Author Topic: Average multiplier as a function of win rate  (Read 5003 times)

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Offline Dooz

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Re: Average multiplier as a function of win rate
« Reply #15 on: August 19, 2011, 09:21:26 am »
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Offline Panoply

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Re: Average multiplier as a function of win rate
« Reply #16 on: August 19, 2011, 09:30:39 am »
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Oh! It should be noted that the actual practical implications of these calculations, namely that you should play more games in one sitting, have been previously outlined by the meticulous and brilliant WaltF4, when he analyzed the special case with a 50% win rate. Quitting at x1 is just common sense.

All I've done is generalize it across all win rates. So, yeah, I have to admit, these equations aren't that useful unless you need precise figures. At least they serve to amuse mathheads, and I had fun figuring it out.

Offline Teeth

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Re: Average multiplier as a function of win rate
« Reply #17 on: August 19, 2011, 09:32:56 am »
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I'm impressed by both the OP and Paul's reasoning. But judging from the OP, for me to calculate my average multiplier, I would have to know my win rate. So if I required to keep track of my win rate, why won't I just keep track my average multiplier instead, which isn't that much harder.

50k gold to the guy who manages to accurately display valour in a calculation of average multiplier.

Offline Spawny

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Re: Average multiplier as a function of win rate
« Reply #18 on: August 19, 2011, 09:39:16 am »
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Playing battle you have a 50% winrate when you play an infinite number of rounds.

Playing siege is a whole different matter though. I rarely get past x3 on a siege server UNLESS there's a clan steamrolling the server and I'm lucky enough to be in their team for some rounds.
Some clans can hold a an x5 for hours on end by playing well together.

Overall, I make much less gold/exp on siege compared to battle.
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Offline BlackMilk

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Re: Average multiplier as a function of win rate
« Reply #19 on: August 19, 2011, 09:39:23 am »
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I understand..

Offline Panoply

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Re: Average multiplier as a function of win rate
« Reply #20 on: August 19, 2011, 09:41:11 am »
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I'm impressed by both the OP and Paul's reasoning. But judging from the OP, for me to calculate my average multiplier, I would have to know my win rate. So if I required to keep track of my win rate, why won't I just keep track my average multiplier instead, which isn't that much harder.

Yup, that's a great point. I figured this out because I'm trying to make a tool for people to use to figure out how much money they'll make or lose based on the equipment they're wearing. While it's true that if you want exact values of either win rate or average multiplier, neither is particularly preferable since the same recorded data would tell you both.

However, I was more thinking along the lines of someone who was guesstimating, and it's much more intuitive for a player to estimate their win rate than their average multiplier. Most people won't know their average multiplier off the top of their head, but they can reason out a win rate.

Eg. I'm an ok player, but I'm in a top notch clan that lets me stack teams in battle, so I probably win about 60-65% of the time.
I'm a pretty good player, but I'm not in a clan, and I mostly play siege with a lot of players, so my individual impact is small, so I probably win about 50-55% of the time.
I'm not that great a player, but I'm a natural leader in siege, so I probably win about 60% of the time.

Playing battle you have a 50% winrate when you play an infinite number of rounds.

Playing siege is a whole different matter though. I rarely get past x3 on a siege server UNLESS there's a clan steamrolling the server and I'm lucky enough to be in their team for some rounds.
Some clans can hold a an x5 for hours on end by playing well together.

Overall, I make much less gold/exp on siege compared to battle.

Actually, siege is a closer approximation to my calculations than battle, for the reasons you stated. You might have an overall win rate of 50% on both battle and siege, but still get a higher average multiplier on battle. The reason for this is that the probabilities across rounds are not independent in battle, especially with heavy banner balance effects. That is to say, when you get your x2, usually you have a higher than 50% chance of continuing the trend and going up to x3, x4, and x5.

Siege team swaps like no other, so your probabilities are more likely to be independent between rounds. Of course, I don't actually have any empirical evidence that battle gives a higher average multiplier than siege, it may well be that the probability linkage balances out multiplier sprees of x2, x3, x4, x5 with bouts of x1, x1, x1, x1. Without meticulous data gathering, the impression that battle gives more gold/exp than siege for the same win rate can easily be chalked up to psychological bias, and a tendency to make a note of x5 sprees, given their salience.
« Last Edit: August 19, 2011, 09:50:02 am by Panoply »

Offline Captain_Georges

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Re: Average multiplier as a function of win rate
« Reply #21 on: August 19, 2011, 10:56:42 am »
+1
So I hurd u like math
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Offline Corrado_Decimo

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Re: Average multiplier as a function of win rate
« Reply #22 on: August 19, 2011, 11:50:25 am »
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The internet went down at my work today, so I decided to see if I couldn't come up with the equation that describes the relationship between average multiplier and the probability of winning a round. I've been working on a tool for players to calculate upkeep and equipment, and I wanted to be able to determine average multiplier if given a certain win rate. In my previous encounters with this problem, I've either programmed a simulation, or I've used simple cases, such as a win rate of 50%.

