#FreeKickEVERYONE: A Study of the Free Kick Count as the Football Fan’s Favourite Scapegoat
I want to kick this off with a bit of an experiment.
Let’s flip a coin 50 times and count how many times tails comes up.
Hopefully we can all agree that a fair coin will have an even 50% probability of showing up as either a heads or tails with each flip. Now that would suggest that when we flip said coin 50 times we should end up with exactly 25 heads and 25 tails, right? 50% of 50 is 25 after all.
Let’s see what happens when we ask my laptop to randomly simulate 50 coin flips.
The outcome is a 29-21 split in tails’ favour – not exactly an even 50-50 split, but at a glance it certainly doesn’t raise any eyebrows as to the fairness of the coin being tossed or the integrity of my laptop’s coin toss simulation. Intuitively it would feel more reasonable to put the unevenness of the result down to pure chance – perhaps it was just random luck that eight more tails showed up compared to heads?
Let’s do the coin toss experiment again, but this time I want to go bigger:
Flip a coin 50 times and count how many times a tails comes up…and then repeat the process 1000 times, tracking the results along the way.
What we end up with this time around is a wide range of outcomes spanning from as few as 15 tails all the way up to 36 tails from our 50 coin flips.
Now, before we can start talking football I need to get a bit (more) mathematical for a second – what we see above is an example of something called the binomial distribution. In short, a binomial distribution describes the likelihood that a specific number of successes (in this case, a tails showing up) will occur from n independent trials (e.g. n = 50 for the coin flip experiment), where each trial has p probability of success (0.5 for a coin flip). As the “bi” in “binomial” suggests, each trial can only have two outcomes – a success or a failure.
The theory behind the binomial distribution states that for a large enough number of trials where the likelihood of a success in each trial (p) is not at the probabilistic extremes (i.e. not near 0 or 1), the distribution will become approximately normally distributed.
In other words, as we run more and more trials of our 50 coin flips, a bell curve-like shape should begin to appear within the total observed number of tails (successes) that we record. Revisiting the previous chart we can see that after 1000 repetitions of our coin flip experiment this bell-curve-like shape is indeed beginning to appear.
Okay, let’s put the stats chat aside for the moment – what does all this have to do with football?
Random Variation and the Free Kick Count
The coin flip experiment above probably feels a little irrelevant to a discussion about football, but there is one key lesson from it which is very transferrable to a discussion about free kick counts.
The concept of random variation is incredibly important to understand when discussing the free kick count in a match of football, but unfortunately it might also be a notion often a little lost on the run-of-the-mill football observer. Random variation is the tendency for something to deviate in a random (duh) and uncontrollable manner from the planned or expected level of performance.
This was evident in the wide range of outcomes of the coin flip experiment and those exact same learnings can be applied to a football match’s free kick count.
Cast an eye across any social media platform and it would seem that the general expectation is that free kicks should be split evenly – there tends to be a whole lot of hoopla when the count becomes lopsided. In this regard, a balanced 50-50 split principally implies fairness and equality in the eyes of supporters – let this 50-50 split represent out planned/expected level of performance.
We know from experience however that football matches do not always end up with a perfectly even free kick count and this is where things can get a bit prickly for some fans.
Much like the coin flip experiment, we can consider the free kick count to be a binomial random variable, where the only two outcomes possible for each “trial” are a free kick for (success) or a free kick against (failure). As a result of the random variation subject to the binomial distribution, we should expect a wide range of results to occur within the free kick differentials of football matches.
Below is an aggregated view of the absolute differential in free kicks within every AFL match player between Seasons 2000 and 2021 (up to Round 20, as I write this).
A nice clear pattern is apparent. Free kick differentials closer to 0 (i.e. a 50-50 split) are the most common, however we can also see matches with double-digit differentials do occur on occasion too.
On one particular Saturday afternoon in May of 2013, a free kick differential of 23 was recorded when North Melbourne was awarded 38 free kicks versus Port Adelaide’s 15.
