Guild Wars 2

Ok, math and logic test.

People claim you will get through if you win more than you lose.

Is that correct? Really?

How many games will it take to progress through emerald at a 51% win rate (20 pips)?

Then how many to progress through Ruby, where you can lose tiers?

Explain your work.

Bonus points: how many hours will it take based on an average of a 5-minute Q?

It’s impossible to answer this since you can lose and gain up to 3 pips. E.g., if you win 3:1 matches, but get 1 pip each win and lose 3 pips each loss, even though your win% is high, you’re still at 0 progress.

the answer to all of this is also terribly variable based on exactly when you win the games in emerald and sapphire. For example, what if you have an exactly 50% winrate because every time you go up a tier, you immediately lose 5 games, but lose no pips. You could then proceed to win the next 5 games and have only forward progress but still an exactly 50% winrate. This doesn’t work in ruby obviously, but the issue still remains.

If that were the case (whether through throwing games, or sheer dumb luck), you would progress through emerald (which is 25 pips btw, not 20) in exactly 50 games.

Ultimately you’re asking a question with far too many variables to be accounted for so it’s completely pointless.

Polismassa.6740:

the answer to all of this is also terribly variable based on exactly when you win the games in emerald and sapphire. For example, what if you have an exactly 50% winrate because every time you go up a tier, you immediately lose 5 games, but lose no pips. You could then proceed to win the next 5 games and have only forward progress but still an exactly 50% winrate. This doesn’t work in ruby obviously, but the issue still remains.

If that were the case (whether through throwing games, or sheer dumb luck), you would progress through emerald (which is 25 pips btw, not 20) in exactly 50 games.

Ultimately you’re asking a question with far too many variables to be accounted for so it’s completely pointless.

The question was, are people correct in saying you WILL progress through these tiers if you win more than you lose?

Are they correct?

Or among people,with the same win RATE, will some get through and others will not?

Will some people of equal skill make legendary and others not make legendary? And if that is the case, is it really about skill?

The question is obviously flawed, but you can make massive and invalid assumptions to answer it if you want.

Assume even distribution (each additional game is 51% chance to win). Assume all games are +/- 1 pip.

In this perfectly assumed world, you will win 1 more game than you lose every 100 games played. On average, it would take you 100 * number of pips games to progress a given distance.

Easy math. Completely worthless analysis, but easy to do.

Fay.2357:

The question is obviously flawed, but you can make massive and invalid assumptions to answer it if you want.

Assume even distribution (each additional game is 51% chance to win). Assume all games are +/- 1 pip.

In this perfectly assumed world, you will win 1 more game than you lose every 100 games played. On average, it would take you 100 * number of pips games to progress a given distance.

Easy math. Completely worthless analysis, but easy to do.

o0

No. Just no. Wrong maths, my friend. You assume, that you lose after each win and vice versa. Or do you really think, that it needs 500 games in average(!) for a tier of 5 pips.

The calculation is much easier, if you bring a given number of games into consideration. For example “how high is the chance to get to league Y until christmas (=x games, depending on your playin habits)” The only assumption here, you can hold the 51%.

Fay.2357:

The question is obviously flawed, but you can make massive and invalid assumptions to answer it if you want.

Assume even distribution (each additional game is 51% chance to win). Assume all games are +/- 1 pip.

In this perfectly assumed world, you will win 1 more game than you lose every 100 games played. On average, it would take you 100 * number of pips games to progress a given distance.

Easy math. Completely worthless analysis, but easy to do.

I don’t mean perfect world. The question is about the actual reality being faced right now.

Obv you can progress even if you have lower winrate than 50%, but only to ruby I would imagine. Once you start losing tiers, it’s gonna get freaking hard. You can be losing a lot and still gaining tiers, it all depends if you get win streaks or not.

Here are some considerations for Emerald.

Best case: if you win 21 in a row you will get through Emerald in 21 games.

Worst case ( I think, correct me please), if you have long win and lose streaks, it takes SO much longer. You win 19 and then lose 18, it will take you (19*20)+1 games to get through. 381 games.

What have I missed?

Laserbolt.6731:

Here are some considerations for Emerald.

Best case: if you win 21 in a row you will get through Emerald in 21 games.

Worst case ( I think, correct me please), if you have long win and lose streaks, it takes SO much longer. You win 19 and then lose 18, it will take you (19*20)+1 games to get through. 381 games.

What have I missed?

