Wuornos

Dec 9th, 2007, 01:08 PM

Although in many respects these ratings are more elementary in their calculation methodology than previous exercises I have undertaken they seek to better represent and model the thought processes of expert opinion in the field of tennis

They are called the DOT ratings because the model developed is based around three factors. The level of Domination of the rated player meaning the concentration of achievement within a limited time frame. Standard of Opposition that are currently active when achieving their measured domination. Tournament being competed in and its importance measured by the players attracted in recent years.

The DOT system is what I would describe as a double iterative process. We will come to exactly what this means shortly.

Achievement is measured on a very basic formula, but should be fit for our purpose. i.e. Players in the majors receive points based on their round of exit. Each round they progress earns them double the points of the previous round. I have never been a believer in the official ratings approach of the progression of a round within an event being worth less than double achievement. If the player numbers halve in my eyes the achievement doubles, hence the above approach. The value of the numbers are irrelevant as this does not effect the relative rankings. Some will notice I am only looking at majors and this is because I have previously received feedback highlighting the fact that some players do not consider the lesser events as important and their performance given the heavy schedule is weakened within these events. Of course Achievements measured in this way would massively favour players like Connors and Agassi, who both had exceptionally long careers, while penalising players like Borg and Laver (who had short careers within the open era).

Next we move onto Domination. Domination is calculated as rolling figure based upon achievement within recent events with more recent events receiving greater weight. Achievement points from the last 4 Majors receive the highest weighting while each year the weighting awarded to the event halves. As you can see more than half of a players dominance is made up of his/her performance in the last 12 months with the remainder being made up of performances over the previous years.

These simple calculations generating a very simple estimate of a players domination ends the first iteration.

The second iteration begins by calculating event weightings based upon the player dominations calculated as part of the first iterative process. Event weightings are reflective of the strength of the tournament. Of course the strength of any tournament is dependant on the players current strength of the world players multiplied by the events ability to attract them. This sounds very complex but in reality the calculation is simple. The average domination score for all players taking part in the event as calculated in the first iteration is sufficiently accurate for our purposes . Remember this implicitly includes player strength and the tournaments status. E.g. If the overall domination points reduce at the top of the player population then the tournament strength reduces proportionately. Likewise if a tournament begins to fail in attracting the top players while dominance levels amongst the top players remain constant, then again we see the tournament strength drop. The results from these calculation lead to the Australian Open receiving less weighting in the mid to late 1970s and early 1980s while the French has also suffered at times. Wimbledon and the US Open remain reasonably high in these calculations. Please note the above methodology ensures the weighting remains directly proportional to the domination of players attracted and therefore is self adjusting and free from human opinion.

The next step in the process is to recalculate the domination ratings. These are calculated in exactly the same way as previously, i.e. achievement multiplied by the year weightings except each is then also multiplied by the relevant tournament strength. This figure then provides a basic indicator of current dominance adjusted by tournament status and dominance of other top players. One piece of feedback I have received in relation to this is that it is slightly self referencing. That is a tournament is stronger if Federer competes and therefore Federer always receives that benefit. I agree with this but do not see it as a problem, it is important that everyone receives the same credit for winning an event and therefore to exclude the player being rated from the strength calculation of that tournament would be equally unfair. The feedback is limited and results only in a slight damping of the rating changes at the top of the scale, which is not something I would necessarily see as a bad thing. The benefits are massive in that we have an independent measure which combines player strength with tournament status which is a big stumbling block in many ratings which give equal weight to all majors irrespective of era and their status at that time.

For the very early periods of the open era it is necessary to use a standard statistical tool to provide a cautious estimate of the domination score had a full 4 years data been available. To do this we take the total weighting which is normally applied to players.

As we can see we now have an adjusted dominance rating for the point in time we have calculated. This gives an indication of the players strength in majors at that point and that point only. Most people assess players on their abilities when they are at their peaks and it is therefore necessary to recalculate the ratings after each major event to identify correctly their peak playing strength.