The message I am seeking to convey here is that the free kick differential between two competing sides should be understood as being subject to random variation – i.e. the free kick differential in a football match is a binomial random variable.
To summarise what this means in practice – and if you only take one thing away from reading this article, let it be this:
Free kick counts do not have to be evenly split.
In fact, they don’t even need to be near to evenly split – just look at wide range of results on the visual above. Over the last two decades 1 in 9 matches played (11.3%) finished with a free kick differential of 10 or more.
Fans may choose to hold the belief that an even free kick count implies fairness in the umpiring of a match, however they should also then understand and accept that variability in the free kick count is a natural occurrence that in no way suggests an umpiring bias favouring one side over the other is in play.
This idea is something I’d love to be more widely understood and accepted by the broader football community and has served as the original motive for writing this article.
I’m going to backpedal a touch here now though – I freely admit it would be all sorts of naive of me to conclude this study right here and entirely refute the possibility that any form of umpiring bias exists in football.
Using an analytical lens (as per usual), I want to explore a few arguments that are all too common to the pubs and living room couches of Australia to see if there truly is any substance to them:
Do some teams receive more free kicks than others?
Does home crowd ambience play a role in influencing umpiring decisions?
Are certain game-styles more likely to draw more free kicks?
All of the above warrant further explanation – it’s entirely possibly that there really are extraneous factors at play which influence the umpiring of football matches.
I’m keen to dig in to this further.
The Free Kick Ladder: Does That Team You Hate Get a Free Ride?
I won’t mince my words here – I hate hearing people complain about lopsided free kick counts against their team.
To me it only serves as a cheap way to shift the blame from one’s team’s own performance onto an external influence supposedly outside of the the team’s control. That is, it is way too easy for football fans to make a scapegoat of the free kick count.
In fact, when I hear or read someone’s commentary on how their team was robbed by the umpires yet again, I tend to think that the only possible supporting arguments for their point of view are:
- They genuinely believe that the umpires have it out for their team/are on the opposition’s payroll
- Nope that’s it, there is literally no other reason I can think of that makes logical sense
Okay rant over. Despite my feelings being very dismissive of any notion of team-specific umpire prejudices, this wouldn’t be a particularly good stats-focused blog if I didn’t now investigate each team’s long-term free kick numbers, so let’s do exactly that.
Clearly there is some variability in the average free kick differentials across the 18 teams, but how much of that can we put down to a supposed umpiring prejudice rather than just being born of the influence of random variation as discussed earlier?
An overly simple take here would be to say that West Coast wins nearly two more frees than they concede per match and therefore must be regularly getting preferential treatment from the umpires. Alternatively, GWS, Sydney and Hawthorn all average more than one free kick less than their opponents over the past two decades and therefore must be consistently copping a raw deal from the men/women in fluoro.
In my own experience this generally tends to be about as complex as most arguments regarding free kick bias on social media ever get. What I want to explore is why we see variation from team to team rather than simply acknowledging its existence.
Looking at where certain teams sit on the “free kick ladder” shown above, I’m sure most reading this would straight away have some pretty solid theories as to why certain teams are where they are – I do too.
Let’s now explore some of the potential contributing factors.
Home Ground/Crowd Advantage & the Noise of Affirmation
The so-called “19th man” is perhaps the most regularly discussed outside influence on umpiring decisions and rightly so. No one in the world can honestly say they’ve never once second guessed themselves when the opinions of the majority around them are all suggesting something else.
The Asch Conformity Experiment is a famous demonstration of how social pressure can influence an individual to conform to the common belief of others – regardless of whether their belief appears to be correct or not. Umpires are regularly subjected to comparably similar conditions to those seen in Asch’s experiment, particularly when adjudicating a game where one team has a home ground – and home crowd – advantage. A vocal home audience where the travelling side is well and truly underrepresented within the crowd can create a sense of social duress upon the umpires which may be a potential contributor to imbalanced free kick counts.
