Wuornos

12-02-2007, 01:59 AM

DOT Ratings V3.2 Methodology

This is the first post of the V3.2 DOT Ratings. I will not go into the methodology behind these again as this is already contained within a thread at http://tt.tennis-warehouse.com/showthread.php?t=165420.

The latest revisions incorporate two significant changes and one minor. However before going into these details I need to confess that in making these changes I found a mistake in the algorithm that calculates tournament strength and provides the appropriate weighting for tournaments. This has now been rectified, however, previous rating posts will have contained this error and outputs were distorted. Apologies for this.

1. Following requests from numerous people, the DOT ratings are now calculated over multiple time periods and the results amalgamated with equal weighting to derive an overall rating. On the new overall scale a player could be considered great at 1,100 points and good at 1,000 points. To put this in perspective the womens’ game has produced 49 players in excess of 1,000 points in the open era, which includes 11 players of 1,100+ points and 1 player over 1,200 points. The mens’ game has had 68 players over 1,000 points, 12 in excess of 1,100 points and two players who have exceeded the 1,200 point barrier.

Ratings are calculated by awarding weights to events based upon the strength of competition present. The strength of the competition is based on their overall dominance over the previous 12 months. Points awarded for each event are multiplied by the weighting to derive the points earned by each player.

Once the points have been calculated five primary outputs are produced for each player with a sixth secondary output. The five primary outputs are as follows:

a) Best Single Event for each player which as defined by most points earned. As can be seen from the methodology above this is a reflection of how far the player progressed in the event and the weighting of the event based on the strength of the competitors at the tournament.

b) Best Single Year. Total of all points awarded by DOT within a single rolling horizon year. This of course does not mean most dominant year as the adjuster for the strength of events might make up for lesser dominance by considering the player competed against stronger competition.

c) Best Five Year Period. As Best Single Year but over a longer period. What more can I say.

d) Best Career Achievement. No time limit. Just the total number of DOT points awarded during the lifetime of a player.

e) Current Year. Not really used in the calculations for the overall rating but produced more out of interest than anything else. Shows how many DOT points have been scored by players in the previous 12 months using the same methodology as Best Single Year.

f) This is the secondary output as it requires each of the first four outputs above to calculate a players overall rating. Each of the periods receives equal weighting using the following methodology. The mean for all outputs with a category is calculated along with the Standard Deviation. A players performance with that category is then converted into a form that is + or – a specific number of Standard Deviations from the mean. The outputs from each category are multiplied by 10 (just to make it more user friendly) and added together. Finally 1,000 points are added to avoid negative numbers in the outputs. The resulting figure provides an overall rating which reflects a players performance giving equal weighting to each category.

Finally and more as a fun item, because the Standard deviations balance out the difference in levels of dominance seen in the womens’ and mens’ games the resulting outputs can be directly compared to evaluate whether a particular woman was more or less successful than a man within their individual populations. You can also produce a best players list of the open era across sexes.

2. The second significant change is that previously DOT calculated a players performance via three input criteria. i.e. a players domination, the opposition strength and the tournament status. I have removed the tournament status as this tends to be reflected in the strength of tournaments anyway and it makes things easier to calculate and understand without compromising accuracy to any great extent.

3. In order to accommodate the first change and be able to keep the four primary criteria both comparable and easy to understand the Primary DOT Outputs are no longer standardised to follow an arithmetic pattern but instead are geometric in nature in the same way that the official ATP and WTA ratings are. In fact this is a very food way of understanding each of the four primary outputs. Just imagine the official ratings remaining constant and were implemented at the start of the open era with each event having a variable weight depending on quality of entrants rather than a fixed weight as is the case at the moment.

Finally while I know these ratings won’t resolve any arguments, I hope they provide the statistical evidence to at least provide some background for various debates.

Take care all and I hope you enjoy the outputs.

Regards

Tim

This is the first post of the V3.2 DOT Ratings. I will not go into the methodology behind these again as this is already contained within a thread at http://tt.tennis-warehouse.com/showthread.php?t=165420.

The latest revisions incorporate two significant changes and one minor. However before going into these details I need to confess that in making these changes I found a mistake in the algorithm that calculates tournament strength and provides the appropriate weighting for tournaments. This has now been rectified, however, previous rating posts will have contained this error and outputs were distorted. Apologies for this.

1. Following requests from numerous people, the DOT ratings are now calculated over multiple time periods and the results amalgamated with equal weighting to derive an overall rating. On the new overall scale a player could be considered great at 1,100 points and good at 1,000 points. To put this in perspective the womens’ game has produced 49 players in excess of 1,000 points in the open era, which includes 11 players of 1,100+ points and 1 player over 1,200 points. The mens’ game has had 68 players over 1,000 points, 12 in excess of 1,100 points and two players who have exceeded the 1,200 point barrier.

Ratings are calculated by awarding weights to events based upon the strength of competition present. The strength of the competition is based on their overall dominance over the previous 12 months. Points awarded for each event are multiplied by the weighting to derive the points earned by each player.

Once the points have been calculated five primary outputs are produced for each player with a sixth secondary output. The five primary outputs are as follows:

a) Best Single Event for each player which as defined by most points earned. As can be seen from the methodology above this is a reflection of how far the player progressed in the event and the weighting of the event based on the strength of the competitors at the tournament.

b) Best Single Year. Total of all points awarded by DOT within a single rolling horizon year. This of course does not mean most dominant year as the adjuster for the strength of events might make up for lesser dominance by considering the player competed against stronger competition.

c) Best Five Year Period. As Best Single Year but over a longer period. What more can I say.

d) Best Career Achievement. No time limit. Just the total number of DOT points awarded during the lifetime of a player.

e) Current Year. Not really used in the calculations for the overall rating but produced more out of interest than anything else. Shows how many DOT points have been scored by players in the previous 12 months using the same methodology as Best Single Year.

f) This is the secondary output as it requires each of the first four outputs above to calculate a players overall rating. Each of the periods receives equal weighting using the following methodology. The mean for all outputs with a category is calculated along with the Standard Deviation. A players performance with that category is then converted into a form that is + or – a specific number of Standard Deviations from the mean. The outputs from each category are multiplied by 10 (just to make it more user friendly) and added together. Finally 1,000 points are added to avoid negative numbers in the outputs. The resulting figure provides an overall rating which reflects a players performance giving equal weighting to each category.

Finally and more as a fun item, because the Standard deviations balance out the difference in levels of dominance seen in the womens’ and mens’ games the resulting outputs can be directly compared to evaluate whether a particular woman was more or less successful than a man within their individual populations. You can also produce a best players list of the open era across sexes.

2. The second significant change is that previously DOT calculated a players performance via three input criteria. i.e. a players domination, the opposition strength and the tournament status. I have removed the tournament status as this tends to be reflected in the strength of tournaments anyway and it makes things easier to calculate and understand without compromising accuracy to any great extent.

3. In order to accommodate the first change and be able to keep the four primary criteria both comparable and easy to understand the Primary DOT Outputs are no longer standardised to follow an arithmetic pattern but instead are geometric in nature in the same way that the official ATP and WTA ratings are. In fact this is a very food way of understanding each of the four primary outputs. Just imagine the official ratings remaining constant and were implemented at the start of the open era with each event having a variable weight depending on quality of entrants rather than a fixed weight as is the case at the moment.

Finally while I know these ratings won’t resolve any arguments, I hope they provide the statistical evidence to at least provide some background for various debates.

Take care all and I hope you enjoy the outputs.

Regards

Tim