Ancient Arithmetic: The Possible Origins Of The Tennis Scoring System, Part One Of Four Pieces On Tennis History

Pondering tennis scoring, abacus in hand, Moreton Morrell, 2019

Why Score Points/Strokes in 15s?

Lovers of tennis have long pondered the origins of the scoring system. In particular, the notion that the first point scores 15, the second point 30 and so on, until one player has scored four points, or, if the score reaches three-all, once one player has subsequently taken two consecutive points.

There are a great many theories about the origins of this convention.

At the time of writing this piece (the summer of 2020) there are two prevailing “origins” theories on the internet, both of which fail the credibility test as soon as some historical facts are thrown into the mix.

The most common of the fallacious origin theories is that tennis scorers habitually used clock faces to score the games, taking the minute hand numbers as scores, i.e. 15 to signify a quarter of the job done, 30 to signify half, 40 (as an abbreviation for 45), 60 to conclude the game.

Unfortunately for this elegant, oft-touted and much-believed theory, there are early written accounts of the 15/30/45 scoring system dating back to the Renaissance; long before anyone had considered the idea of minute markings on clock faces. While it is possible that such devices might have been used at times in the last 300 years, this simply is not a credible “origins” theory.

The second style of origin theory, often to be found on the internet, is connected with the chase markings on a real tennis court. Variations of this theory include the notion that there were traditionally 14 chase lines on the floor, so the concluded point was called, to avoid confusion, 15. The other main variation of the “floor plan” theory is that the court was traditionally 90 feet long (45 feet on each side) and that the server had to advance 15 feet on winning the first point, a further 15 on winning the second etc.

Lovers of the early forms of the game, known variously as real tennis, royal tennis, court tennis and jeu du paume, will recognise that there is no such standardisation of courts, whether on length or on court markings (or even on how to name the game). Just naming it “tennis” pleases me best.

There was a tradition in France at one time to have 14 floor marks on the service side, but that French tradition of floor marking was initiated long after the scoring system was established. It is possible that the French floor marking style was a nod to the fact that the scoring system was based on 15/30/45/60, but it cannot have been the cause of that scoring system.

While Internet Babble Might Hinder, So Might Historic, Original Sources, Now Available Freely Through The Internet, Help

So internet babble couldn’t solve this one for me. I needed to retreat into ancient texts on tennis. There I found such a rich collection of writings I could happily generate several essays on the origins of many aspects of the game; indeed I intend to do just that.

The Willis Faber Book Of Tennis & Rackets by Lord Aberdare (I had to purchase this one; it is not in the public domain) is an authoritative book on the subject. Aberdare shows documentary evidence that 15/30/45 were used as far back as the Middle Ages. Heiner Gillmeister quotes an early 15th Century Middle English poem about the Battle of Agincourt, which uses a game of tennis as a metaphor for the battle and quotes the scores XV, XXX and XLV. A poem by Charles d’Orleans, dated in the 1430s, also mentions 45 in the context of tennis. Erasmus’s Colloquies c 1518, mention the scoring of a love game as Quindecim, Trigenta, Quadraginta quinque.

Lord Aberdare also tells us that writers as far back as the 1430s wondered “why 15s?”, but could find no satisfactory answer.

Aberdare also quotes and lists his sources extensively. A great many of those original sources are now freely available on-line through the internet archive and other such public domain sources. I have provided links in this article where such sources exist.

In The Renaissance Period, The Italians & The French Were Doing Most Of The Running In Tennis

The very first treatise on tennis, attempting to set down its rules comprehensively, was written by Antonio Scaino in 1555, Trattato del Giuoco della Palla (Treatise of the Ball Game). Like so many of these ancient texts, it is freely available on-line through the Internet Archive – click the preceding link or image below to read the document.

I need to rely on Julian Marshall’s translation and interpretation of that text in his wonderful, seminal English work on the history of tennis; The Annals Of Tennis, 1878, which is also freely available through the internet archive. Julian Marshall’s work will feature large in some of my later pieces on tennis history. Lord Aberdare relies on Marshall heavily for the history of the game.

According to Marshall, Antonio Scaino advances a rather convoluted theory for the use of 15, based on (as he sees it) three types of game and the five points required to turn a 0-40 position into a game in one’s own favour.

While Scaino’s theory seems rather weak to my modern, forensic mind, yet it is still fascinating to note that Scaino speaks of this kind of scoring, including the use of deuces, as a standard thing for almost all ball games. Marshall writes:

This was, evidently, even then a matter of universal custom which needed no comment; and, with the “setting” of the game at deuce (a dua), it was common, Scaino says, to all ball-games, with the exception of foot-ball…

In La Maison Academique – 1659 – the first French book on games – also available on-line today – a much earlier, late 16th century work: Signification de l’ancien jeu des chartes pythagorique et la déclaration de deux doubtes qui se trouvent en comptant le jeu de la paume by Jean Gosselin is quoted at length, debating his “deux doubtes” (two doubts) about the origins of the scoring system:

…why we should count, as from time immemorial we have counted, 15, 30, 45 and then game, which latter should be equivalent to 60, rather than by any other numbers greater or lesser than these.

