Concentration of power

MichielK

Guest
W16 update

Points-based:
C4: 75.42% (+ 2.13%)
HHI: 15.66% (+ 0.47%)

Village-based:
C4: 73.68% (+ 2.21%)
HHI: 15.02% (+ 0.49%)

By popular demand:
Number of players that could be a top 20 tribe: 250 (+52)
Number of players that could be a top 15 tribe: 92 (+15)

Discussion
Concentration of power in W16 increased quite a bit this week, mainly due to 14 TKR members moving into BANG. Too early to tell the exact effect of this, since it does not appear to be fully done yet.

Aside from that, we have our first solo tribe in the top 20. As you can see above, 250 players could be a top 20 tribe...well, as it turns out the player ranked 250th is the number 20 tribe. I imagine it's a pretty well coordinated one :icon_razz:

No projects this week due to statisticians block (it's like writers block, but nerdier). Remember, if you have a request for a project, I'll gladly take it into consideration!
 

MichielK

Guest
W16 update

Points-based:
C4: 77.77% (+ 2.35%)
HHI: 16.29% (+ 0.63%)

Village-based:
C4: 76.08% (+ 2.41%)
HHI: 15.67% (+ 0.65%)

By popular demand:
Number of players that could be a top 20 tribe: 253 (+3)
Number of players that could be a top 15 tribe: 135 (+43)

Discussion
Another week with a big increase in concentration of power, almost exclusively due to the BANG-TKR merger (given the name change, I think it's safe to call it that). In fact, the effect of this merger was mitigated by the movement of BANG inactives into TKR, though that should provide an increased rate for the weeks to come.

This week marks the emergence of a true top 4 in W16. While meaning no disrespect to tough independent tribes such as Dust and MK, the size gap between the top 4 and the rest of the world is huge, and only likely to increase as inactive eating continues (TKR & Ni), wars progress (Ad Inf), and casual expansion takes its toll (WWE).

Project: concentration of players

In an attempt to clean the stats from clutter, this project is aimed at analysing the players that tribes consist of, and how tribes stack up if the small and statistically insignificant players are removed. For the purpose of this project, I will limit my analysis to the 581 players currently above 100,000 points.

(Yes, I realise this will bother the rim players under 100K. However, other players on the outer rim have managed to grow to 1-2 million points by now. If you are outgrown 10-1 by many and 20-1 by the extremely skilled, you're not going to be a factor in this world...ever.)

Here is how the players over 100K are spread:

Plight: 79 (13.6%)
LSHRV: 74 (12.7%)
BANG!: 72 (12.4%)
C²: 70 (12.0%)
Dust: 53 ( 9.1%)
Ad Inf: 45 ( 7.8%)
Ni!: 35 ( 6.0%)
=WWE=: 29 ( 5.0%)
TKR: 23 ( 4.0%)
Coal: 21 ( 3.6%)
*MK*: 9 ( 1.5%)
LSHRVa: 8 ( 1.4%)
|BFL|: 5 ( 0.9%)
I Wolf: 5 ( 0.9%)
I.A.R: 4 ( 0.7%)
~HF~: 4 ( 0.7%)
ORC: 4 ( 0.7%)
ATE: 2 ( 0.3%)
CND: 2 ( 0.3%)
BRW: 2 ( 0.3%)
PNR: 2 ( 0.3%)
TWcrew: 2 ( 0.3%)

Others: 5 ( 0.9%)
Solo tribes: 7 ( 1.2%)
Tribeless: 17 ( 2.9%)

That's all. There are currently only 22 tribes left in W16 with more than one player over 100K. In fact, if you look further the concentration is even stronger. Many of the other tribes that make the list are in fact legacy tribes, inactive repositories, tribes that quit or academies: Ni!, TKR, LSHRVa, |BFL|, ORC, CND, BRW and TWcrew all fall into one or more of these categories.

