Followers of this series can be forgiven for thinking that court tennis was exclusively an up-market game played only by cardinals and kings, because their courts, which tended to be in palaces, probably survived disproportionately. More people wrote about them too.

This, however, is not entirely the case. There was much gambling on the game, and that activity supported far more courts than did the medieval elites. Indeed, there were periods when the very survival of the game itself was dependent on it.

Gambling requires a credible chance that either player will win or a disproportionate payout if there is an upset. There are many ways to do this including making the better player ride a horse or a donkey while trying to play. Roller skates and bicycles have also been used to impede those of greater skill. Maces and bootjacks have been used by the better players instead of rackets, and gamblers have offered to play left-handed though they were sometimes equally skilled on both sides. Lesser players have caught the ball and thrown it back all with the intent of evening mismatched players and betting on the outcome.

Inappropriately restrictive clothing, which, in times past, meant really restrictive, slows the swift and the nimble. There are countless historical anecdotes to this effect, but in one case, the better player wore a full marching uniform of the French National Guard including knapsack and cross belt while carrying a rifle with fixed bayonet in his left hand.  Such an event would likely have had a salutary effect on alcohol sales at the bars, which were often attached to the courts.

I myself once played an early Sunday morning tournament match against an opponent who had but recently left the Saturday night dance. He was still in black tie and evening shoes. There was evidence that he had also neglected customary training discipline. My upset win was decisive, but this particular handicap must be thought of as unintentional.

Other attempts to even out the results were less quirky and probably more precise. They involved restrictions on the better player (one serve, for example), banning the better player from hitting certain winning shots, allowing the lesser player to simply claim a key point (a bisque) or requiring the better player to win more points than the lesser one to win each game.

Me ‘N Jake Go Way Back

“I have to win more points than you” is easy, but “just how many more points” is more challenging.

That was the question that drew the attention of Jacob Bernoulli in 1686. The noted Swiss mathematician wrote a “letter to a friend” in which he set out the odds of two unequally skilled court tennis players winning a match.

If wondering how to make an interesting court tennis match out of two opponents of differing ability was a good enough topic for a man who would side with Gottfried Wilhelm Leibniz in a battle over calculus with Sir Isaac Newton, it is good enough for me.

In his time, Bernoulli invented the law of large numbers, which more or less makes probability possible (and stock market forecasting, such as it is). He figured out the importance of frequent compounding in calculating returns on investments. Those are among the ones I understood in a long list of mathematical accomplishments.

He and his math-rival brother also have a lunar crater named after them, which sounds like it would be kind of cool.

If a person today is thinking about the same sorts of things that Jacob Bernoulli thought about in the late 1600s, he can probably avoid being designated a crackpot. Avoidance of crackpot status is a near term goal, while the crater naming opportunity is more of a stretch assignment.

Goal Setting and Challenges

Last month, we introduced the topic of the worldwide handicap system that is used in court tennis to make games competitive even if the skills of the opponents differ. Often significantly.

The story was about the purchase of the handicap system for the game so that it could be operated like a public utility for the benefit of everyone. We did not discuss our hopes for what else it could do, as those will be covered later in a “looking – forward” chapter.

For now, we will think a little bit about the pros and cons of the handicap system and how they fit into the broader goals for the game.

There are two challenges.

The first will be obvious to anyone who has ever been involved in group decision making. Not everyone agrees on the broader goals for the game. Nor do they agree on the relative priorities.

Difficult as that is to overcome, the second challenge is worse. The system must necessarily involve math.

A brief digression.

Law students learn early on that they get to define the meanings of certain terms simply by saying so, then capitalizing them (hereinafter referred to as “Defined Terms.”)

Later in their careers, the law students discover that Defined Terms work fine in contracts, but very poorly in any other form of written communication.

The reason for this is understandable. As soon as regular human beings see Defined Terms, they stop reading.

Here endeth the digression.

So it is with math. Regular human beings stop reading at the very thought of math let alone the sighting of anything resembling an equation or any reference to statistics.

If there is to be any discussion or consensus building, references to math must be carefully avoided. I will even use the English term “maths” in an effort to make the idea more soothing.

We are simply going to assume that, if we can agree on what we want the system to do, the maths can be made to do it.