In the real world an arithmetic progression in standard would yield a geometric increase in dominance. For this reason, ratings have been standardised to a linear scale. They have also been adjusted to reflect a particular standard. The standard used is the minimum level of play necessary to achieve a major quarter final when the standard or dominance at the top of the professional game is at its lowest. This standard has been set at 2500. By and large players who can exceed this standard by a clear 200 points, i.e. 2700, are those players who can expect to win 4 or more majors in an average length career. Of course some players over achieve while others under achieve so this is not a hard and fast rule.

I have taken great time and trouble to ensure the adjustments for tournament strength, which are effected by the standard of the top players in the population and the respective tournament status, are precisely balanced. A player existing in the general population stands an equal chance of increasing or decreasing in rating following the arrival within the population of an outstanding player. Any increase is therefore due to a change in the actual players standard as the reduction in iteration 1 dominance points is balanced by the tournament weightings in the second iteration. A good example of this is Andy Roddick. When he won the US Open in 2003 he had a DOT rating of 2630. In 2004 Federer’s domination of the mens’ game began, but at the end of that year Roddick’s rating had bearly moved at all despite the reduced opportunities in majors. His rating was 2629. 2005 and Rafael Nadal won his first major along with Safin, but Andy Roddick was improving slightly at this time and his rating edged up to 2636. 2006 saw Federer and Nadal take over the top of the men’s game completely. Despite this domination, Roddick’s rating was stable at 2638. Finally in 2007 Roddick’s rating has remained exactly the same at 2638. I hope this reassures some people concerning the validity of the adjustments made to the ratings balancing the relative increase or decrease in rates of dominance by other players at the top of the game.

I hope you all enjoy these ratings as much as I have in putting them together. Any questions please ask. Or should you just wish to know about an individual players peak rating or how their rating progressed over time, who were the top players at what time etc, then just ask away.

I certainly don’t expect this to answer the GOAT question but at least it should help provide some informed discussion over and above personal opinion and based on ‘value added’ statistical data.

I am seeking a publisher for a book giving a more detailed anlaysis relating to methodology and outputs of these data early next year. If you are in position to help me, please get in touch.

Take care all

Tim :)

They are called the DOT ratings because the model developed is based around three factors. The level of Domination of the rated player meaning the concentration of achievement within a limited time frame. Standard of Opposition that are currently active when achieving their measured domination. Tournament being competed in and its importance measured by the players attracted in recent years.

The DOT system is what I would describe as a double iterative process. We will come to exactly what this means shortly.

Achievement is measured on a very basic formula, but should be fit for our purpose. i.e. Players in the majors receive points based on their round of exit. Each round they progress earns them double the points of the previous round. I have never been a believer in the official ratings approach of the progression of a round within an event being worth less than double achievement. If the player numbers halve in my eyes the achievement doubles, hence the above approach. The value of the numbers are irrelevant as this does not effect the relative rankings. Some will notice I am only looking at majors and this is because I have previously received feedback highlighting the fact that some players do not consider the lesser events as important and their performance given the heavy schedule is weakened within these events. Of course Achievements measured in this way would massively favour players like Connors and Agassi, who both had exceptionally long careers, while penalising players like Borg and Laver (who had short careers within the open era).

Next we move onto Domination. Domination is calculated as rolling figure based upon achievement within recent events with more recent events receiving greater weight. Achievement points from the last 4 Majors receive the highest weighting while each year the weighting awarded to the event halves. As you can see more than half of a players dominance is made up of his/her performance in the last 12 months with the remainder being made up of performances over the previous years.

These simple calculations generating a very simple estimate of a players domination ends the first iteration.

