SUNDAY, 26 JANUARY 2025

In the fan forum run by the PinkUn, the press and online media that reports on all things Norwich City Football Club which I visit almost every day, there is a poster who loves statistics. In many of his posts, perhaps even a majority of them, there’ll be a reference to xG or xGA, or a heat map of where a player has been on the pitch during a game, or more obscure and convoluted diagrams which leave me totally flummoxed, all serving as evidence to support the argument he’s making. But it’s common for the two of us to disagree strongly on the pertinence of this data. Perhaps it’s generational, perhaps it’s because my background is in the arts rather than the sciences, but we have widely different opinions about the significance and value of these numbers.

The most basic stat in football, of course, is a goal scored. This is simple: if a player kicks the ball and it ends up in the net, he has a goal to his name. There is a slight complication about what happens if the ball is deflected in off one of the defenders: the general rule is that if the ball would have ended up in the net anyway without this intervention, it counts as a goal chalked down to the forward; if not, it is registered as an own goal.

A second simple stat these days is the ‘assist’: this is the last touch by any player on the same team before the scorer nets his goal. It is usually a pass or cross of some kind. However, there are problems even with something which sounds so simple. First, a wildly misplaced pass counts as an assist if a second player on the same team is the first to touch the ball afterwards and scores a goal. Indeed, there is no need for the first player to have even tried to pass the ball: if it bounces off his knee and falls favourably for a second player who scores, the first player is awarded an assist. Also, if the first player makes a wonderful pass which gifts the striker an open goal but he fluffs the shot, there is no assist. So there is obviously an element of chance involved in these figures and not all assists are equal in merit. This wouldn’t matter if the assists for each player over the course of a season numbered in the hundreds, since probability would even out the element of luck, but most footballers get a very limited number of assists in any one season, generally in single figures. So if our best player of the 23/24 season, Gabriel Sara, got 14 assists, that is almost certainly meaningful, but the difference between players who get four and six assists is likely to be down purely to chance.

The measure xG is even more tenuous. This is a figure which shows the number of goals a team might expect to have scored in a game based on a range of criteria, such as where the player who shoots is placed on the pitch, whether there are defenders between him and the goal, the difficulty of angle involved, and so on. These things are weighted based on historical precedent of the likelihood that a shot will hit the back of the net under these conditions. I assume this is all done by machine algorithms and there is no little man watching the game and ticking boxes, which in theory rules out subjective influence, although it can be argued that the original decision that, say, a player being 20 yards from the goal is worth 0.2 points must have been to some extent a subjective evaluation of its goal potential relative to other criteria.  

Obviously football is no longer merely a game: it’s big business. This means that measures which are available to the fans such as xG are relatively crude compared to the mountain of stats that clubs now gather behind the scenes. In the past, the managerial team on the bench would be watching the game and judging by the ‘eye test’; these days they are usually poring over their laptops getting the latest data on the match as it evolves. In a business where the potential profits are huge but the margins between success and failure are often paper-thin, nothing escapes measurement. For example, the latest buzz phrase is data-based recruitment, by which new players are no longer signed mainly from the reports of scouts watching them in games, but according to their figures on a screen, which are based on a huge accumulation of facts about them, such as how fast they can run, how many miles they cover each game, what percentage of successful passes they make, and so on. And even a sceptic like me has to concede that this has worked wonderfully for Brighton, propelling them to the top half of the Premier League, so every other club is rushing to jump on the bandwagon and setting up similar recruitment systems.

So statistics now play a crucial role in football, but some will argue that ultimately football is only a game, so if we want to make important judgements about the value and usefulness of stats, we should turn our attention to a field where they can make the difference between life and death: medicine. In modern medicine we have available a plethora of stats to measure red and white blood cells, haemoglobin, cholesterol, triglycerides, blood sugar, vitamins, minerals, liver function, and so on ad infinitum, and major decisions, such as whether to put someone who is asymptomatic onto statins are made based on these figures. As a result, a sizeable proportion of the adult population in the US (around 35% in 2018/19 according to the NIH) now takes statins, many of whom have never had a heart attack or even any symptoms to suggest that one might happen soon. Markers are treated as if they are symptoms, but many people with high LDL levels do not suffer cardiac problems while others who have low levels sometimes do. All we can ever do, it seems to me, is play the odds and hope for the best, while figures and statistics can suggest a sense of certainty and control which isn’t justified.