Today, however, I decided to generalize it. Worse yet, I would do it by hand, without the aid of WaltF4's previous posts, which when I look at now, would have given me some solid hints on how to proceed. The algebra was a bitch by hand, but it was all worth it, when all the terms canceled out to yield this gem:

y = x^4 + x^3 + x^2 + x + 1

y is your average multiplier
x is your win rate, eg. if you win 50% of the time, x = 0.5; at 87.22%, x = 0.8722, etc.

So at 50% win rate, your average multiplier (not including valour) would be 1.9375. This is well established and simple to do by hand, since x = 1 - x.

I ran a simulation over 100,000 rounds at each percentile, and the data matches up perfectly with the above equation, so I can say it is correct with confidence.

Most of you are likely indifferent to this information, and some of you will hopefully have a passing curiosity, but I thought I'd share it anyway. Personally, I'm pretty proud, as probability often makes my head spin.

really nice! but... there is a but. for instance if i know i'll have a free hour to play, i'll play for an hour and i'll probably leave only when my multiplier goes back to x1 (as most of us do). so, sometimes, i hop in, win 5 rounds and when i get x1 again i'll leave instead trying to regain multi (stuff to do outside the games).

and i still think people with really good teamwork skills have a higher average multiplier. even with a unlucky unbalanced random team, can flip the tide of battle. or for instance, if a full clan will only jump in a server when they can bannerstack will probably have a higher multiplier than the average player.

so.. i really don't know.. it's not just a matter of probability. only devs can tell if it's right or wrong by looking at the stats to see who is in the top for round won and how much is the average multy.

not to mention the win probability grows as a player usually roll in full gear even when the team is losing. this add some little chance to win the round (equip give you better chances yes. countless times i end a round alive with something like 5% hp and if i didn't took my jarids with me, that cav i killed probably would have killed some infantry on my team so...).

Playing siege is a whole different matter though. I rarely get past x3 on a siege server UNLESS there's a clan steamrolling the server and I'm lucky enough to be in their team for some rounds.
Some clans can hold a an x5 for hours on end by playing well together.

Overall, I make much less gold/exp on siege compared to battle.

exactly. often clans like to steamroll sieges because with good numbers and teamwork you can set up a rock defence, or in attack you can quietly ninja the backdoor or use ladders, or in overall set up a 6-10 players commando to steamroll and push in one side instead of random swarming ladders, siege tower, backdoor, walls, flag...

i had good balanced and funny matches with 2 or 3 clans in sieges... but the steamroll occurs when there is a clan alone.

this rarely happens in battle. for instance, when 5-6 mercs go in a server, usually there are also some 22nd, some greys, some fallens, risens.

but siege is really more teamwork based so... a good elite random pubbers can go kill half server but with no coordination will still fail against a good coordinated but average skilled clan with teamspeak. and the multi with it.

also to note that in siege, upkeep is higher (higher chance to break items) because round duration is in average longer. but some easy ninjable maps, often rounds ends in 1min and in about 15 min you can lose something like 8-10k.
« Last Edit: August 19, 2011, 12:02:02 pm by Corrado_Decimo »

Offline Teeth

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Re: Average multiplier as a function of win rate
« Reply #23 on: August 19, 2011, 03:16:45 pm »
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(click to show/hide)
Yeah, there are differences between average multipliers between players, thats exactly why win rate is a variable :wink:

Offline Warpeasant

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Re: Average multiplier as a function of win rate
« Reply #24 on: August 19, 2011, 03:40:21 pm »
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 :rolleyes: Spelling Bee goes as follow's

WTF?!?
 
Can you give me an example:

What the fuck, why did i drop out of high school now i can not play mount and blade and be more effectiv...

Can you tell me the origin please:

No i can not! You sux, because you don't play the game as a math whizz and quit whenever your down to x1 but you quit anytime you don't feel like playing anymore... Anyways ask Stephen Hawkins he will know the origin....