You’ve missed the fact that a loss can give -3 pips. You’ve missed the fact that a loss can give +1 pips. You’ve missed the fact that a win can give +3 pips. You’ve missed the fact that matchmaking is imprecise and will not necessarily be matching you with equal skill opponents.

Laserbolt.6731:

How many games will it take to progress through emerald at a 51% win rate (20 pips)?

(For the purpose of calculation let’s just make the whole math a bit easier. So let’s just assume 1 pip per win / loss and the games you loose don’t happen on the safe spots.)

51% win rate = 51 wins and 49 losses in 100 games = +2 pips per 100 games or +1 pip per 50 games.

To gain 20 pips you need to play (50*20) = 1000 games.

1 game takes about 10 minutes (between 8 and 15, can’t really be accurate here, I would get 12 on average, but let’s just take the more favorable 10 minutes) + 5 minutes queue time = 15 minutes per game / 4 games per hour.

To achieve the 1000 games, you need to play 250 hours.
(If you every day the whole season, you need to play more than 4 hours every day to climb with a 51% win rate through emerald.)

Including the safe spots would ofc reduce this.

Fay,

Thank you. I was honestly asking, not daring people to find what I missed.

So, the plot thickens as to how much skill and how much luck is involved in the leagues.

Fay.2357:

Laserbolt.6731:

Here are some considerations for Emerald.

Best case: if you win 21 in a row you will get through Emerald in 21 games.

Worst case ( I think, correct me please), if you have long win and lose streaks, it takes SO much longer. You win 19 and then lose 18, it will take you (19*20)+1 games to get through. 381 games.

What have I missed?

You’ve missed the fact that a loss can give -3 pips. You’ve missed the fact that a loss can give +1 pips. You’ve missed the fact that a win can give +3 pips. You’ve missed the fact that matchmaking is imprecise and will not necessarily be matching you with equal skill opponents.

You have missed the fact that Your team will consist of 5 pugs and enemy team will have at least 3 premades

Teutos.8620:

Laserbolt.6731:

How many games will it take to progress through emerald at a 51% win rate (20 pips)?

51% win rate = 51 wins and 49 losses in 100 games = +2 pips per 100 games or +1 pip per 50 games.

To gain 20 pips you need to play (50*20) = 1000 games.

1 game takes about 10 minutes (between 8 and 15, can’t really be accurate here, I would get 12 on average, but let’s just take the more favorable 10 minutes) + 5 minutes queue time = 15 minutes per game / 4 games per hour.

To achieve the 1000 games, you need to play 250 hours.
(If you every day the whole season, you need to play more than 4 hours every day to climb with a 51% win rate through emerald.)

But you need to take streaks of wins and losses into account. That is what really happens, and we can’t ignore that just to make the calculation easier. Because then we’ll get a wrong answer.

Your analysis (which is how I first approached it as well) assumes no uneven streaks. But we know those happen based on who is in the queue during your several hours of gaming. You can win 7 and then lose 6, that’s 13 games right there to get one pip. Or you can lose TWO pips. It is complex.

I enjoy hearing people better at this than I showing how to figure this out and understand the reality of how the leagues are working and what we are up against.

So it is a Bell Curve with most people of equal skill taking x number of games, but some (of equal skill) taking many more games to do it (unlucky), and some taking a lot less (lucky).

Laserbolt.6731:

But you need to take streaks of wins and losses into account. That is what really happens, and we can’t ignore that just to make the calculation easier. Because then we’ll get a wrong answer.

Since my over exaggerating calculation is not good enough, I wrote a VB-calculation to consider the safe spots (programm should be correct; I am still only considering 1 pip per win / 1 pip on loss if not on a safe spot).

Results over 1.000 simulations:
min: 38 games
max: 394 games
average: 134,195
to get through emerald (5 tiers).

This! You all assume win-lose-win-lose and so on.

Assumptions:
51% win ratio, stable
only +/-1 pip

20 pips

Chance of doing it in 20 rounds (all wins)

0,51*0,51*…(20 times) = 1,41E-6 = 0,0002% Chance that this happens

Chance of doing it in 21 Rounds (20 wins/one loose/it doesn´t matter, where the loose happens, so 20 variations)

0,51^20*20= 5,55E-5 = 0,006 %

22 Rounds (two looses, whereever they happen in the row, (n(n+1))/2, n=22 variations):

0,51^20*231 = 2,27E-4 = 0,03%

hundred % chance to get 20(y) pips with 51%(x) in how many games n?