Let’s take a look at the free kick differentials for each team when they play with a distinct home ground advantage over their opponents. A home ground advantage here refers to playing a team playing at their usual home ground (or regular alternative – e.g. Tasmania for North & Hawthorn) versus an interstate side (Geelong v a Melbourne-based side at Kardinia Park is also considered a home ground advantage here).
It’s really intriguing to see that nearly every team averages a positive average free kick differential when playing with a home ground advantage. Perhaps there truly is substance to the noise of affirmation? West Coast, Western Bulldogs and North Melbourne appear near the top of the tree just as they did on the previous chart depicting free kick differentials across all games.
The only two sides who don’t see a long-term positive free kick differential at their home ground advantage games are the two fledgling clubs in Gold Coast and GWS. It may be a somewhat blunt observation, but it feels logical to ask the question here whether significantly smaller crowds at Gold Coast and GWS home games would diminish the effect of crowd influence on umpiring decisions.
In that case we should ask:
Do larger crowds escalate the impact that the noise of affirmation has on umpires?
While they haven’t been a great time for football in general, the COVID-19 affected seasons of 2020 and 2021 have provided an opportunity to observe a sort of “control group” of matches without crowds which we can compare to the figures seen in the above chart.
As of Round 20 2021, we’ve had 55 matches with no attendees since the onset of COVID. We can split these 55 matches into two distinct sub-groups – those where a home ground advantage was at play (n = 27) and those that were played at a neutral venue (n = 28).
These samples probably aren’t large enough to use as a baseline, but for what it’s worth the home side averaged +0.93 free kicks when they had a home ground advantage, as opposed to -0.46 when playing at a neutral venue.
Regardless of those sample sizes for games with no crowds are large enough to draw inference from (and I sincerely hope we don’t have to witness too many more), I’m interested to see how crowd size has historically affected free kick counts at neutral venues as compared to games played with a home ground/crowd advantage.
Let’s look at the free kick differentials of home teams (so that we aren’t double counting for each match) over the last 20 years:
There are a few interesting things which I take away from what I see above:
- At games where a home ground advantage exists, the bigger the crowd, the greater the average free kick differential for the home side. Conversely, games with small crowds of less than 10,000 saw an average free kick differential of very near to zero, regardless of whether there was a home ground advantage or not.
- No matter which crowd size bracket (0-10k, 10k-25k, 25k-50k and 50k+) we look at, the average free kick differential is greater at games where a home ground advantage exists than the equivalent crowd size at neutral venues.
- Looking specifically at games played at neutral venues, it is interesting to see that the average free kick differentials are all positive regardless of crowd size, albeit to a limited extent. On average the the home side at a neutral venue has won 0.71 more free kicks than their opponent over the last two decades.
It’s important to remember that the numbers we are looking at here are long-term averages. These findings do not mean that every time a team has a home ground advantage and a big crowd in the house they will have a win the free kick count.
Nonetheless, with a sample more than 2,000 matches where a home ground advantage is present and more than 10,000 spectators are in the house, it does appear to me as though the noise of affirmation may truly have a noticeable influence on umpire behaviour.
Whether it is influential enough to be of concern to the integrity of the game I am a bit more doubtful on – that one I’ll leave for you to decide for yourself!
The Relationship Between Game Style & the Free Kick Count
Fact – In their premiership winning year of 2016, the Western Bulldogs were awarded 112 more free kicks than they conceded – an average free kick differential of +4.3 per game.
Also Fact – In 2016 the Bulldogs ranked #1 for contested possession differential (average +16.5 per game) and disposal differential (average +42.7).
Plenty of fanfare surrounded the Bulldogs’ tactics in their premiership year, specifically regarding whether it was their ultra-contested style of play that could be credited for their astronomically positive free kick differential or whether that just came down to having the rub of the green (or perhaps something else?).
While I’ve already made my feelings about the (non) existence of team-specific umpiring prejudices known, I do find myself thinking whether certain game styles – such as the Bulldogs’ contested ball approach – may facilitate winning more free kicks than others.
A team’s game style can be identified to some degree by their proficiency or otherwise in certain statistical areas.
