.
Appendix
Formula derivation
Rating x Opponent Ave Rating x Number of games x Win rate / 100 = Final score
Rating x Opponent Ave Rating x Number of games x Win rate = Final score x 100
Number of games = Final score x 100 / (My Rating x Opponent Ave Rating x Win rate)
Therefore...
Number of games needed daily = Final score x 100 / (My Rating x Opponent Ave Rating x Win rate x Number of days in the relevant month)
NB: all results are rounded up and therefore the formula is more likely to overestimate the number of games needed daily rather than to underestimate.
Weighting Distribution
Season 10's, 11's, 12’s, 13's, 14’s, 15's, 16’s and 17’s results were given a weight of 1, 2, 3, 4, 5, 6, 7 and 8 respectively to calculate the weighted average rating and number of games needed to play daily.
For players with different ratings, what is the average rating of the opponents they win against?
Players with a stable rating of 150, 200, 250, 300 and 350 were randomly selected and their past 30 game history were examined. From that history, the ratings of their opponents were recorded. Most of the data was collected at the end of the season where sigma would be at its lowest for most players and their rating would be more stable and less volatile. After recording over 1000 data samples, here are the results:
It is worthy to note that this data provides the average rating differences for opponents won or lost against. Since we are only interested in the rating difference for the opponents won against, naturally all negative differences should be larger (except for 350) and all positive differences should be smaller. This is because you are more likely to win against an opponent with a lower rating rather than a higher one.
It is also worthy to note that the highest rating observed was around 350. Based on this, we will assume that this is the highest rating realistically achievable for our calculations.
As the results suggest, the system tends to match make you with an opponent with a rating of 200-250 since the lowest differences in rating were found within this range. Therefore it is reasonable to suggest that the bulk of the players online playing Quick Match at any given time have a rating of 200-250. And so if we were to plot the ratings of all online players playing Quick Match at any given time, it would look something along the lines of this:
And so based on all these findings, it is reasonable to form the following assumptions for our calculations:
- A player with a stable rating of 350 will win against an opponent with a rating of 315 on average
- A player with a stable rating of 300 will win against an opponent with a rating of 285 on average
- A player with a stable rating of 250 will win against an opponent with a rating of 245 on average
- A player with a stable rating of 200 will win against an opponent with a rating of 200 on average
- A player with a stable rating of 150 will win against an opponent with a rating of 165 on average
What win rates are needed to maintain different ratings?
Based on how current rating system works, it would be reasonable to suggest that:
- If you are constantly being paired up with opponents that have a rating lower than you, you would need a win rate > 50% to maintain the same rating. This is because the net effect of 1 loss and 1 win should produce a fall in rating.
- If you are constantly being paired up with opponents that have a rating higher than you, you would need a win rate < 50% to maintain the same rating. This is because the net effect of 1 loss and 1 win should produce a rise in rating.
- If you are constantly being paired up with opponents that have the same rating, you would need a win rate = 50% to maintain the same rating. This is because the net effect of 1 loss and 1 win should produce no change in rating
Based on the above points, the fact that the bulk of Quick Match players range from 200-250 in rating, the fact that Kyle has informed me via PM that the median rating is 186, personal data from season 12 which can be examined here, and on the win rates of the 35 players whose 30 game histories were examined; the following assumptions have been formed for our calculations:
- To maintain a stable rating of 350, a player would need to a achieve a win rate of 70%
- To maintain a stable rating of 300, a player would need to a achieve a win rate of 60%
- To maintain a stable rating of 250, a player would need to a achieve a win rate of 55%
- To maintain a stable rating of 200, a player would need to a achieve a win rate of 50%
- To maintain a stable rating of 150, a player would need to a achieve a win rate of 40%
To examine all the hard data used to formulate all the assumptions click here.
Acknowledgements
Thank YOU for reading my article! I hope you have found it interesting!
I would like to also say a special thank you to my E2E guild mates Bayfighter, BraveBaldrick, Ballyworld, GuardianAngel, Jacob31088 and Tmakk for proofreading my article, giving me helpful suggestions and encouraging me.
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