Football Scores

Earlier this year, there was a big association football tournament in Europe which enjoyed some meaningful coverage across the continent, called 'Euro 2020'. (Plainly, organisers forgot to update the title after postponing from the previous year because of Covid-19.) I don't typically follow this sport, but it seemed to capture the attention of many people in my orbit and I found myself watching some of the matches. After spending some time perplexed about why everyone kept spontaneously falling over whenever they entered a special rectangle drawn on the lawn near the opponents' goal, I started thinking through some of the other rules of the game. It seemed to me that the scoring system was rubbish.

A game I have enjoyed watching for much of my life is tennis. At the same time as Euro 2020 was underway, so was Wimbledon. I was lucky enough to get tickets for Centre Court this year with my girlfriend, and we had the opportunity to watch Denis Shapovalov, a rising Canadian star, take on the Serb Novak Djokovic, one of the most successful players in history.

Unlike football, which has a very simple scoring system, that of tennis is notoriously quirky. Each match is split into 'sets', of which there can usually be a maximum of either three or five - stipulated in the rules of the tournament. The winner of the match is the first to reach an insurmountable number of sets (so either two or three, respectively). Each set is then further subdivided into 'games'.

A player wins a set by being the first to win six games - although the player must win by a margin of two games, meaning that play continues until one of the players breaks ahead by a wide enough margin. At least, that was the original rule, but a moment's reflection reveals that a tennis match could continue until the end of the universe, or one of the players collapses from exhaustion (whichever first) so the 'win-by-two' rule was somewhat relaxed by the introduction of 'tie-break' games with their own idiosyncratic scoring system, which need concern us no further.

At the level of an individual game, yet another scoring system is in use. In each game, one of the players is designated as serving throughout. The serving player alternates between the two sides game-by-game through the match. Within a game, the score starts at 0-0 (which is pronounced "love all") and each time a player wins a point, they advance their score for the game along a scale which runs: 0 ('love'), 15, 30, 40, game. The first player to reach 'game' wins the game. Except, once again, they must do so by a margin of two points. If the score ever reaches 40-40 (which is pronounced "deuce") then the next player to score a point will have their score labelled as 'advantage'. If they proceed to win the very next point after that, they win the game. If not, the score returns to deuce, and everything repeats itself, ad infinitum¹. Simple. (A little further reflection shows that the game would be functionally identical if the scores simply ascended 0, 1, 2, 3, 4, ... until someone achieved a score that was both greater than or equal to 4 and also at least two larger than the opponents score.)

(Sorry if you already knew the scoring system in tennis. You probably did, but I quite enjoyed writing it out.)

Now here's where I think scoring systems get interesting. Some time after I first learnt the scoring system for tennis, possibly while watching Andy Murray grittily cling on to a roughly equal scoreline in a match where he was clearly underperforming his opponent, it occurred to me that one could win a tennis game despite scoring far fewer points overall than one's opponent.

Indeed, to take an extreme demonstration, suppose you lose all your receiving (i.e. non-service) games to love. Further, suppose you valiantly hold your own service games, despite a ferocious onslaught of competiton from the opponent, such that each service game is held only after reaching deuce. In this way, the sets could be shared equally, and then the games of the deciding set also shared equally almost to the end. And then finally, you clinch one good game to break the opponent's serve and win the match. You would have scored something like half the number of overall points in the entire match than your adversary but nevertheless you would have won.²

I was appalled. How could this make any sense? How could it possibly be fair on the clearly better player? Did the people who invented this ludicrous system not even think about it long enough to notice such a glaring hole in the proposed scheme?

But of course, the more tennis matches I watched - glued to the nail-biting drama - the more times I saw a player suddenly spring back from a several-games-long lull of form to 'break back serve' and clinch a critical set from the jaws of defeat. It became clear that tennis is exciting to watch, in large part, specifically because of its strange scoring system.

The key point, I believe, is the breaking-down of scoring into distinct segments of play, which once won or lost only count for a single 'point' at that level of the heirarchy, with all other information about what happened in that segment being unrecorded in the final score. So if you play particularly well in a set of tennis, you score one point, and if you continue to play well in the second set, but narrowly lose it to an ascendant opponent, the score in sets becomes simply 'one all', regardless of how comprehensively you thrashed the opponent in the first set.

For fans, this is how matches get their drama and excitement. A losing player has a lot of leeway to level the score, which means supporters take longer to totally lose faith in their poorly performing favourites. This very often leads to players suddenly finding a bout of form which propels them back into contention, and so matches can seem far closer fought than if a simpler scoring system was in use. The ultimate effect is that the game becomes much more psychological.