Handicaps are not Just Numbers

Handicaps are like badges. Lower ones confer distinction and higher ones don’t. The players of our game have egos, more or less like anyone else. Most would rather be in the top 10% than in the middle or bottom 10%, and they do get used to their present position relative to others.

The primary challenge for court tennis is that results must be measured against your opponent rather than against a constant. In golf, you keep score both relative to par, which determines your handicap and against your opponent, which determines who buys the drinks after the round. They are separate.

There is no similar mechanism in court tennis nor is it likely there could be. We don’t have a concept of par, nor any way to measure a result other than against an opponent.

In golf, two players can have their best days ever and both handicaps will go down, but in court tennis they can have their best days ever and the loser’s handicap will go up.

This can be the cause of much disappointment.

The Young and the Old

Like other games, court tennis has two groups of players. The first group is younger and generally getting better, while the second group is older and generally getting worse. If you are concerned about the total number of players and making the game more popular, you probably want to encourage the younger improving players by letting them see their rankings improve faster.

On the other hand, you don’t want to discourage the older players (on whom we are unusually dependent) by seeing daily numerical evidence of their declining skills.

One group wants to see immediate gratification, while the second wants to avoid immediate despair.

Golf solves this problem by counting the best 10 of your last 20 scores (or maybe it is changed to the best five of your last 10). The player who is improving gets to see immediate gratification while the pain is deferred for those in decline.

Are All Assumptions Good?

Historically, there has been an assumption that the total amount of skill (as measured by handicap points) in a given population is constant. One player takes points from another based on results of matches, but the total number of points for that population must remain the same.

I differ with this one and offer the example of two reasonably skilled players who land on a truly magical desert island that includes a court tennis court and an unlimited supply of rackets and balls. (As I said, magical.) Since they also have food, water and lodging, pretty much all they do is play court tennis all day.

They are evenly matched so they alternate winning and losing. Their handicaps never change but they are playing so much that they are both improving.

When they are finally rescued (assuming that they would want to be) they return to the worldwide court tennis community with handicaps that might be accurate relative to each other but are far too high as compared to those who did not enjoy their sojourn on the magical island.

Hmmmm… perhaps we also need to assume a steady supply of training videos? And maybe champagne.

 A Maths Guy Sets Some Goals

For those unconvinced by Bernoulli’s interest in court tennis handicapping and now shaking their heads and wondering why bother, meet Alastair MacKeown, a player who has circulated a lengthy email on redoing the algorithms that control our system. It includes lots of maths so you will be spared the details.

MacKeown suggests certain goals that the system should achieve.

First, it should be understandable to everyone.  Perhaps he would accept my addition of the word “intuitive.”

At present if you beat me in the final of a tournament 6–5, 0–6, 6-5, you will collect a lovely silver trophy and the admiration of all. Well, all except the handicap system, which is based on total games won. It would say I won 16 games (5+6+5 = 16) while you only won12 (6+0+6=12). As our system now exists, my handicap got better and yours got worse. But you won.

That outcome is neither understandable nor intuitive so it reduces confidence in something that is important to the game.

To his list of goals for the system MacKeown would add

• ease of administration
• mathematical rigor
• and faster achievement of accuracy

Those seem reasonable to me but the devil is often in the details.

On the subject of mathematical rigor, MacKeown would like to see the handicaps change as a result of different skill levels rather than chance. Though we have the concept of draws in which neither handicap changes, apparently what we call wins and losses are often statistically insignificant and should be disregarded. He relies considerably on the coin toss experiments that plague high school mathematicians to reach this conclusion.

The odds of heads or tails are 50-50, but it is not at all uncommon to flip heads three or four times in a row. Such an outcome does not change our long-term view on the likelihood of a coin landing heads or tails. To a maths person, such a run is statistically insignificant. So is a 6-4 win argues MacKeown.

Unfortunately, more draws would be contrary to another of his goals — faster achievement of handicap accuracy. Like our shipwrecked inhabitants of the magical island, we do want a player’s skills to be properly measured as quickly as possible.

Goals for Whom?

Different people play for different reasons. Some are intensely competitive and travel to tournaments around the world. At the highest levels, the handicap system is almost never used. All that matters is who won. That can easily be learned from the score line.

