Nation Wars Math and Dynamics

[LaceyPip]

A HUGE THANK YOU TO AND COURTESY OF NOCHT ANGEL, ARCHOSAUR SERVER PWI

Its a long read, but its an amazing read for those who are really interested in Nation Wars and how the wheels turn inside...from advantages/squads and how to get the most tokens.

It made a few of us understand the dynamics of Nation Wars much better and I hope that whoever is interested in reading this, will find it helpful

Nation War Math

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Personal Credits per instance:

Defending or Attacking does NOT affects the amount of personal points you get in battle. As long as you run into 'big fights' (both in terms of quality of enemy and time in battle), the total available credits will be high.
You get points for all 10 instances as long as you manage to physically teleport inside all 10 instance. I know where this is going and it is not advisable to build an entire credit-strategy behind it because:

1). You will be sent back to base if just one of instances gets full before you walk in.
2). You will be sent back to base if you try to leave a battle and the last position is under attack, under control of another enemy, or under protection.
3). Even if you managed to join and leave multiple instances in a row, you will earn tiny amount amount of credits for each instance because you will most likely get very low rank in most of the instances.

Personal credits is always a 'fraction' of the 'total available credits
This fraction depends on (i) ranking & (ii) number of people in the same team (higher ranking = bigger share of the credits) (more people on the same team = smaller personal share of the total available credits)

How to get higher Ranking?
1). Deal damage
2). Receive damage
3). Kill People!
4). Don't Die (at least try not to...)
You simply have to perform than others in the same instance to get higher ranking. (Other stuff like healing, etc... have NOT been confirmed to get higher rankings).

Parameters which inflate the 'Total Available Credits':

1). Final Battle Score & Duration
(In empty instances 20 v/s 0, this parameter will generate around 1000 available credits for the winning team)
2). Sum of [Soul force of each enemy * his/her time on the battlefield]
(For an enemy team of 20 people in 5min, this parameter can generates around 2000~4000 available credits. Stronger enemy generates more. Longer fights generate even more)
3). Total Damage output of enemies.
(This is the parameter that contributes the most to inflate the total available credits; every 100k points of damage received by your team will generate around 1000~2000 available credits for your team. Absolute ratio not yet confirmed - but the order of the ratio is right).

In general, if you run into heavy resistance, the 'total available credits' will be high. If you run into small resistance, the 'total available credits' will take more time to build up.

By observation, big fights over long period of time (e.g 20v/s20 over 15min+) will always generate the maximum amount of available credits (24750). Also, if the fight is too short (less than 5mins), the total available credits would not have enough time to build up => low amount of available credits.

1). Being a cleric or not, does not matter.
2). Level, does not matter.
3). Saying that you were in the winning nation is pointless if you cannot provide the actual score distribution of that NW.
(There is a difference between a winning nation with a score 250 and another winning nation with a score of 300)
4). Whatever you do inside an instance
(wherever you want to afk, eat, fight, fart, heal, dance, run flags or spawn kill)
you still get a ranking based on the number of people inside that instance. Ranking is what gives personal credits.
5). Whether or not you are going to earn tokens or no tokens does not depend on your personal credits.
6). Whether you come late or leave early does not really matter either.

My first guess is soul force. It was a tip from a +12 friend who gets rank 1 in empty instances. But this is only a factor that contributes little to ranking... In other words, once you get into pvp, minor factors gets overridden by the 3 major factors: dealing damage, tanking damage, killing.

Honestly, I am not looking to confirm any of the minor factors like: buffing, healing, or soulforce because

1). Minor factors will always get overridden by being engaged into pvp.
2). In instance where there is no pvp, the total amount of credits available is very small anyways.
3). As a observer point of view, it is more difficult to measure/compare buffs/heals to damage.

Trying to find the answer to question like 'How much is the value of 1 buff in terms of damage?' is close to impossible.... unless a developer decides to be nice and post all the details, assuming that some of the minor contributors even exits. On the other hand, pvp factors are more obvious and can be quantified/compared.
I can check my HP charm or my damage log to know that I tanked over 100k damage in 1 instance or I open the map to check on my kills and compared it to the total allied kills.

Anyways, you've still got more credits than him for capping both flags. ~600(you) v/s ~290 (him). If you were to be rank 1 instead in that situation, the additional credits would be 33...


