akv89

05-19-2009, 11:36 AM

I just finished my semester and decided to waste some time on something that interested me: the ranking system. I've heard many people say how the ranking system may not accurately reflect how good players are currently since it equally weighs ranking points for the last 52 weeks. However, only looking at the most recent results is not a reflection of a player's consistency. Hence, I developed a ranking system that weighs more recent results more so than ones more distant in time. For example, the results from French Open last year are weighed very little since it is the furthest tournament after this week and Madrid masters from last week is weighed the most.

There are many weighing systems that can be used to do this. The two that I experimented with were a linear system (where the difference in the weight applied to two consecutive weeks is always the same. In essence, plotting the weight of a given week against how far away that week is will show an increasing straight line) and a gaussian system (where the aforementioned plot would like a the first half of a gaussian bell curve).

The rankings of the top 4 from the last year without any weighting are given below. The ranking points from last year are normalized to this year's ranking system. For example, Federer was given 1200 points for his RG final last year based on this year's system as opposed to the 1400 he received from last year's system.

Rafael Nadal: 14295

Roger Federer: 9600

Andy Murray: 8580

Novak Djokovic: 7725

Below are rankings with a weight applied to them:

Linear:

Rafael Nadal: 13100

Andy Murray: 8657

Roger Federer: 8506

Novak Djokovic: 8252

Gaussian:

Rafael Nadal: 13854

Andy Murray: 8916

Roger Federer: 8750

Novak Djokovic: 8589

It seems like the biggest difference from the current rankings is that Murray is ranked #2, above Federer. Since this ranking system is a better reflection of how good a player is currently than the current ranking system, it could also show trends in how the rankings would look in the near future.

There are many weighing systems that can be used to do this. The two that I experimented with were a linear system (where the difference in the weight applied to two consecutive weeks is always the same. In essence, plotting the weight of a given week against how far away that week is will show an increasing straight line) and a gaussian system (where the aforementioned plot would like a the first half of a gaussian bell curve).

The rankings of the top 4 from the last year without any weighting are given below. The ranking points from last year are normalized to this year's ranking system. For example, Federer was given 1200 points for his RG final last year based on this year's system as opposed to the 1400 he received from last year's system.

Rafael Nadal: 14295

Roger Federer: 9600

Andy Murray: 8580

Novak Djokovic: 7725

Below are rankings with a weight applied to them:

Linear:

Rafael Nadal: 13100

Andy Murray: 8657

Roger Federer: 8506

Novak Djokovic: 8252

Gaussian:

Rafael Nadal: 13854

Andy Murray: 8916

Roger Federer: 8750

Novak Djokovic: 8589

It seems like the biggest difference from the current rankings is that Murray is ranked #2, above Federer. Since this ranking system is a better reflection of how good a player is currently than the current ranking system, it could also show trends in how the rankings would look in the near future.