 4 out of the first 8 matches at the World Cup finals had been won by a team conceding the first goal. Obviously the excitement touched on maths, and every now and then I try to provide a little helpful maths advice on Twitter. It rarely ends well: I suppose I bring it on myself – there are a lot of things you can easily convey in 140 characters or less, but I suspect nuance and binomial theory aren’t two of them. And I shouldn’t wade in with a complex unexplained formula early on in the piece. I choose to blame FIFA and their “technical report” on the 2010 World Cup. First of all, who’d trust FIFA with anything technical? Decades since other sports started using science to aid their officials, soccer has belatedly waded in with goal-line technology, which – despite its first successful use in this morning’s France vs Honduras match – is still less useful than something to aid the apparently far-more-prevalent contentious offside and penalty decisions. It is amusing, though, that after each goal has scored, the ball has bounced around in the net a little and been picked out by a grumpy goalkeeper, the TV replays still insist on showing this image, like a mirthless government official handing down an unwelcome rejection:
Oh, all right – yes, “technical” is not the same as “technological”. Rant over. Amongst reams of numbers, FIFA’s technical report tells us the following about comebacks: It’s the sort of data chunk that makes me think, “Here we are at FIFA, filling in all the boxes so we can say we wrote the report” – a bunch of observations without even the barest hint of inference. On the face of the bald data, it might be tempting to conclude that something has changed in football – so many comebacks in just the first week of the World Cup, against so few in 2010. As far as analysing comebacks – assuming that is the point of reporting “wins after conceding first goal” – surely it’s worth noting that not all comebacks are equal.
There is surely a difference between:
- coming back from a goal down / 2 goals down / 3 goals down
- coming back from falling behind to a goal in the first minute / 45th minute / 85th minute
- coming back and winning within 90 minutes / after extra time / on penalties
- coming back as a favourite / underdog
And any analysis should include the facts that:
- in a 0-0 game, nobody is attempting a comeback
- comebacks include matches in which teams take the lead, then fall behind, then win
- in final group matches, some teams are content to draw and qualify for the next round, rather than win
- coming from behind to take the lead, but ending up with a draw, could also be relevant?
The last question tries to bring to the fore what is in the background: what are we actually trying to prove with this data? Is it that football at the World Cup is generally more open? That teams have become better at attacking an opponent which is intent on defending? Or have become worse at defending an opponent committed to attack? If early goals are easier to come back from, are we seeing an unexpected number of comebacks, or just an unexpected number of early goals? If favourites make comebacks more often than underdogs, are we simple seeing more favourites fall behind? Are we seeing the re-emergence of whatever resulted 10 “comebacks” in 2006 (assuming that after all the caveats, those numbers still stack up)? Selecting one (or more) of these questions or inventing others will be the first step to establishing the best data to answer it. One further thing to keep in mind: the FIFA report has a statistics section which goes for dozens of pages. Facts collected include data on the performance of under-23 players, the amount of time the ball was in play in each match, and whether goals came from corners, wing play or penalties. Of that much data, the probability of not finding a dramatic change in one metric or another is almost non-existent. Generally the confidence threshold for testing a discovery using data is 95% – ie, “the likelihood that this number of comebacks is caused by normal variation is 5% or less”. If you test 10 different data elements from the 2014 World Cup, the probability of none of them reaching that threshold is 0.9510 = around 59.9%. The other 40% of the time, you’ll look at the numbers and feel compelled to write an article about, say, how heaps more goals get scored from the corner kicks these days. For instance, if it was 1987, and you knew nothing at all about football, but looked at these results, you’d probably conclude that there’s just something about high-stakes matches that brings out attacking, exciting football – the goals-per-game average is immense! Whereas a broader survey of Euro and South American finals, later World Cup Finals and [insert your own example] might tell the opposite story, or looking at metrics other than just “goals scored” a more nuanced one. I write all this not to be carping, but because I really like reading sports journalism that includes maths to tease out the reasons behind the numbers. But the real story – not just the story that seems to jump out at first glance. So, I am sorry Michael – I didn’t mean to sound like a boring know-it-all :-‘( If you do want to write an article about it, I’d even like to help. I’m sure someone else will write the “gee, look at all those comebacks” article – but that would be no more useful an analysis than “I guess Aussies just can’t play football” as an explanation of the Socceroos loss to Chile. But you could be the first one – probably the only one – to publish the story behind the story!* Meanwhile, let’s hope there are more comebacks in Brazil. It may have little significance mathematically – but it sure is entertaining to watch.