Why isn’t the FA Cup like a work of Harlequin fiction?

Michael Lynch, your little soccer secret is out. We know you have a little thing for cup competitions, and you’re sad because Australia doesn’t have one. Otherwise why would you write about it all the time… like here, here, here, here, here and, most recently, here?

A little bit of dream-weaving, before we get into the maths.

Michael has been pushing Football Federation Australia to get a move on organising a national knock-out cup competition. In this article, he invites us to envision it… “Imagine how fascinating things might be if Melbourne Victory was drawn away to the intriguingly named Floreat Athena in Perth, or Alessandro Del Piero and Sydney FC had to travel to Somers Street to take on the Melbourne Knights…”.

I can imagine it. I can also imagine if Floreat was drawn to play Melbourne, but forfeited because they couldn’t afford to make the trip. I can imagine if they came, only to get crushed 10-0, in front of huge stands of supporters dressed as empty seats, on a freezing Wednesday night in July. I can also imagine that if Floreat defeats Victory, the game’s detractors could hold up the result not as “romance”, but as evidence of the underwhelming strength of the A-League, the A-League franchises’ lack of interest in or commitment to the Cup, or the fickleness of the sport in general.

[/rant] [/imagining]

Now, let’s talk numbers. In the 6 articles linked to at the start of this post the word “romance” is used 4 times.

What’s all this about romance? Whole webpages are dedicated to it and it’s a staple of any commentator’s introduction to an early-round game.

It does happen. Frances Awaratife was part of the giant-killing  Sutton United team which defeated Coventry 2-1 in the 1989 English FA Cup, and parlayed that into a long playing career in Australia (including a few Socceroo appearance), a long broadcasting stint on SBS and a short coaching career at Melbourne Victory.

You don’t have to be the New Statsman to know how unlikely such scenarios are (the Sutton United result, not the coach sacking); their rarity and improbability are their appeal – like the hero/ine in a Harlequin Romance. And, just like real-life relationships, real-life soccer upsets have probability to thank rather than the alignment of the stars – meet enough people, or play enough soccer matches, and something a bit special (or unusual, or a little bit naughty) will eventually happen.

In its simplest form, the occurrence of upset results is governed by an incredibly simple formula:

E(X) = n.p

In plain English, this means “The expected number of upsets is equal to the number of matches played multiplied by the probability of an upset.”

So, if the probability of an upset is 0.01, and 1000 matches are played, the expected number of upsets will be 10. Obviously, this is just a generalisation – the probability of a victory by a weaker team varies game to game. Still, not too romantic, is it? Perhaps, rather than printing shirts for the weaker team sponsored by “0.01 win probability”, it would help to describe the mechanics of a minnow vs shark match-up?

One of the few available proxies for the collective strength of a soccer team is how many shots it has, and how many of these are on target. This is a seriously blunt measure. As any enthusiast will tell you, the game is about far more than just repetitively bashing shots in the direction of the goal until one goes in. In fact, it’s that very nature of the game that gives rise to “upset” results – in many, if not most, sports with slightly easier goal-scoring objectives (basketball, water polo, Australian Rules), a clearly superior team with the weight of goal-scoring opportunities – including more high-quality opportunities – will rarely lose.[citation needed]

Is that the case in soccer?

If you gather data from across a series of matches where demonstrably stronger teams meet weaker ones – early rounds of the English FA Cup, for example – stronger teams do have more shots, and more shots on target (also – staggering research outcome – more goals).

The figures below come from round three of the English FA Cup – the point at which Premier League clubs enter the competition – in 2011-12 and 2012-13. Only the 29 matches where an EPL team met a non-EPL team were used.

The blue edges first table shows the proportion of games in which EPL (and non-EPL) teams scored a nominated number of goals. The purple middle of the table combines these to make scores and predict a frequency for the event (this experimentally treats them as independent variables, which clearly they aren’t; a team which has scored 1 goal will be more or less enthusiastic about scoring a second depending on whether their opponents have 0 or 2 goals). For instance, the EPL scored 1 goal 13.79% of the time, non-EPL 51.72% of the time; multiplying these together predicts a 1-1 draw 7.13% of the time.

goals

This next table repeats the experiment, this time using “shots” as the key statistic. EPLs shot at goal an average of around 12 times per game, scoring almost 19% of the time; for non-EPLs it was 9 shots, scoring 8.5% of the time. This is the ultimate de-romancifying of upset results: if the game is conceived as simply the generation of opportunities to shoot at goal, how many are likely to score for each team and how often will each win? These figures yield the following table:

Shots

And now, one more time, using only shots that were on target:

target

So, which is the best predictor of the actual results?

predictions

Exciting reading for romance fans! If you used shots or shots on target to predict how often EPL teams prevail, you’d over-estimate their wins considerably. Although stronger teams have more shots on goal, get a greater proportion of these shots on target, and score goals with a greater percentage of the on-target shots, this dry, mechanical dissection understates by half the romance factor that generates unexpected results much more frequently… there’s something much more mysterious – dare I say, romantic – than E(X) = n.p going on.

So, Michael, perk up! Just keep on going out and meeting nice soccer matches… the right one is out there waiting for you… somewhere.

valentine

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