About six years ago, when I was living in Portugal, my doctor arranged for me to have a CBC (complete blood count). This showed that I had a high level of LDL (around 180) and he suggested that I might want to consider taking statins, especially since there is a history of heart disease in my family. He put the data from my CBC into the computer, including other facts like my age, my height and weight, and my family history, and the NHS programme he was using calculated the likelihood of my having a heart attack within the next five years as a percentage down to a single decimal point. It all felt impressively scientific, but I still declined the drugs. To be fair, my doctor listened to my arguments and didn’t harangue me even though I must have been a nightmare patient armed with bits of information which I’d picked up from the internet and talking as if I knew it all. I know my experience is anecdotal, but I feel it shows how figures can gain a life of their own and give an unwarranted impression of exactitude, and how doctors under the pressure of time are going to use them to make key decisions, while most patients, unlike an awkward sod like me, will accept their doctor’s best advice and start taking the tablets.

Another problem with medical statistics is how poorly they are reported in the press, especially how journalists ignore the difference between absolute and relative risk. There is a huge difference between stating that eating a specific food doubles our risk of getting colon cancer and describing the same statistics as an increased risk of being diagnosed in any one year to be up from 1 in 10,000 to 1 in 5,000. The newspapers, not unnaturally, will always go for the more dramatic figure in their search for readers or clicks. Then, of course, there is cherry picking of data, where advocates of a plant-based diet will highlight different research from someone who aims to push the benefits of a carnivore one. And this doesn’t even start to address the host of problems around nutritional research in general, such as the drawbacks of self-reporting or the existence of publication bias or the over-reliance on meta-analyses which clump disparate studies together in order to get an adequate sample size. Finally, academics are not always innocent victims in skewed reporting, with some of them making ridiculously exact claims such as every glass of wine takes twelve minutes off your life expectancy, knowing full well that this is what newspapers will pick up on and feature in their headlines, so their research will get near to the top in search engines after all those clicks, and they are therefore more likely to get further funding in future.

Another area where stats have become enormously significant is education. The desire for higher standards has led to schools being placed in league tables based on the quality of their education, which tends in practice to mean their exam results, both because these may be what parents care about most and because they are easily quantifiable in a way that quality of teaching isn’t. The problem is that this changes the way that teachers teach and they start to teach to the test rather than taking a broader approach to giving a child an education. Many other key decisions, such as where people choose to live, follow on from this, with the so-called postcode lottery where two families who live close to each other but in different administrative districts might end up with their children going to different schools with very different reported standards, so house prices soar in the area with higher-ranked schools. In their desperation to get higher up the league table, some schools might choose not to enter weaker students for examinations, since failures will drag down the school’s score and lower their position in the league tables. In short, as soon as we have statistical gathering of data, we will get individuals and organisations gaming the system.

Obviously it’s easy for people like me, who are not trained in the collection of data and its interpretation and don’t fully understand all the ins and outs, to use a famous quote such as ‘Lies, Damned Lies, and Statistics’ to come up with smartass headings, and to pooh-pooh the use of data. But it is certainly true that the amassing and presentation of big data has become a powerful tool in public discourse, and for this reason we should approach it with more than just a quip and a cynical shrug of the shoulders. On the plus side, from comments I see online, even on my PinkUn message board, I sense that the ubiquity of data online has led to a growing sophistication among the general population about statistics and a greater scepticism (compare the fairly basic content of a popular book of the 1960s, How to Lie with Statistics by Darrell Huff, with some of the more advanced material we find these days on the best of the internet if we look carefully). As a result, there seems to be more awareness of the potential to twist and misuse data, and it is no longer only scientists who come out with the hoary old truth that ‘correlation is not causation’.

Despite this, however, I still feel that figures and charts and tables can create a sciency feel and it remains easy to be dazzled by them and to switch off our critical faculty, not least because they often back up our biases and set off our weakness for logical fallacies. Also, many of the problems mentioned in this essay are not intrinsic to statistics but are unforeseen secondary consequences of their use (as, for example, an important outcome I didn’t mention, but which is potentially crucial – the power of opinion polls to influence voting behaviour during elections). Many of these problems, perhaps, could be addressed by the compulsory teaching of data analysis at secondary school. This might not have much of an effect in the here and now, but should make future generations better able to fight off the tendency to be bamboozled by what is sometimes the deliberately sly and illegitimate use of statistical data and their graphic representation.