Let's look at the top four tribes. They currently have:

  • 51% of all players in W16 (over 100K)
  • 93% of all players in the top 100
  • 88% of all players in the top 200
  • 84% of all players over 1 million points
In fact, if you add MK, the first player outside those 5 tribes comes in at rank 78.

Now, let's look at the top 10. They currently have:

  • 85% of all players in W16 (over 100K)
  • 99% of all players in the top 100
  • 98% of all players in the top 200
  • 98% of all players over 1 million points
Conclusion? The players in W16 are just as concentrated as the power in W16 is. Not only do the big tribes have more points, but they have more players with a significant amount of those points as well.

Hardly a surprise, but the numbers are impressive, aren't they? :icon_wink:
 

DeletedUser

Guest
Where is the degree of error in the equation , w16 has alot of players leaving , so fast and so big there arent enough nobles to go around and big barbs are popping up everywhere . It seems the designers took this in account since w1 is still going , and seems to be activity being key ,the winner will be who stays the longest without giving up. I think in the next couple of months we will be back reminiscing over all these old maps and remember whens ....cause the world will look a little different.
 

DeletedUser

Guest
Those are insane... I understand most of it and it's absolutely amazing the conclusions you can draw from thos statistics. We sure are lucky to have you MK. :icon_wink:
 

MichielK

Guest
W16 update

Points-based:
C4: 79.18% (+ 1.41%)
HHI: 16.78% (+ 0.49%)

Village-based:
C4: 77.53% (+ 1.45%)
HHI: 16.17% (+ 0.50%)

By popular demand:
Number of players that could be a top 20 tribe: 255 (+5)
Number of players that could be a top 15 tribe: 124 (+32)

Discussion
This is the third week in a row with big changes in CoP, mainly due to the conclusion of the BANG-TKR merger. Our C4 is up by 6% in the month to date, which is much higher than the ~1% a week we normally reach.

As a result, we're inching closer and closer to the 80% mark, which is the topic of this week's project.

Project: C4 at 80%- what does it mean?

Aside from being a nice round number, there is some significance to an 80% C4 ratio: it's halfway between the scores for an oligopoly (60%) and a monopoly (100%*). First off, let's explain these terms for the non-economists here:

- Monopoly: a situation where a specific company has so much control over a specific product that it can dictate the terms on which others have access to it.
- Oligopoly: a market form where the industry is dominated by a small number of sellers or producers.

W16 is currently in an oligopoly state. The top 4 tribes (C², Plight, LSHRV and BANG!) have significant control over access to points and villages in W16. Continental dominance shows this clearly:

Plight: 28 continents
C²: 25 continents
LSHRV: 17 continents
BANG!: 15 continents
Ad Inf: 6 continents
Sunny: 5 continents
Ni!: 2 continents
*MK*: 1 continent
Coal: 1 continent

In other words, 85% of all continents are dominated by the top 4 tribes, and this number is likely to increase due to e.g. BANG's progress against Ad Inf and Plight's control over Ni.

The tribes outside the top 4 are in what economists call "niche markets": a subset of the market targetted by a specific product. They do own continents, but it could be argued that they're targetting a different market ("rim", "local dominance") than the top 4 ("world").

The importance of the monopoly state is clear, since it signifies the end of the world by conquest. While a C4 of 100% is not the only requirement for that (see note at the end of this post), it is an important one.

Luckily for those of us who want to play on, the HHI shows that we are still under moderate concentration; while the 4 top tribes may dominate the world, there is no single tribe exercising significant power over the others. Our world is currently similar to a world with 6 equally sized tribes and no others...clearly, we still have some work to do :icon_wink:

Finally, as a little bonus, I've looked for an industry which also has a 79% C4 and found one: airplanes. Those of you who are frequent flyers will have a decent comparison if they consider what types of planes they usually fly with...



* Note: a C4 of 100% is a requirement for a monopoly, but not the only one. In other words, every monopoly has a C4 of around 100% but not every market with a C4 of 100% is a monopoly.
 