As a general rule of thumbs (applicable to most US servers)

In a nation with a score of around 300, people will earn around 20 tokens for every 1000 credits.
In a nation with a score of around 240, people will earn around 15 tokens for every 1000 credits.
In a nation with a score of around 220, people will earn around 12 tokens for every 1000 credits.
In a nation with a score of around 190, people will earn around 10 tokens for every 1000 credits.
In a nation with a score of around 130, people will earn around 5 token for every 1000 credits.

Note: actual numbers usually fell within +-25% margins from NW to NW, which corresponds to variation of number of people in nation, loosing nation score, server, player performance within a nation, base-locking etc...


The Equation:
Personal credits = (Number of Personal Shares)/(Sum of Shares of all people on the same team) * (Total Available Credits)
Each person is allocated a number of Shares based on his ranking (Source1, Source2)

Rankings and their corresponding assigned number of Shares:
Rank 1 gets 40 Shares
Rank 2 gets 35 Shares
Rank 3 gets 30 Shares
Rank 4 gets 24 Shares
Rank 5 gets 23 Shares
Rank 6 gets 22 Shares
Rank 7 gets 21 Shares
Rank 8 gets 20 Shares
Rank 9 gets 19 Shares
Rank 10 gets 18 Shares
Rank 11 gets 17 Shares
Rank 12 gets 16 Shares
Rank 13 gets 15 Shares
Rank 14 gets 14 Shares
Rank 15 gets 13 Shares
Rank 16 gets 12 Shares
Rank 17 gets 11 Shares
Rank 18 gets 10 Shares
Rank 19 gets 9 Shares
Rank 20 gets 8 Shares
Rank 21-30 gets 2 Shares
Rank 31+ gets 1 Share

Credit Bonus/Penalties/Limits & others:
1). Digging and capturing the flag is worth 165 extra credits). Digging & dying = 15 credits only (flag does NOT give higher ranking, but contribute to extra credits at the end).
Flag capture does not contribute to personal ranking, only to extra contribution at the end.

*Killing the flag carrier: indirectly gives you more points by increasing the chance of winning the instance. In general, when you chase the flag carrier, it is very likely that there will be enemies supporting the flag carrier. Lots of enemies group-up is the perfect situation to blast some AOE to earn higher ranking. Damage on multiple enemy > damage on single target.


*** People who only pk's are usually don't give a fudge or don't understand the implication of loosing. For the people who only read superficially, I will just put it in highlight. ******


1). Losing a battle = credit Penalty (-60% credits of what you are supposed to earn)
YOU DONT WANT TO LOSE ANY BATTLE. LOSING BEARS HEAVY PENALTY ON PERSONAL CREDITS. YOU ONLY GET 35%* OF WHAT YOU WERE SUPPOSED TO EARN IF YOU LOSE.
*35% is just an estimate. My other 2 estimate is 33.3% and 40%. But those are still considered to be heavy penalties
2). Winning a battle gives 10% extra bonus credits (as per a recent update in dec)
3). The opponent's rankings and credits are calculated separately in a different pool. This would imply that you should not care about enemies getting ranking off you by killing or dealing damage to you. Only focus on getting your own ranking up by competing with people in your own team.
4). Even if you are alone, the share of the credits is as if there were 5 people on the same team. (i.e minimum total Shares = 152)
5). The maximum amount of credits that can be earned by 1 person per battle is 3000.
6). Teams of more than 20 people happen on regular basis when people leave the battlefield or got killed more than 5 times. The calculation take into consideration everybody, including people beyond rank 20.


The formula basically dictates that the any nation (wherever they 1st, 2nd or 3rd) with more than 220 score (25% of the total score) will get extra tokens. That is, a nation with 30% of the score will always get more than 30% of the tokens (bonus)

However, the lower the score of the loosing nation, the smaller is that bonus.

So, if you are any of the leading nation and you are attacking the last nation, you get extra score for stealing land, but the amount of extra token decreases (increasing penalty on gains) the more you feed on the last nation.

On the other hand, if you are part of any of the leading nation and you are attacking any nation but the last one, you get extra token. (but there is no penalty on the extra token).

In short form, if your nation (the leading nation) wants to maximise the amount of bonus tokens, do not feed on the last nation.