Technically, the handicap system does not intend to tell you who won. It is intended to tell you whether you played better than expected and whether your opponent did or did not do the same. If he or she did play better than expected, did he or she do so by more than you did? The best players don’t care. They just want to know who won.

Further down the scale, There are those who have been playing with the same three friends every Tuesday and Thursday at 11 for the last 20 years. They barely care who won or how they rank versus the rest of the world and might only replace a member of the foursome when one of them dies.

In between are the consumers of the handicap system who want to play in events against those of similar ability (flighted events like in golf) or against their demographic peers (over 60, 70 or now 80).

Some do like competitions that test whether you exceeded expectations by more than I did, and there is a player in Australia who specializes in exactly that.

Though he is getting older, he was one of the best in the world and, when his skills began to fade, he took up handicap events. He might be in a match that requires him to begin each game at -40 (seven points to win a game) and his opponent to begin at +30 (only two points required to win). He might also be limited to one serve, have the court arbitrarily diminished in size on every ball he hits and have certain targets denied him. This requires intense concentration, which is presumably what he is testing in himself.

Unfortunately, it results in dreadful matches.  A superb player playing his hardest versus a hapless beginner or an 80-year-old is not a bit fun to watch nor much fun to play. The better player hits every ball the best he can and the lesser player hits almost none of them back.

If a match I am involved in is uneven and the first set is a 6–0 or 6–1 run away, I will often offer my opponent a second set with a larger handicap or say, “this serve is working well for me today so I will not use it in the second set. Instead, I will work on this other one that I’ve always wanted to learn.” That evens things out very quickly and we still get to have rallies, which, to me at least, is sort of the point.

Unfortunately, such matches can’t be measured and don’t count for handicap purposes.

Opening a Discussion

 This is a logical exit for those who don’t play court tennis. You have learned some more quirky things about a game you might never have seen and we are about to turn our attention to those who do play and like to imagine ways to improve an already wonderful game.

What would we like to encourage and how can we avoid drawbacks? Still, no maths allowed, just goal setting.

I offer the following as discussion starters and encourage more and better ideas in the comments.

The mathematical handicap system, begun under the leadership of Chris Ronaldson in 1979 and establishing Alan Lovell, the best amateur at the time, as handicap 0, has been a great success. It has made it possible for significant numbers of players to gather in Melbourne for the Boomerang and in the Basque Country for the Trois Tripots, but more than four decades of improvement in computing makes more things possible and exploring those possibilities implies no criticism of the original.

Getting each player to accuracy requires more results to be posted. I would accomplish this by making players want to post results rather than by arm twisting.

It is empirically well known that the pain of loss is two times the pleasure of gain. It is also well known that tiny rewards (0.2 points) do more harm to those who don’t get them than they do good to those who do. If the lowest handicap is minus 20 and the highest is near 100 and we measure to the 1/10^th of a point, we have 1200 separate handicap levels for at most 12,000 players. Do we really need that many?

If MacKeown’s maths are correct, we should have far more draws than we do. To help improving players get to the right standard faster, why not establish tests of serving and shot making that could be administered by the professionals? Make them objective – a 40s player has to be able to hit 5 of 10 balls rolled off the penthouse into the grille, for example.

Make it a top priority that the games be fun. Can we devise a way to avoid having one player destroy another to preserve his handicap? Can the value of different serves and shots be quantified so that barring them will result in parity?

Doubles also seems problematic. The lesser player in a friendly match is more or less required to “play up,” which means he hits far fewer balls. Is that really fun for him?

One of the delights of the game is the need to think clearly and carefully. (Age and cunning beats youth and skill.) Do the bisque and half bisque help to accomplish this and should they be used more often? Maybe we should ask this question to the server at five all 40 all who calls bisque before he crosses the net to attack chase the nick? He should be rewarded for his knowledge of the game.

This is not intended to be an exhaustive list of suggestions. That would leave little room for what are certainly creative ideas from elsewhere. Let the conversations begin. What can we do better?

Acknowledgements

Much of the historical and anecdotal information about handicapping is drawn from Real Tennis Yesterday and Today by John Shneerson. The information about Jacob Bernoulli comes from Wikipedia.