Gosselin comes up with two “solutions” to his doubts. One based on astronomy or a sextant, being a sixth part of a circle itself consisting of 60 degrees and sixty minutes. Unfortunately, at that time, a set tended to comprise four games, not six as has more recently become common, so his 60 times four does not complete the circle.

His second theory is based on geometry and a rather convoluted theory around Roman measures, as four fingers =1 palm, 4 palms = 1 foot and 1 Clima = a square of 60 feet by 60 feet, 1 Actus = 2 Climates in length and breadth, 1 Jugerum = 2 Actus in length and 1 Actus in breadth.

After dancing around his two theories for a while, Gosselin concludes that he has solved the matter decisively, Q.E.F. (as the French say).

Readers might form their own views on Gosselin’s “extremely complicated” (as Lord Aberdare puts it) geometrical theories and the somewhat arrogant tone of Gosselin’s certainty that he has solved the doubts about the origins of the scoring system.

But I shall shortly return to the notions, which are undoubtedly so, that the origins are buried in antiquity and that, again as Lord Aberdare summarise it:

…the number 60 often represented a complete whole in mediaeval times…

While Italian written sources go back to the mid 16th century and relevant French ones to the late 16th century, there are no English authorities on tennis until the 19th century; just the occasional fragment or mention of tennis in other works.

On the question of using the term “forty” rather than “forty-five”, which several correspondents have raised, I have written a short Appendix:

Ancient Arithmetic Appendix: On The Use Of “Forty” Or “Forty-Five” To Count The Third Point In A Game Of Tennis

19th & 20th Century English Contributions To Tennis History

The first English book on tennis was published in 1822: A Treatise on Tennis By a Member of the Tennis Club, now attributed to Robert Lukin. “The Club” referred to in the title was the James Street Court in Haymarket; at the time the club acted as “guardian of the laws” of tennis, until “the Tennis Club” closed and handed that guardianship role to the Marylebone Cricket Club (MCC) in the 1860s.

Again, these days, you can simply click the link and read the whole book on the internet archive. A fun and short read. That book is strong on odds/handicaps and also has a fascinating appendix with historical notes about notable royal lovers/players of the game, but the scoring system is merely stated as fact with the aside that strokes:

…are reckoned in a manner, which makes it at first very difficult to understand.

The first Stroke or point is called 15

The second…30

The third…40 or 45

…

So it really isn’t until Julian Marshall’s 1878 book, The Annals of Tennis (previously mentioned and linked, but, heck, here’s the link again) that the origins of the scoring system is given thoughtful coverage in English. Marshall’s influence spans lawn tennis as well as real tennis, as I shall explain in a subsequent piece about the intriguing ways the two games have developed, like conjoined twins, somewhat independent and yet in several ways metaphorically joined at the hip. Marshall was also a prominent MCC member who played a major role in the codification of the laws of tennis in the last few decades of the 19th century.

But Marshall doesn’t progress the thinking about the origins of the scoring system, he simply catalogues the Italian and French writings on the topic authoritatively and helpfully.

More recently, in the 1990s, the subject has had in depth and well-researched coverage in Heiner Gillmeister’s book, Tennis: A Cultural History:

Gillmeister is a leading expert on the history and origins of ball games generally and in particular tennis. Gillmeister’s extensive research leaves him in little or no doubt that the game we recognise today as tennis, including the scoring system, has its origins in medieval Europe and that scoring games using base 60, divided by four, is probably related to money matters at the time.

Whisper it, people, but medieval tennis, once it became popular among the secular classes, was not played for honour and valour; it was primarily played for money. It was a mechanism for the players and also sometimes spectators, to wager.

Many jurisdictions had wager limits embedded in the law. Nuremberg commoners are:

…enjoined not to play for more than sixty “haller”and for no object or possession valued at over sixty “pfennige”

A similar edict from Munich in 1365 limits stakes to 60 “denare” (deniers). But there is no direct evidence that such limits were applied in France, nor is there direct evidence that these regulations, which were applied to dice games, would also have been deemed to apply to wagers on tennis.