DeletedUser

Guest
Fpr those of us with no economics skills whatsoever (read:ME) that is a really great explanation. BTW remind me never to play poker with you MK...you are way to good with the statistics....
 

MichielK

Guest
Fpr those of us with no economics skills whatsoever (read:ME) that is a really great explanation. BTW remind me never to play poker with you MK...you are way to good with the statistics....

LOL!

Like most things, poker is more than simply being good at statistics. Numbers don't help you much unless you know how to use them effectively...turn them into information. That's what I'm trying to do in this thread.

I realise many people do not have the knowledge of economics or statistics to do this type of analysis, but my goal is to make sure you don't have to. Common sense and a good knowledge of TW should be enough to understand my posts, and if it's not that's my failure, not yours (which is why it's important to get feedback; if I post something that doesn't make sense to anyone, I've wasted everyone's time including my own).
 

DeletedUser

Guest
Your posts are great. I love the comparison with the airplane industry :)
 

DeletedUser

Guest
Fancy coming to world 18 MK? We could do with more threads like this :p

Thanks for putting the info into terms simpletons like myself can understand.
 

DeletedUser75807

Guest
I do want to say that I really enjoy this thread. I am a numbers guy and this is like going to the candy store.
 

MichielK

Guest
Thanks for the compliments :)

I already have my project for next Saturday picked out, but remember that you can always contact me on the forums or in-game if you have requests. I can't promise that I'll do them, but I promise I'll try...I generally have more trouble coming up with ideas than executing them :icon_wink:
 

MichielK

Guest
W16 update

Points-based:
C4: 79.62% (+ 0.44%)
HHI: 16.95% (+ 0.17%)

Village-based:
C4: 78.07% (+ 0.54%)
HHI: 16.37% (+ 0.20%)

By popular demand:
Number of players that could be a top 20 tribe: 234 (-21)
Number of players that could be a top 15 tribe: 91 (-33)

Discussion
After three weeks with big CoP changes, our numbers are back to normal. They're a bit lower than what we're used to, but that's because it's been a short week between posts (5 days instead of 7). I'll try to get back to a regular Saturday posting schedule again next week.

Most surprising change this week is in the number of players that could be a top 15 or top 20 tribe on their own; for the first time, we have a significant drop in numbers there. This is mainly due to recruitment by several smaller tribes (notably I Wolf and ORC).


Project: Feeding patterns

In the project for this week, I have decided to do something a bit different. Instead of determining by how much the top tribes dominate this world, I've decided to make an attempt at finding out why they are the ones dominating. In other words, what is necessary to be a top tribe?

(Don't worry though, I'll get back to concentration of power at the end of my post!)

Everyone has an opinion about this topic, and commonly heard explanations include that a top tribe has superior skill, takes better targets, is more aggressive, deals with inactives better, and many others. In this projects, let's move away from theory and see what the facts support :)

First, I've organised the tribes of W16 into three distinct groups:

  • Tier 1 tribes: tribes with worldwide influence/dominance.Size of top 40 members > 50 million points
  • Tier 2 tribes: tribes with regional influence/dominance.Size of top 40 members between 5 and 50 million
  • Tier 3 tribes: tribes with little to no influence/dominance. Size of top 40 members < 5 million
After that, I have collected all conquers by tribes in each tier for a period of roughly a week (midnight Nov 20 to the evening of Nov 26). These conquers are divided into groups based on target, relation to the target and (in case of barbs) size.

