DAVIS CUP , OLYMPICS , POINTS & MONEY & OUTSIDE THE LINES THINKING

Written by: Staff on 30th November 2014

DAVIS CUP , OLYMPICS , POINTS & MONEY & OUTSIDE THE LINES THINKING |

This being the week after Davis Cup, there have been the usual tennis articles bemoaning the lack of participation in tennis’s oldest international competition.

While we were reading (or, mostly, not reading) those, we were also working on problems in game theory, the mathematical discipline devoted to finding best strategies for solving particular problems. Which naturally set us to thinking. Is there a way to increase Davis Cup participation? To answer this, we have to look at the costs and benefits of playing.

What are the rewards for a player playing Davis Cup? We can think of three, actual or potential:

1. The chance to support one’s country and/or win the Cup itself

2. The chance to earn points

3. The chance to earn an Olympic berth

The penalty of Davis Cup participation is the risk of injury and fatigue.

Roger Federer celebrating after he beat Richard Gasquet during the Davis Cup Final between Switzerland and France.

Roger on Twitter: “I got this after match point, falling on the clay”.

We could try to model how each player decides whether to play Davis Cup based on these four factors. We doubt this would prove very interesting or very successful. But what we can say with certainty is that, in order to increase player participation, we must either increase the rewards or decrease the costs.

Decreasing injury and fatigue problems can be done only by decreasing either the number or the length of matches. There are ways to do this, but all involve fiddling with the format. The ITF has shown great resistance to this.

So can we increase the rewards? Or, alternately, can we increase the perception of the rewards?

There isn’t much we can do about the nationalistic motives of #1. These are, quite simply, idiosyncratic and can’t be legislated.

The award of points, in #2, is also beyond us. The difficulty, as we have pointed out in the past, is that awarding big points for Davis Cup is simply unfair, for two reasons. First, one’s results are not dependent on one’s own performance. This should be a deal-breaker in and of itself, but somehow it hasn’t been. But the other reason why it’s not reasonable is that anything that carries enough points to matter must be open to all. Davis Cup is not — even if your team is in the later stages of the Cup, the coach may decide you are not wanted on the team. Or you may be from a nation like France or Spain that is very deep — and find yourself ranked high enough to get into any regular tournament but not high enough within your national ranks to get on the Davis Cup team. For these reasons, Davis Cup cannot be given really big points, and cannot be made a required event. There must always be alternatives — the current alternative being playing a 500 point event, which awards the same or better points for a lot less effort and requires that effort in only one week rather than throughout the year. Possibly there are incentives that could be offered — “Play Davis Cup and you get to count one more other event” — but these are tricky.

So odds are that we must focus our attention on item #3, the chance to earn an Olympic berth. This one is already gathering some attention — the Davis Cup organizers want to require more ties of the players to earn their Olympic spots. Our suspicion is that this will decrease, not increase, Davis Cup participation, because it will make the effort of qualifying too great for the reward. Players want to play the Olympics — far more than they want to play Davis Cup — but the cost of participating can’t be set impossibly high.

Why? This is where game theory comes in. It’s something formally called the “Discount Factor,” and usually denoted by a lower case Greek delta (δ). An informal title is “the shadow of the future.”

The discount factor tells you how much a future reward is worth to you today. For example, which would you rather have, ten dollars today or eleven dollars a year from now? If those two are equally attractive to you, you have an annual discount factor of about 89% (89% of $11 is about $10). Which would you rather have, $10 today or $20 ten years from now? That is a ten year discount factor of 50%.

Now look at it from a player’s standpoint: We see a lot of Davis Cup participation in the year before the Olympics, because the players get immediate payoff. The year before that, the participation is much lower. We don’t have exact statistics on this, and can’t gather them (since we don’t know who volunteered for Davis Cup but was turned down), but it is clear .that, for the players, the discount rate represents a big mark-down.

And this, it is important to note, produces a lot of selfish behavior. Back in 1984, the famous mathematician and interdisciplinary economist Robert Axelrod published his book The Evolution of Cooperation, which examined the circumstances in which two parties can cooperate in a game called Prisoner’s Dilemma. This work proved to be very important in everything from economics to international relations to zoology, but the basic result is quite simple: two parties will ordinarily cooperate only if they encounter each other a lot and if the discount rate isn’t too low. (That is, they’re more likely to cooperate if the discount rate is 90%, meaning not much discounting, than if it’s 10%, meaning a tremendous amount of discounting.) Davis Cup certainly fulfills the first of these conditions, about the repeated encounters — it’s mostly the same players forming a team year after year. It’s the second one that is the problem.

Is there a solution? The discount factor is, like the value of nationalism, somewhat personal and idiosyncratic. It is hard to manipulate directly. But if you can give more immediate gratification, the discount factor will be less of a concern. One proposal we’ve made is to have an Olympic Festival every year. Qualification would be based on Olympic rules. The points would be equivalent to the Olympics. You could build it into the schedule every year, so that the Olympics wouldn’t mess things up so much. Suddenly, you have a big event and a big motivation — and the discount factor would be much smaller. The incentive for Davis Cup goes up substantially.

This isn’t the perfect solution. It isn’t the only approach, either. For example, you could give more value to Davis Cup participation in the early years of an Olympic cycle — for instance, require fully ten tie-equivalents to qualify for the Olympics, but a tie in year one is worth four, in year two is worth three, in year two is worth two, and in year one is worth one. Or something like that; we haven’t worked the math on this — it is, after all, unfair to younger players.

There are doubtless other ideas. The key is very simple: Get rid of the discount factor and you’ll get more participation.

Story via Bob Larson Tennis News Service

Topics: Davis Cup, Itf, Tennis, Tennis News

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November 30, 2014 at 11:58 am

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