Experimenting with Ranking Systems

[akv89]

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.

 

[aphex]

sorry, but your system is fail---it gives more weight to the most recent surface

 

[akv89]

sorry, but your system is fail---it gives more weight to the most recent surface

That comes without saying. It's a way to gauge who has the most momentum going into the next tournament.

 

[Leublu tennis]

I don't buy it. So you give Madrid some kind of extra benefit. That is a big plus for Federer but it ignores a couple of quirks. The 4 hour ordeal that Nadal went through played a role in Federer's win. And Roddick, one of the worst clay court players of all time (for a top 10 player, that is) gets a w.o. thus gaining disproportionate merit. I am O.K. with straight line points for this tournament (if I understand your system) but can't accept the extra benefits that Federer and Roddick gained from this tournament based on your new system.

Back to the drawing board, I say.

LT

 

[akv89]

I don't buy it. So you give Madrid some kind of extra benefit. That is a big plus for Federer but it ignores a couple of quirks. The 4 hour ordeal that Nadal went through played a role in Federer's win. And Roddick, one of the worst clay court players of all time (for a top 10 player, that is) gets a w.o. thus gaining disproportionate merit. I am O.K. with straight line points for this tournament (if I understand your system) but can't accept the extra benefits that Federer and Roddick gained from this tournament based on your new system.

Back to the drawing board, I say.

LT

Let me know when there's a ranking system that can account for the intricacies of walkovers and match length, because it certainly wasn't my intention to make one that does . The "advantage" you mention isn't really that significant considering it's just one tournament.

 

[rubberduckies]

That comes without saying. It's a way to gauge who has the most momentum going into the next tournament. We would also see more gradual movement and more movement in general in the rankings as earlier tournaments are devauled each week.

It's an interesting idea. It does better reflect momentum and recent level of play.
It wouldn't work when trying to find a year-end number 1 or the top 8 for the Masters Cup.

I'm curious how exactly you came up with those numbers.

What slope are you using for your linear model and how are you plotting time points? It would be pretty difficult to find a fair way to determine those details.

Same goes for your bell curve. I'm also wondering why you would even use a bell curve to weight tournaments because there isn't really any underlying distribution going on.

 

[akv89]

It's an interesting idea. It does better reflect momentum and recent level of play.
It wouldn't work when trying to find a year-end number 1 or the top 8 for the Masters Cup.

I'm curious how exactly you came up with those numbers.

What slope are you using for your linear model and how are you plotting time points? It would be pretty difficult to find a fair way to determine those details.

Same goes for your bell curve. I'm also wondering why you would even use a bell curve to weight tournaments because there isn't really any underlying distribution going on.

Good questions. Firstly, the slope for the linear model would affect the number of points each player would have but not the order of players in the rankings. I wanted to use a slope that can be used to compare the results with the existing ranking system. If the maximum weight is 2 and the minimum weight is close to 0, then the average weight in the linear model would be about 1. Therefore, the ranking would be comparable to the current rankings. Same goes for the Gaussian model. If a player's ranking is lesser than his current ranking (as is the case with Nadal and Federer) it means that their best results are further back in time and if it is higher than their current ranking (Murray and Djokovic) their best results are closer in time.

The idea behind the gaussian model comes from my research dealing with image processing. Smoothing images involves applying a gaussian function on each pixel of the image, so that the intensity of a certain pixel is affected by it's own intensity and those of neighboring pixels. This reduces the effect of random artifacts; in tennis, this would be analogous to reducing the effects of an uncharacteristic tournament for a player by looking at more events. The current ranking system tries doing that by looking at 52 weeks instead of just 1, but since it weighs them all equally, it doesn't do a good job if you're interested in seeing how good a player has been recently.