The second iteration begins by calculating event weightings based upon the player dominations calculated as part of the first iterative process. Event weightings are reflective of the strength of the tournament. Of course the strength of any tournament is dependant on the players current strength of the world players multiplied by the events ability to attract them. This sounds very complex but in reality the calculation is simple. The average domination score for all players taking part in the event as calculated in the first iteration is sufficiently accurate for our purposes . Remember this implicitly includes player strength and the tournaments status. E.g. If the overall domination points reduce at the top of the player population then the tournament strength reduces proportionately. Likewise if a tournament begins to fail in attracting the top players while dominance levels amongst the top players remain constant, then again we see the tournament strength drop. The results from these calculation lead to the Australian Open receiving less weighting in the mid to late 1970s and early 1980s while the French has also suffered at times. Wimbledon and the US Open remain reasonably high in these calculations. Please note the above methodology ensures the weighting remains directly proportional to the domination of players attracted and therefore is self adjusting and free from human opinion.

The next step in the process is to recalculate the domination ratings. These are calculated in exactly the same way as previously, i.e. achievement multiplied by the year weightings except each is then also multiplied by the relevant tournament strength. This figure then provides a basic indicator of current dominance adjusted by tournament status and dominance of other top players. One piece of feedback I have received in relation to this is that it is slightly self referencing. That is a tournament is stronger if Federer competes and therefore Federer always receives that benefit. I agree with this but do not see it as a problem, it is important that everyone receives the same credit for winning an event and therefore to exclude the player being rated from the strength calculation of that tournament would be equally unfair. The feedback is limited and results only in a slight damping of the rating changes at the top of the scale, which is not something I would necessarily see as a bad thing. The benefits are massive in that we have an independent measure which combines player strength with tournament status which is a big stumbling block in many ratings which give equal weight to all majors irrespective of era and their status at that time.

For the very early periods of the open era it is necessary to use a standard statistical tool to provide a cautious estimate of the domination score had a full 4 years data been available. To do this we take the total weighting which is normally applied to players.

As we can see we now have an adjusted dominance rating for the point in time we have calculated. This gives an indication of the players strength in majors at that point and that point only. Most people assess players on their abilities when they are at their peaks and it is therefore necessary to recalculate the ratings after each major event to identify correctly their peak playing strength.

In the real world an arithmetic progression in standard would yield a geometric increase in dominance. For this reason, ratings have been standardised to a linear scale. They have also been adjusted to reflect a particular standard. The standard used is the minimum level of play necessary to achieve a major quarter final when the standard or dominance at the top of the professional game is at its lowest. This standard has been set at 2500. By and large players who can exceed this standard by a clear 200 points, i.e. 2700, are those players who can expect to win 4 or more majors in an average length career. Of course some players over achieve while others under achieve so this is not a hard and fast rule.

I have taken great time and trouble to ensure the adjustments for tournament strength, which are effected by the standard of the top players in the population and the respective tournament status, are precisely balanced. A player existing in the general population stands an equal chance of increasing or decreasing in rating following the arrival within the population of an outstanding player. Any increase is therefore due to a change in the actual players standard as the reduction in iteration 1 dominance points is balanced by the tournament weightings in the second iteration. A good example of this is Andy Roddick. When he won the US Open in 2003 he had a DOT rating of 2630. In 2004 Federer’s domination of the mens’ game began, but at the end of that year Roddick’s rating had bearly moved at all despite the reduced opportunities in majors. His rating was 2629. 2005 and Rafael Nadal won his first major along with Safin, but Andy Roddick was improving slightly at this time and his rating edged up to 2636. 2006 saw Federer and Nadal take over the top of the men’s game completely. Despite this domination, Roddick’s rating was stable at 2638. Finally in 2007 Roddick’s rating has remained exactly the same at 2638. I hope this reassures some people concerning the validity of the adjustments made to the ratings balancing the relative increase or decrease in rates of dominance by other players at the top of the game.

I hope you all enjoy these ratings as much as I have in putting them together. Any questions please ask. Or should you just wish to know about an individual players peak rating or how their rating progressed over time, who were the top players at what time etc, then just ask away.

I certainly don’t expect this to answer the GOAT question but at least it should help provide some informed discussion over and above personal opinion and based on ‘value added’ statistical data.

I am seeking a publisher for a book giving a more detailed anlaysis relating to methodology and outputs of these data early next year. If you are in position to help me, please get in touch.

Take care all

Tim :)