Gillmeister also says, regarding such gambling regulations:

…they do without doubt prove one thing: by at least the end of the thirteenth century and during the fourteenth century, the time when sous worth fifteen deniers were in circulation, games played for stakes of over 60 deniers were forbidden

Now Mr Gillmeister might know a heck of a lot about linguistics and the history of ball games, but I’m not as convinced that he has quite such a strong grasp on the history of money. While there were many variations of coinage at that stage of the medieval period, the relative standard of 12 deniers to the sous and 20 sous to the livre was fairly well established across Europe. In England this was expressed as 12 pennies to the shilling, 20 shillings to the pound. There were many local variations, including a coin known as the patard which was, at times, in circulation and worth 15d. At the higher end of the scale, Gillmeister mentions the double royal d’or and the gros denier tournois, but frankly neither of those coins became a standard based on sixty sous or fifteen deniers.

Still, I find compelling the arguments that medieval tennis was regularly played for stakes and that a maximum stake of 60 pfennigs (or 60 deniers, or 60 pennies) per game might have been a de facto standard regulation at a vital stage of the development of tennis. I find the “coinage arguments” for division into 15s less convincing, but it is quite possible that the principle of “the first to four wins the game, unless…” was well-established, making 15 the natural point counter, if you seek to get to 60 points for a game.

A further point regarding money, which Gillmeister misses but I recognise and find compelling, is the notion that, if 60 represents a game, 240 would, at that time, have represented a set. Until relatively recently, a set was, more commonly, the first to four games, not the first to six. Sets of tennis mostly being to six emerged as a standard in the last 200-300 years. So while Gillmeister agonises over coins that might or might not have been valued at 15 deniers in various places at various time, he misses some clear evidence in plain view, that a set of tennis, if counted to four games of 60, i.e. 240, would almost universally in Europe have represented a livre, or, as we say in English old money, 240 pennies makes one pound.

Gillmeister is far more convincing and consistent on the “medieval chivalric” case for deuces, or at least the principle that games should be determined by a margin of two points, not just one point. Jan Van Berghe – he of the early 15th century Agincourt poem, discusses, in a later work, the continuation of play from deuce until one player has won two consecutive chases.

Scaino, our Italian Renaissance correspondent from 1555, is emphatic on this point in his Trattato:

The method of fighting such a distinguished battle should be removed from any suspicion of chance or fortune. He who wins must be sure that he has won by his own valour, not by any outside favour. Who does not see now that the game could not be devised with good reason to end with only one point? The good and staunch Cavalier is judged not by one thrust of his lance; the elegant Dancer not by just one leap, however bold and skilful…

Less convincing, to my mind, is Gillmeister’s alternative view on the origins of the term “love” to describe the “lack of” score for the unfortunate player who has not yet won a stroke. He is not convinced that “love” is a bastardisation of the French word “l’oeuf”, i.e. egg, representing “0” – zero. He prefers the Dutch or Flemish word “lof”, meaning honour, or “nothing more than the love of the game”. Gillmeister is a linguist as well as a ball game historian, so what do I know when I say that I find the “oeuf” explanation more convincing than the “lof” argument?

The Stuff Of Ancient Legend; As Deep In Antiquity As Can Be

Gillmeister starts his book Tennis: A Cultural History with a fascinating legend from the late 12th century.

A young, intellectually-challenged trainee monk does a deal with the devil in order to shine in his studies. One day he falls ill and has a near-death experience, during which he descends into a hellish valley where demons fashion his soul into a ball and play jeu de paume (medieval tennis) with it.

The story is recorded in the early 13th century work, Dialogus Miraculorum, by Caesarius of Heisterbach – yet another of these wonderful old texts that is freely available on-line if you wish to read or just look in awe at the ancient text.

This legend, along with the Gillmeister’s central numerical point about the scoring system; that the use of base 60 was important in medieval Europe, brought another, much earlier culture to my mind.

The very earliest civilisation known to have urbanised, the Sumerians in Southern Mesopotamia.

They started writing stuff down around 5000 to 5500 years ago, did the Sumerians. Most of the stuff they wrote down was rather dull, accounting type records, in cuneiform, on clay tablets.

The Sumerians used the sexagesimal (base 60) counting system. Sexagesimal is, in many ways, a more sensible base for counting and dividing stuff up than the decimal system we use today. As the wikipedia entry so succinctly puts it:

The number 60, a superior highly composite number, has twelve factors, namely 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, of which 2, 3, and 5 are prime numbers.

Given that the Sumerians basically wanted to count crops, divide them up and pay for them, sexagesimal made a great deal of sense. They also wanted to measure angles and stuff; these latter habits in sexagesimal became so deeply established in ancient times (the Greeks and Romans persevered with those aspects) that elements of sexagesimal have found their way into measures in our society still; 360 degrees to a circle, hence latterly 60 minutes to an hour, 60 seconds to a minute, etc.

Unlike the hotch-potch of currencies and translation rates known to have existed in medieval Europe, records indicate that Sumerian money was unequivocally denominated in terms linked with base 60. The basic monetary unit was the shekel. There were 60 shekels to the mina and sixty minas to the talent.

