Hi guys, I really like the Arena mode, I read lots of interesting posts about it, about the strategies to climb it and about the level of the leagues. So I had the idea to study how fast you can expect to climb it depending on your level, and hope it can bring valuable insights to these discussions. It can also help people to strategize. Sorry by advance for my english or if something sounds french, by the way 
I first tried to calculate the probabilities, but quickly understood that the maths were not that easy, so I did some rough Excel ("Excel et bourrinisme"
) and simulated 100 000 series of 30 one-on-one games, depending on the arena parameters (how many points you win or lose), and on how many games you're expected to win (from 10 to 90% of your games).
First scenario: a new game is launched, or the season is just beginning... you are in bronze league and only play against bronze, win is worth 3 stars, loss is 3 stars.
Of course it can be very quick: you just have to win your first 3 games... but you're not always that lucky. What we can see is that an average player, who wins every other game (purple), has around 40% chances to get promoted after 10 games, and 83% after 30 games. If you are above average, it should be quick, if you are below average it can be quite long: after 30 games, your odds are 54% if you win 40% of your games, 23% if you win 30%, 5% if you win 20%, and 0.4% if you win only 10%. So if he is only paired with bronze players, a weak player will probably stay there a long time.
Second scenario: you are ahead, let's say silver, and are only paired with bronze. A win is worth 2 stars, losing costs 4 stars.
OK, it's clearly harder. Of course, you have to win at least 5 games to go to gold, and every defeat is expensive. A very strong player should still go fast, and 8, or even 5, games are often enough. If you can expect to win 60 or 70% of your games, it starts to be long ; if you are average, it will be hard, and if you are weaker the odds are really not in your favour. Of course, you will eventually find other silver opponents, and it will get easier.
Third scenario : you are behind. It is quite common after a month in the season, when there are lots of players in Elite and you are in the league just below. You win 4 stars and lose 2.
If you are a strong player, it should be a quick walk. Even if you win 50% of your games, after 6 games there is 50% chances that it is done. What is interesting is what happens for weaker players. Even if you only win 30% of your games, there a re stong odds that it is done after 30 games, and I guess it is almost certain after 50. A player who wins 1 games out of 5 will probably end up promoted too, and a player who wins 1 out of 10 can be lucky.
Of course it doesn't really happen like that in real life because you will be paired with platine and diamond players too, but it gives an idea. And it can explain why people feel there are weak players in Elite (they can achieve it by being patient or lucky).
I didn't do the same exercice for 5-1 or 1-5 configurations yet, or when starting at 0 instead of 1, but it is pretty easy if you are interested. I hope some of you enjoyed this post, don't hesitate if you want more information, in english or french.
I first tried to calculate the probabilities, but quickly understood that the maths were not that easy, so I did some rough Excel ("Excel et bourrinisme"
) and simulated 100 000 series of 30 one-on-one games, depending on the arena parameters (how many points you win or lose), and on how many games you're expected to win (from 10 to 90% of your games). First scenario: a new game is launched, or the season is just beginning... you are in bronze league and only play against bronze, win is worth 3 stars, loss is 3 stars.
Of course it can be very quick: you just have to win your first 3 games... but you're not always that lucky. What we can see is that an average player, who wins every other game (purple), has around 40% chances to get promoted after 10 games, and 83% after 30 games. If you are above average, it should be quick, if you are below average it can be quite long: after 30 games, your odds are 54% if you win 40% of your games, 23% if you win 30%, 5% if you win 20%, and 0.4% if you win only 10%. So if he is only paired with bronze players, a weak player will probably stay there a long time.
Second scenario: you are ahead, let's say silver, and are only paired with bronze. A win is worth 2 stars, losing costs 4 stars.
OK, it's clearly harder. Of course, you have to win at least 5 games to go to gold, and every defeat is expensive. A very strong player should still go fast, and 8, or even 5, games are often enough. If you can expect to win 60 or 70% of your games, it starts to be long ; if you are average, it will be hard, and if you are weaker the odds are really not in your favour. Of course, you will eventually find other silver opponents, and it will get easier.
Third scenario : you are behind. It is quite common after a month in the season, when there are lots of players in Elite and you are in the league just below. You win 4 stars and lose 2.
If you are a strong player, it should be a quick walk. Even if you win 50% of your games, after 6 games there is 50% chances that it is done. What is interesting is what happens for weaker players. Even if you only win 30% of your games, there a re stong odds that it is done after 30 games, and I guess it is almost certain after 50. A player who wins 1 games out of 5 will probably end up promoted too, and a player who wins 1 out of 10 can be lucky.
Of course it doesn't really happen like that in real life because you will be paired with platine and diamond players too, but it gives an idea. And it can explain why people feel there are weak players in Elite (they can achieve it by being patient or lucky).
I didn't do the same exercice for 5-1 or 1-5 configurations yet, or when starting at 0 instead of 1, but it is pretty easy if you are interested. I hope some of you enjoyed this post, don't hesitate if you want more information, in english or french.
