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  1. #1
    Senior Member Pat Jay's Avatar
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    Top 100 - Do you have what it takes?





    Introduction


    TL;DR (too long; didn't read) summary is located at the end in red

    Ever since the top 100 leaderboard changed from being based on rating to score, there has been much heated debate on what it takes to rank top 100.

    Some have argued that all it takes to finish top 100 is sheer effort in playing copious amounts of games and no skill is required. Others have taken a balanced point of view and have said that it takes both effort and skill to finish top 100.

    So who is right? And to what extent does the current system favour effort over skill? Or vice versa? More importantly... how does the system favour my skill level and do I have what it takes to finish top 100? This is my attempt to answer all these questions. I hope you find it interesting!


    The Top 100 Rewards


    Each season starts and ends usually on the first day of the month between 5-10AM GMT. At the end of the 1 month long season, prizes are awarded to the top 100 players with the highest scores. These prizes are as follows:




    To view the top 100 scores for the current season and previous seasons, click here


    What is in these packs?

    A prize pack contains two exclusive foil cards which cannot be found in all other packs. A premium foil pack contains 5 random foil cards. Finally, a Shattered Fates pack contains 1 hero card, 10 common cards, 3 uncommon cards and 1 rare or epic card from the Shattered Fates expansion. For more information about these packs, click here.

    How is score calculated?

    For every quick match game played since the start of season 10, the winner scores an amount of points equal to their rating multiplied by the loser's rating divided by 100; whilst the loser scores no points. If the match ends early or in a draw, then no points are awarded.

    How is rating calculated?

    Rating is calculated via a system similar to the Trueskill system on Xbox. Your rating resets to 0 at the start of the season and can increase up to 500.

    Your rating is also accompanied by an invisible number called "sigma", which represents how confident the system is that your current rating represents your true rating. Sigma decreases over time as you play more and more games. This is because the system becomes more and more confident over time that your current rating is an accurate representation of your true rating.

    Your rating naturally increases with wins and decreases with losses. Your rating will increase or decrease more significantly when sigma is large. This is the because the system is not confident where your true rating lies; and so it will increase or decrease your rating more significantly as it tries to narrow down where your true rating lies as you play more games. This explains why your rating changes more significantly at the start of the season compared to the end.

    Your rating will also increase or decrease more significantly if the system did not expect you to win or lose. For example, if you won against someone with a higher rating, then your rating will increase more significantly when compared to a win against someone with a lower rating. This is because the system did not expect you to win against the player with the higher rating.

    All in all, the system is designed to primarily match you with a player of a similar skill level or rating so that the match is likely to be a close one rather than one-sided and boring. Click here or here for more information on this topic.


    The Top 100 Results


    Here is a chart that details how many points each top 100 player scored and what rating they achieved at the end of seasons 10 through to 16:




    Observations

    From ranks 100 to 20, score increases around 1,400 points per rank. From ranks 20 to 1, score increases around 19,000 points per rank. Ranks 20 to 1 is also the same range that foil Legendary cards are awarded. Scores are generally higher when the season is played out during a month that has 31 days.

    The top 100 ratings range from 231 to 311 (excluding the top and bottom 5%) with a weighted average rating of 272. From ranks 100 to 20, the weighted average rating was 271 with a standard deviation of 23. From ranks 20 to 1, the weighted average rating was 276 with a standard deviation of 22.

    It is important to note that these ratings were achieved by players whose intent was to play as much as possible. This is in contrast to seasons 8 or earlier where the top players tried to play the least amount of games as possible. And so the top players' sigma values would have been much lower in seasons 9-17 compared to 8 or earlier.


    The Analysis


    Having answered the following two questions:

    1. For players with different ratings, what is the average rating of the opponents they win against?
    2. What win rates are needed to maintain different ratings?

    Refer to the appendix to see how these two questions were answered

    We can then use the top 100 results to calculate how many games are needed to be played to rank top 100 for players with different ratings. Here are the results:




    Refer to the appendix to see how the formula, used to calculate these numbers, was derived.

    Interpretation of data

    Since an overwhelming majority of players have a sub 300 rating, it is reasonable to suggest that the majority of players will need to play at least 10 games a day to rank top 100. Players who can only play 5 games a day or less have no chance to rank top 100.

    A player with a 200 rating needs to play 26 games a day to achieve rank 100. To me, this is way too much effort for one to sustain for a whole month. It is therefore reasonable to suggest that players with a 200 rating or less do not have what it takes to rank top 100. The fact that the top 100 weighted average rating was 272 at the end of seasons 10 through to 17 supports this interpretation to a large extent.

    200 and 300 rating compared

    Why is it that the 200 rated player does not have have it takes to rank top 100 and the 300 rated player does? Here are some probable reasons:

    • The 300 rated player scores more than twice the amount of points per win compared to the 200 rated player
    • The 300 rated player inherently is winning more games (10% more as per assumptions in the appendix) compared to the 200 rated player
    • The 200 rated player will be exposed to low rated players with high sigma values moving up the rating scale. The 300 rated player is positioned high enough up the rating scale to not frequently encounter these sort of players
    • As a result of all the above points, the 200 rated player needs to play 2.5 times more games compared to the 300 rated player in order to achieve the same score. This is undoubtedly a huge disadvantage!


    TL;DR Summary or Conclusion


    If you have a rating of 200 or less, then you do not have what it takes to rank top 100. That is unless you can play 26+ games every day for a whole month.

    If you cannot play more than 10 games a day, then you also do not have what it takes to rank top 100. This is because you cannot score enough points per win to rank top 100 even with a very high rating.

    If you do have a rating that is 250 or more and can play more than 10 games a day, then you do have the basic credentials to rank top 100.

    Evidently, it takes both effort and skill to rank top 100. To say that skill is not required to rank top 100 would be unfair to the top 100 players whose weighted average rating was 272 at the end of seasons 10 through to 17.

    This thread will updated once the conclusions made are no longer relevant.

  2. #2
    Senior Member Pat Jay's Avatar
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    .

    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.

  3. #3
    Senior Member AnomalousT's Avatar
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    This was really cool. I enjoyed reading it. Now to go try to somehow use this information to help me win game XD

  4. #4
    Senior Member Deja Vu's Avatar
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    Fantastic stuff, Pat Jay! Thank you!

    Hope a mod will sticky this.
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  5. #5
    DP Visionary Direwulven's Avatar
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    Awesome write up Pat Jay.
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  6. #6
    DP Visionary Index's Avatar
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    This article scares me!
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  7. #7
    1.27 Tournament Champion Raphael Majere's Avatar
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    Quote Originally Posted by Direwulven View Post
    Awesome write up Pat Jay.
    +1. Excellent work. u are a boon to SE community

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  8. #8
    Senior Member kraken's Avatar
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    Wow! Awesome article. Lots of great info!

  9. #9
    DP Visionary Rated GG's Avatar
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    Thank you for the info! i find myself defending the rating system often. Grinding at 270+ is a lot of hardwork and far from brainless... although the rushdown/early quitting should be hotfixed. The idea of sigma/confidence is a flaw in SEs rating system. If someone was playing BB earlier in the season, but switches to Victor... how confident can the system be in predicting this players skill? or if a player was playing GB earlier in the season, but switches to Amber. These players will be grinding at a rating that they might not belong in.
    Last edited by Rated GG; 01-03-2014 at 08:41 AM.
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  10. #10
    Senior Member Palestitch's Avatar
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    Very good read.
    Expect the Unexpected! - TJs worst writer.

    For the player I am now, I would like to thank:

    Busti: For always chatting and helping me out.
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    Formerly known as Barcafan.

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