1=x^y*((n*(n+1))/2
2/(x^y)=n(n+1)
0=n^2+n-(2/(x^y))
…
n=(1/4+(2/x^y))^(-0,5)-0,5
n=1188 Games to bring it to Emerald with 51% win ratio. But this is only the 100% Chance to get it. And No(!), the average is not 1188 divided by two. Or is it? Who knows

edit: this is without the safe tiers

kitten wrong prefix…

I think(!), the correct formula is:

n=(1/4+(2/x^y))^(-0,5)+0,5

n= number of games needed (with 100% chance, i know, bad statistics)
x= win ratio/100
y= number of pips to climb without safe zones

There is a pretty extensive solution that was posted to Reddit a few days ago that appears to use correct methodology (though they assumed a 50% win rate). I’ll run their code on my machine in a minute and see what the result is with a 51% win rate.

EDIT: Results:

Assuming 10 minutes/game and a 51% win rate, if you play 40 hours/week you have a 65% chance of making it to legendary within one season.

Expected Number of games to advance through each tier:
Amber → Emerald: 30 Games
Emerald → Sapphire: 140 games, 170 games total
Sapphire → Ruby: 140 games, 310 games total
Ruby → Diamond: 640 games, 950 games total
Diamond → Legendary: 840 games, 1770 games total

paleon.7609:

There is a pretty extensive solution that was posted to Reddit a few days ago that appears to use correct methodology (though they assumed a 50% win rate). I’ll run their code on my machine in a minute and see what the result is with a 51% win rate.

That sounds interesting.

Oh hey, they found an analytical solution to the number of games (in one of the comments). Again re-running with 51% win rate (and rounded to nearest game):

Amber→Emerald: 29 Games
Emerald→Sapphire: 142 Games, 171 Games Total
Sapphire→Ruby: 142 Games, 313 Games Total
Ruby→Diamond: 656 Games, 969 Games Total
Diamond→Legendary: 843 Games, 1812 Games Total

paleon.7609:

Oh hey, they found an analytical solution to the number of games (in one of the comments). Again re-running with 51% win rate (and rounded to nearest game):

Amber->Emerald: 29 Games
Emerald->Sapphire: 142 Games, 171 Games Total
Sapphire->Ruby: 142 Games, 313 Games Total
Ruby->Diamond: 656 Games, 969 Games Total
Diamond->Legendary: 843 Games, 1812 Games Total

I would suspect that is the most likely number, bot it will vary on other factors ourside of player skill, and that there will be players of equal skill that could take plus or minus 30% or those totals.

But lets say it’s 1,812 games at 4 games per hour on average, with waiting times.

That’s 453 hours in 8 weeks.

Laserbolt.6731:

paleon.7609:

Oh hey, they found an analytical solution to the number of games (in one of the comments). Again re-running with 51% win rate (and rounded to nearest game):

Amber->Emerald: 29 Games
Emerald->Sapphire: 142 Games, 171 Games Total
Sapphire->Ruby: 142 Games, 313 Games Total
Ruby->Diamond: 656 Games, 969 Games Total
Diamond->Legendary: 843 Games, 1812 Games Total

I would suspect that is the most likely number, bot it will vary on other factors ourside of player skill, and that there will be players of equal skill that could take plus or minus 30% or those totals.

But lets say it’s 1,812 games at 4 games per hour on average, with waiting times.

That’s 453 hours in 8 weeks.

What’s interesting is that a handful of solo players can actually grind 2k games throughout the season. Literally, pvping 24/7. It’s how they were top 5 in the beta ladders.

The thing is, they would have to play 4x as much to reach Legendary in Leagues. The grind exceeds the length of the season.

It’s good in Anet’s eyes because they want to promote teams. Bad for solo players looking to be anywhere near the top, they’ll likely never pass Ruby in a season.

I’m fine with this, imo, inspite imminent QQs from casuals without a team.

paleon’s first post is essentially correct for the problem stated (I get 139.59 as the expected games to move through emerald).

If you want to get a bit more nuanced on the odds – losing lowers your MMR, which increases your odds of winning the next game, while winning raises your MMR and decreases your odds of winning the next game. This causes the number of games you need to advance a division to be higher than this estimate.

There is also the chance of gaining / losing more than one pip from a match. These are a huge deal when they happen (getting 2 pips from a win has roughly four times the value of getting 1 pip from a win) and drastically decrease the number of games you need to play to rank up.