In mathematical form, that constant, being present in both the denominator and numerator of the formula in the ratio 1:4, determines the threshold which separates the winners from the losers. That threshold is exactly at 1/4 of the total score (score of 220/880)

Any nation with 1/4 of the credits are neither winners nor losers. (no bonus, no penalty)
Any nation with more than 1/4 of the credits are winners (bonus tokens)
Any nation with less than 1/4 of the credits are losers (token penalty)

Illustration:
For a team of 20 people, global sum of Shares is given by 40+35+30+24+23+....+8 = 377 Shares
Rank 1 has 40 personal Shares and therefore earns 40/377 = 10.6% of the total available credits.
Rank 2 earns 9.3% of the total available credits
Rank 3 earns 8.0% of the total available credits
Rank 4 earns 6.4% of the total available credits
Etc..
Rank 20 earns 2.1% of the total available credits
Beyond Rank earns 0.5% of the total available credits.

Current Active Worksheet:
If you want to compare, check formula, inconsistencies, you may use the link below
Nation War Worksheet

Nation Score:

Rules:
1). At intervals of 10 min, each nation gains 1 credit for each land owned starting at 20:30, 20:40,..., 22:00 and 22:10 (up to 11 times in total)
2). Each nation starts with 19 Lands (Total 76 Land). The 4 spawn base value cannot be attacked and are worthless: 0 credit.
3). At 22:20 (at end of nw), all 4 nation gains 11 credits.
4). A specific sum of supply tokens are then distributed among the nations based on nation credits earned. Nation with highest number of credits gets the biggest share of tokens.


Implications:

1. The sum of all 4 nations' credits at the end of nw is always 880.
2. All Nation Rankings are already sealed at 22:10 (10 mins before the end of the nw). e.g If the cookie nation is leading at 22:10, the cookie nation will still lead at the end of the nation war.
3. The distribution of token among the 4 nations is sealed at 22:10. But you can still get personal credits to get more tokens. (Battle has to end before 22:20 to earn any credit)
4 HOLDING LAND is more important than just winning fights. Attacking and winning land from other nation will be pointless if you lose it immediately after. E.g If you win a land at 20:32, you have to defend it until 20:40 in order for your nation to earn a single nation

Supply token distribution to Nations

Formula:
Quote:
Number of supply token earned by a nation =
[(region_score-(4.4+0.6*min_region_score))/(880-4*(4.4+0.6*min_region_score)] * (Total amount of Token)

min_region_score is the score of the last nation.

Total numbers of supply tokens are server-dependent values: Archosaur earns 81 816, Heaven Tear earns 78 408, and Sanctuary earns 77 980 consistently every nw, etc... "

Illustration:
Source: HT Sunday 18 Nov 2012
Dark: 213 Score with 18,334 Tokens
Flame: 180 Score with 12,355 Tokens
Light: 179 Score with 12174 Tokens
Frost: 308 Score with 35545 Token

Light is the last nation with a score of 179. Hence, min_region_score = 179.
The total amount of supply token distributed in that particular nation war is 78408.

Calculating frost share of tokens...
Given Frost nation score = 308
Number of tokens = [78408] * [ (308 - (4.4+0.6*179) / (880 - 4*(4.4+0.6*179) ] = 35544.5

Note: In the above example, although frost nation only got 35% of the land credits, they got 45% of the share of supply tokens.

Implications:
1). If a nation scores is exactly 25% of total score, that nation will earn 25% of the token share.
2). If nation score > 25% of total score, that nation will get a bigger percentage of the token share than the percentage of the score[/color]. e.g A nation with 30% of the score, will always earn MORE than 30% of the total amount of supply tokens distributed.
3). If nation score < 25% of total score, that nation will get a smaller percentage of the token share than the percentage of the score. e.g A nation with 15% of the score, will always earn LESS than 15% of the total amount of supply tokens distributed.
4). Hence, You may consider yourself on a Winning Nation if your Nation has more than 220 Score (>25% of total). In the previous illustrations, only frost is winning (by a huge amount), while dark, flame, and light are all on the loosing side since they have less than 220 score.
5). The minimum amount of token distributed to a nation is zero. This happens when the nation score is 11. (That will happen when the nation instantly looses all their land in the first 10mins, not likely to happen ever)

Illustration: Attacking the Right Victim (Nation-based Strategy).
As the leading faction, it might not be the best idea to feed on the weakest nation. From the above example,
If frost (strongest) steals an extra land from light (weakest), frost nation tokens will increases by 91 (35,545->35,636)
If frost (strongest) steals an extra land from any other nation than light, frost nation tokens will increases by 180 (35,545->35,725).