For example, a team whose strategy depends on winning stoppages to score will generally need to rely on a high volume of contested possessions and clearances.
Teams that are more focused on winning the ball back in general play through pressure may instead be more dependent on intercept possessions and tackles. The list goes on.
This leads to an important question:
Does a team’s free kick count correlate with any other key statistics?
If we are able to find a degree of correlation between a particular stat and the free kick count (either total or differential), it could go some way to explaining why some sides – such as the 2016 Bulldogs – have much higher free kick differentials than others.
Let’s begin by looking at some correlations between key stats and free kicks, both by total and differential. Note that free kicks are actually counted as contested possessions by definition, so we’ll correlate free kicks against contested possessions less free kicks to avoid any overlap in what we are measuring.
No need to adjust your screen brightness for that visual – the pale shades are no mistake. Correlation coefficients of near to 0 across the board indicates that there is next to no correlation between the free kick count and any of the commonly-used statistics listed.
I’m not hugely surprised by this, but seeing statistical proof of the lack of correlation can never do any harm.
The data above provides the highest level view possible of each statistic’s correlation with the free kick count – the sample includes all games across the last two decades as one. But what if we were to break that sample up into subgroups for each of the 18 teams?
That way we could see if any teams observe a higher degree of correlation between their stats and the free kick count.
Still not a whole lot of bright colour when we break it down on a team-by-team basis. Across the whole league, the strongest correlation between the free kick count and any major statistic since 2000 is just 0.27 (correlation between free kicks and tackles for North Melbourne) which is still a very, very weak result.
The team-by-team correlation matrix for free kick differentials (rather than totals) returned similarly unconvincing results (and therefore did not feel the need to include it).
I came into the writing of this with a suspicion that either the contested possession or tackle differential may have a slight sway on a match’s free kick split. The above would suggest I’m off the mark on that, so just to really drive the point home:
If you can find any semblance of a pattern in there, you’re lying or you’re nuts. To me this means no meaningful link exists between either contested possessions (less free kicks) or tackles and the free kick count.
Circling back at the case study of the 2016 Bulldogs now knowing what we know, perhaps rather than holding the view that:
“In 2016 the Bulldogs won more free kicks than anyone BECAUSE they were also an elite contested ball side.”
It should instead be less cause-and-effect in nature, i.e.:
“In 2016 the Bulldogs won more free kicks than anyone AND were also an elite contested ball side.”
It seems logical here to state there is no significant relationship between any statistical indicators and the free kick count.
By extension it would also appear difficult to reasonably say that a certain team’s game style would elicit more free kicks than another team’s style. Personally, I’m happy to put that one to bed.
Closing Thoughts
The reason I originally wanted to write about the free kick count is because it irks me to no end when I hear fans on social media blaming their team’s loss on the opposition having been given a supposed armchair ride by the umpires, with nothing but a free kick count to support that claim.
While the umpires absolutely do have the power to sway the outcome of a match (hello Mark Blicavs holding the ball non-decision v Brisbane, 2021), I truly can’t bring myself to believe that using an imbalanced free kick count to justify a team’s win or loss is a logical process.
I found it surprising to see the extent to which crowd noise – particularly where a home ground advantage exists – plays a role in affecting the free kick count. While it certainly makes sense from a social pressure angle, I wasn’t expecting to see such a profound impact on the numbers.
The fact that none of the regularly used statistics had any correlation with the free kick count is a meaningful finding in itself too. It may be a slightly long bow to draw, but this may mean the theory that certain game styles elicit more free kicks is more myth than fact.
Taking ourselves back to the start of the article, I feel like the coin flip experiment might be the single best demonstration of why we see uneven free kick counts. It may not be a popular conclusion for those playing along at home, but to me random variation is the absolute king when it comes to finding an explanation for the phenomenon of imbalance. While it may seem like that team you hate is consistently getting the rub of the green, for me I choose to believe that it is nothing more than a human misconception and that the real culprit here is simply an elaborate extension of luck of the draw!