Not only did the Sumerians leave plenty of evidence of proto accountants, they also left evidence of proto lawyers. The Code of Ur-Nammu is the oldest known legal code, more than 4000 years old (c.2100 BC). Only some of this code survives, sadly. But those surviving passages include fines and compensation rates, which include the following:

If a man divorces his first-time wife, he shall pay (her) one mina (60 shekels) of silver.

If it is a (former) widow whom he divorces, he shall pay (her) half a mina (30 shekels) of silver.

If the man had slept with the widow without there having been any marriage contract, he need not pay any silver. (Love).

If a man commits a kidnapping, he is to be imprisoned and pay 15 shekels of silver.

We also know that the Sumerians (and their successor civilisation, the Babylonians) were very keen on games. Boards for the Royal Game Of Ur have been found dating back more than 4500 years. Some boards have been found with additional counters, believed to be evidence of gambling on the games.

The game is a proto-game closely related to chase games popular today, such as ludo and backgammon. Sumerians used several four-sided dice for this game. A rules tablet for the Royal Game Of Ur was discovered and translated in the early 1980s.

“So did the Sumerians play ball games?”, I hear you cry.

Yes, they did.

Unfortunately, we, as yet, have very little on record as to what those ball games might have been like.

But the Epic Of Gilgamesh, arguably the earliest surviving work of great literature, written more than 4000 years ago, has passages that allude to ball games at the start and end of the epic.

At the start of the epic story, Gilgamesh exhausts his male companions through the playing of ball games while exercising his droit du seigneur on the local female brides. He’s not a nice chap, that Gilgamesh.

The final part of the story (in some ways disconnected from the earlier parts) is known as Gilgamesh, Enkidu and the Netherworld. In this story, Gilgamesh’s ball and ball-playing implement (sometimes translated as a mallet) has found its way into the Netherworld. Enkidu, who is Gilgamesh’s companion and/or nemesis throughout the epic, descends into the netherworld to retrieve the ball game apparatus, with predictably epic results.

This last story is hauntingly similar to the medieval story about a hellish game of tennis at the beginning of Heiner Gillmeister’s tennis history. It is also achingly similar to folklore tales throughout the world. A fascinating academic paper on this topic, The Ball Game Motif in the Gilgamesh Tradition and International Folklore by Amar Annus and Mari Sarv, can be found on Researchgate through the preceding link. Many traditional folk stories have ball games as their plot triggers, including Persian direct descendants of the Gilgamesh legends and the Estonian stories described in the “Ball Game Motif” paper.

Conclusion: An Absence Of Claims But A Wealth of Interesting Stuff

Let me be clear about this; I am not claiming that the ancient Sumerians played tennis or even anything like it. The ball games played in Sumeria were probably more akin to hockey or polo. But while we don’t know exactly how they played ball games; we do know for sure that they played such things, with implements, to the extent that such artefacts were the subject of legend.

We also know for sure that the Sumerians counted, divided and used a monetary system in base 60. We know that Sumerian regulations used denominations of 15, 30 and 60 as compensation payments and fines. We also know that this very ancient civilisation not only played ball games but also board games using four-sided dice. We strongly suspect that they gambled.

We know that lawyers and accountants tend to get involved in games as guardians of the rules and as scorers. In more modern times, the MCC is a living example of that phenomenon (in the matters of cricket and tennis anyway) and has been so for several hundred years.

The Sumerians devised the abacus too.

One of the other truly intriguing things about the Sumerian civilisation is that we still have so much to discover about them. Only a fraction of the relics that are almost certainly preserved and buried there waiting to be discovered have yet been excavated from Southern Mesopotamia. So we (or our descendants) might yet learn some further fascinating details about Sumerian games and scoring systems.

But my main point in this piece is that legends, cultural mores and gaming traditions have a strange habit of surviving and/or re-emerging across centuries and millennia.

Our game, tennis, undoubtedly emerged in medieval times and evolved from there. The extent to which the scoring system was novel in the middle ages, based on the monetary system and gambling regulations, or was based on traditional counting and gaming conventions handed down across the centuries and millennia, is unknown and cannot be known. Such mysteries are part of the fun playing and observing a game so steeped in traditions and history.

Other Pieces On Tennis History

This piece is part one of four pieces. The other three pieces are:

Horrible Histories: The Primordial, Honourable & Ignoble Arts Of Tennis Handicapping

Odds Oddities: 18th & 19th Century Tennis Handicaps & Traditions, Some Stranger Than Others

Scoring Synchronicity: How Real Tennis Scoring Was Adopted For Lawn Tennis Scoring, Then Lawn Tennis Handicapping Methods Wormed Their Way Into Real Tennis

Also, the following appendix to this piece, which explains why the third point is colloquially called as “forty” rather than “forty-five”:

Ancient Arithmetic Appendix: On The Use Of “Forty” Or “Forty-Five” To Count The Third Point In A Game Of Tennis