Supply Tokens earned by Player (In progress)

Formula:
Quote:
Amount of Token Earned by Player = (Personal Credits)/(Sum of Personal Credits of all participant with same Nation) * (Tokens Earned by Nation)
The amount of token earned by player is proportional to the amount of personal credits. If someone gets 50 token for 5,000 credits, another person in the SAME nation will get 100 tokens for 10,000 credits.

If the frost nation got 3 times more tokens than Flame nation, it does not imply that a frost person will get 3 times more tokens than a flame person with the same amount of credits. The reason is that the distribution of personal credits also varies from nation to nation. Certain high-performing nations tend to have more high-performing players, all, earning lots of personal credits. Hence, 'the amount of credit required to earn the average amount of token of that nation' tend to be higher for winning nation than for loosing nations.
In other words, having a lot of noobs in your nations will make your nation earn less land and overall tokens, but it may also skew the credit distribution curve towards your advantage.

Myths that are in process to be busted:
1). There is strictly NO evidence of any class-based distribution of tokens. That is, belonging to a certain class does NOT give extra token.
2). There is strictly NO evidence of any level-based distribution of tokens. That is, being higher level does NOT give extra token.
3). Current data points towards there is no minimum threshold value to earn tokens. (i.e the rumour that 'you need at least 2000 credits to start earning credits' seems to be WRONG). It is possible to get tokens with 1400 credits only. It is also possible to get NO token with over 3000 credits. Current data is also pointing out that 'not getting any token' affects all nations equally (or randomly). Currently exploring the hypothesis: 'you need to be part of a minimum number of winning instances (3) to start earning credits'.


I've have never seen any person getting more than 30 tokens for every 1000 credits.
Yet, you manage to show numbers as high as 60 tokens for every 1000 credits. On other populated servers, getting 47 tokens out of 2.5k credits in a winning nation is a very-realistic number.

I know for a fact that... momaganon is a underpopulated server like lotharis with 150< people per nation (as compared to 300 on other servers):
Total tokens are lower, performance is different, strategy is different..

[Jammy]

Wow thanks for this this is interesting as fk

[Lyra]

Yes, thank you so much for this. I was JUST, yesterday, wondering how the rewards and everything were calculated. Thank you, again.  :smiley:

[JHIN]

thanks  :smiley:

so i just need to DD, tank damage, and kill to earn more tokens?  :sad:

[hot_panini]

Nothing new to read up on really, but overall great guide. I've been playing NW in Sanctuary ever since it came out. I did a lot of observations and including testing theories (I.E If you afk in instance, you do or don't get any personal credits nor Supply Tokens).

Don't forget: Always have fun during NW

[Kirasath]

What i understood is hit more,die less.

[shelleysqrd]

WOW!
 Thank you for this guide. It's awesome and you really put a lot of thought and work behind this. The scoring/tokens won and how is much clearer. Always wondered how they came up with the number of tokens awarded.

[JHIN]

i followed this and improved my token tally from 20pcs > 340 pcs.  really thankful.

[LaceyPip]

WOW!
 Thank you for this guide. It's awesome and you really put a lot of thought and work behind this. The scoring/tokens won and how is much clearer. Always wondered how they came up with the number of tokens awarded.

Thank you but it wasn't my work, I just got this from one of my gaming friends on PWI.  And I am very glad that it was helpful

[LaceyPip]

i followed this and improved my token tally from 20pcs > 340 pcs.  really thankful.

WHOOHOO  JHIN I am so glad that the guide helped!!  I will pass this on to Nocht Angel

[JHIN]

WHOOHOO  JHIN I am so glad that the guide helped!!  I will pass this on to Nocht Angel

thanks to the both of you for the awesome guide. 

[LessQQMorePewPew]

These calculations were posted originally by at least one other person back in 2012 old news Nought_Angel should give credit where its due, her source probably:

http://pwi-forum.perfectworld.com/showthread.php?t=1542891

[Rinadiel]

I must read this when I'm not lazy D: skimmed through it though looks awesome ^^

[LaceyPip]

These calculations were posted originally by at least one other person back in 2012 old news Nought_Angel should give credit where its due, her source probably:

http://pwi-forum.perfectworld.com/showthread.php?t=1542891

Does it really matter?  The fact that we found this guide very useful, is the only thing that matters

[Бумер]

Probably the most useful thing I've read so far!
Thank you very much for the guide!
Altough I've heard some where that the more you die the more points you get, I guess it's false?