Consider the Djokovic-Shapovalov match we watched at Wimbledon. In that game, Djokovic scored a grand total of 116 points, while Shapovalov scored 104. Pretty closely fought, one might imagine. The truth is that although the game really did feel very close throughout (the crowd was heavily behind the rising young Canadian player - the David to Djokovic's Goliath), the actual final scoreline had Djokovic winning comfortably in straight sets: 7-6, 7-5, 7-5. The explanation for why lies in the 'break point' statistics, which record how successful each player was at stealing the opponent's service games - a critical part of pulling off the win-by-two rule for sets. Djokovic created 10 break point opportunities and converted 3 of them. Shapovalov created 11, but only converted one.

The battle to break serve in tennis is the big strategic key to winning matches. Everyone wants to break serve. Typically, games are won by whoever serves, because serving confers a sizeable tactical advantage at the level of an individual point. So if a set "goes with serve" nobody breaks away to win-by-two (which, of course, is the whole reason the win-by-two rule exists in the first place). The consequence is that breaking serve is one of the big intermediate goals of winning a tennis match, which means that individual points are not created equal in tennis.

Football (and a lot of other games) have what I will call a 'linear' scoring system. Scores simply accumulate, 1, 2, 3,... from the start of the alloted time until the end. Whoever has scored more points at the end wins. It is literally the simplest possible scoring system for a game, and in such a system, each point really is created equal. It matters not under what circumstances you scored a goal, nor what the scoreline looked like at the time you did it. A goal is a goal is a goal: they all count the same in the final tally.

In tennis, we get the excitement of rising and falling action throughout the match. The 'story' of the match develops, as the player struggling from behind strives to create the all important break opportunities, and even more importantly tries to convert them. Specific points in the game become absolutely pivotal, and the players' nerves, determination, focus and stamina are all thoroughly tested in those crucial moments of high drama.

Other games share similar features to tennis. Snooker, a marvellous spectator sport (believe me), which I've enjoyed since childhood, has matches broken down into 'frames'. Matches are won on the basis of reaching a predefined target number of frames before your opponent, but the frames are otherwise entirely independent events. The same 'story arcs' we get in tennis can arise in snooker for precisely this reason. Darts works like this too, with its legs and sets reminiscent of tennis' games and sets. Cricket has a famously tricky scoring system, which includes a breakdown into innings. I don't know much more about the intricacies of cricket though, so perhaps a cricket fan can help confirm or deny my hypothesis?

As I was watching some of the Euro 2020 matches, it dawned on me that the linear scoring system was responsible for making the game less exciting to watch in some ways. Conservative play is heavily incentivised, especially near the beginning when scores are equal, and most especially near the end when one team has a lead (even by just one goal) and the clock is running down towards the end of the alloted time. Many modern teams, including Gareth Southgate's England side at this tournament, have been criticised for passive, defensive play. They try to maintain possession of the ball above all else, hoping to carefully develop a scoring opportunity even if it takes half the game to do it just once. Then, with a goal in the bag, they will try to retain possession until the final whistle blows and the victory is held.

There's nothing fundamentally wrong with this approach. I'm arguing that it is naturally incentivised by the scoring system of the game. Indeed, by playing like this throughout, England had one of its best historic performances in decades, reaching the final but ultimately losing to Italy.

So here's my hare-brained takeaway from the whole thing: football needs a new scoring system. The rest of the rules can stay the same (although maybe the rules around throwing oneself to the ground with abandon could be shored-up somewhat...) Here is my suggestion:

• A match is broken down into segments: call them sets.
• Conventional football scoring is used for each set.
• Each set runs for a fixed period of 9 minutes, and there are ten sets in total.
• Each side is deemed to be 'on serve' alternately for each set. If a set ends in an equal score, the set is simply awarded to whichever side was on serve.
• The match is won by whichever side has the most sets at the end. However, a win-by-two rule applies, so further sets are played if needed beyond the base of ten. Of course, some form of tie-break rule could be introduced if organisers wish to limit the maximum possible length of a match.

These rules set up a strong incentive to 'break serve' at all times throughout the match: since each set only lasts 9 minutes, and since you always need to try and win the set, there will be far less of the slow, passive passing around of the ball in defensive configurations, and a lot more creative, attacking football. Numbers of 'shots on goal' would likely increase dramatically, and a catastrophic performance in a single set wouldn't spell the end of the excitement or sign the death warrant of the offending team. 'Losing serve' would further incentivise bold, attacking play in the very next set, as the struggling team tries to recover to get the match back 'on serve'.

Of course, these rules would undoubtedly change the tactical and strategic feel of the game of football, possibly beyond recognition. And with a long and illustrious history, no one will want to interfere. My final observation is to point out that everything I've said must necessarily be completely wrong. Football is the single most popular sport on planet Earth. The global governing body of the game, FIFA, estimates that it is played by about 265 million people, and enjoyed by about 3.5 billion fans: half the population. Thus, it cannot be the case that the game is boring, so I must just be wrong. Ah well.