Offline Panoply

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Re: Average multiplier as a function of win rate
« Reply #25 on: August 19, 2011, 07:13:27 pm »
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really nice! but... there is a but. for instance if i know i'll have a free hour to play, i'll play for an hour and i'll probably leave only when my multiplier goes back to x1 (as most of us do). so, sometimes, i hop in, win 5 rounds and when i get x1 again i'll leave instead trying to regain multi (stuff to do outside the games).

and i still think people with really good teamwork skills have a higher average multiplier. even with a unlucky unbalanced random team, can flip the tide of battle. or for instance, if a full clan will only jump in a server when they can bannerstack will probably have a higher multiplier than the average player.

so.. i really don't know.. it's not just a matter of probability. only devs can tell if it's right or wrong by looking at the stats to see who is in the top for round won and how much is the average multy.

Actually, the equations only work if you leave with an x1 multiplier. This is because multipliers do not carry over between sittings, but this equation assumes that they do. So the fact that you only leave with a x1 multiplier actually *helps* this equation be more accurate in describing your average multiplier over time.

The rest of the points in your post seem to just say, "a lot of factors affect win rate". Win rate is exactly accounted for in the equation. If you only play when your clan can stack teams, then you'll have a higher win rate, and so a higher x. If you wear better equipment, you'll have a higher win rate, and so a higher x. If you're a good leader in siege, you'll have a higher win rate, and so a higher x, etc. I don't need to know exactly what factors are affecting win rate, I just need to know that win rate varies, and with it, average multipliers. So these concerns are accounted for in the equation.

You've started talking about upkeep, which I haven't even mentioned yet. However, you should know that upkeep is NOT higher in siege than battle. Yes, the longer rounds mean that there's more chance your items will break in one round, but they also mean you get more ticks, so you get more gold per round too. If you average out gold gained per tick and gold lost per tick to upkeep, they are the same in both battle and siege. There are a LOT of misconceptions regarding upkeep floating around, which is a big reason why I'm planning on making a tool for people to calculate their upkeep.

Offline Torp

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Re: Average multiplier as a function of win rate
« Reply #26 on: August 19, 2011, 07:22:55 pm »
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The biggest problem is not calculating your gold/exp gain as a function of win rate, the real hard stuff is calculating your win rate since it depends on so many things.

The only way to do it accurately is by simply playing alot and counting your wins and losses... but you'll have to do it for a lnog time since you will play in different gear at different times and play with your clan sometimes and sometimes you won't, which also affects your multiplier.

For a skilled player who minds his multi, chooses servers wisely and plays with his clan often/once in a while, i dont see the problem in getting n average multi above 2.

Offline The_danish_lost_viking

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Re: Average multiplier as a function of win rate
« Reply #27 on: August 19, 2011, 08:07:00 pm »
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The internet went down at my work today, so I decided to see if I couldn't come up with the equation that describes the relationship between average multiplier and the probability of winning a round. I've been working on a tool for players to calculate upkeep and equipment, and I wanted to be able to determine average multiplier if given a certain win rate. In my previous encounters with this problem, I've either programmed a simulation, or I've used simple cases, such as a win rate of 50%.

Today, however, I decided to generalize it. Worse yet, I would do it by hand, without the aid of WaltF4's previous posts, which when I look at now, would have given me some solid hints on how to proceed. The algebra was a bitch by hand, but it was all worth it, when all the terms canceled out to yield this gem:

y = x^4 + x^3 + x^2 + x + 1

y is your average multiplier
x is your win rate, eg. if you win 50% of the time, x = 0.5; at 87.22%, x = 0.8722, etc.

So at 50% win rate, your average multiplier (not including valour) would be 1.9375. This is well established and simple to do by hand, since x = 1 - x.

I ran a simulation over 100,000 rounds at each percentile, and the data matches up perfectly with the above equation, so I can say it is correct with confidence.

Most of you are likely indifferent to this information, and some of you will hopefully have a passing curiosity, but I thought I'd share it anyway. Personally, I'm pretty proud, as probability often makes my head spin.

Are you sure with that math?
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Offline Jacko

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Re: Average multiplier as a function of win rate
« Reply #28 on: August 19, 2011, 08:12:41 pm »
+3
My head hurtz.
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Offline Torp

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Re: Average multiplier as a function of win rate
« Reply #29 on: August 19, 2011, 09:32:20 pm »
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I was just thinking about something... Each tick gives you 50x gold and 1000x exp (at gen 1 with x being multi)... and gives you y% chance of each item breaking... But do those break chances add up and give you 4Y% break chance in a 4 minute round, or is it calculated each minute? cause if it's calculated each minute the total break cost would be lower since the same item cant break twice, and if it breaks during the first minute, it cant break again.