Here is how the various groups grow:

Tier 1 tribes: C², Plight, LSHRV, BANG!
[SPOIL]
32zp35e.jpg

[/SPOIL]
Tier 2 tribes: Ad Inf, Sunny, Ni!, *MK*, TKR, Coal, =WWE=
[spoil]
2u7agt2.jpg
[/spoil]
Tier 3 tribes: everyone else, for example ATE, I Wolf, LSHRVa, I.A.R and ORC
[spoil]
2vns5xe.jpg
[/spoil]

So far, the "classic wisdom" appears to emerge victorious. Based on the analysis so far, the following observations can be made:

  • Top tribes take larger villages: average conquer size is 8843 points for tier 1, 7954 points for tier 2 and 5164 points for tier 3
  • Top tribes take less barbs: 31% - 38% - 69%
  • Top tribes take larger barbs: 7206 points - 6439 points - 4197 points
  • Top tribes deal with inactives faster: 46% - 30% - 15%
  • Top tribes overnoble less: 2% - 5% - 14%
These numbers confirm that top tribes pick their targets better (player v barb, size), deal with their inactives better (or at least faster), and is more skilled (less overnoblings).

However, there's one common explanation missing. What about aggressiveness? Here is what the numbers say:

  • Tier 2 tribes take more "live" targets: 23% - 31% - 15%
  • Tier 2 tribes take more tribal villages: 14% - 29% - 11%
  • Tier 2 tribes take more tier 1 targets: 4% - 12% - 0%
If aggressiveness is a requirement for being a top tribe, why are the mid-level tribes showing more of it? Why are they spending relatively more nobles against player-owned villages, enemy tribes and top tribes?

I believe the answer consists of many points, but the three main ones are below.

  • Scale: while the tier 2 tribes take relatively more villages that require aggressiveness, the tier 1 tribes take more in total. Since there's a limited amount of enemy villages available, the tier 2 tribes have an easier time getting their percentage up.
  • Location: by their nature, tier 2 tribes lack the solid/safe backfield that most tier 1 tribes have. As a result, a relatively larger portion of tier 2 territory borders enemy tribes, while a relatively larger portion of tier 1 territory borders tribemates.
  • Diplomacy: while tier 1 tribes generally choose to go to war, tier 2 tribes are generally chosen. They take relatively more enemy villages because they have relatively more enemies. In tier 1, C² and LSHRV are at war with eachother while BANG is at war with Ad Inf. In tier 2, two tribes are under control of a top tribe (Ni and TKR), and all the others are involved in at least one war: Ad Inf v BANG, Sunny v LSHRV, *MK* v Coal, Coal v *MK*/LSHRV, WWE v everyone.
While this does not prove that aggressiveness is a necessary quality for a top tribe (I believe it is), it also doesn't disprove it. Based on this data, that's probably the best we can accomplish.

Conclusions

  • Top tribes show more skill, better target sense and faster inactive eating
  • Aggressiveness may be a factor, but the evidence is inconclusive
A note on concentration of power

The data above also tells us something about concentration of power:

  • Tier 1 tribes nobled 1071 villages, while tier 2 and tier 3 combine for only 327
  • Tier 1 tribes gained 202 villages against the rest of the world, but lost only 30 to everyone else
  • Tier 1 tribes conquered 338 barbarians in this period, while tier 2 and tribe 3 combine for 147 barbarians
  • In points, the difference is even bigger: 2.4 million versus 0.8 million
Since the top tribes gain 172 net villages against the rest of the world and gain points from barbarians 3 times faster, it's clear that this world will only become more concentrated.

[Thanks to SavikTKR for advice on data organisation!]
 
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DeletedUser

Guest
MK, I'm very impressed with the visuals in this week's update. I have a few questions though about the categorization you used in your pie charts. Could you elaborate on how you accumulated some of your statistics? For example, what is "External Nobling" and how is it different from everything aside from Internal Nobling and Overnobling? It seems like everything else, from the tier system to barb ennoblement, would be encompassed in External Nobling. Great work! :D
 

DeletedUser

Guest
I think external nobling is nobling the inactives of the smaller, "junior" tribes.

So that would be like:
Bang! nobling from TKR
Plight from Ni!
LSHRV from LSHRVa
C2 from BFL

At least that's what I think it is.
 

DeletedUser

Guest
MK, I'm very impressed with the visuals in this week's update. I have a few questions though about the categorization you used in your pie charts. Could you elaborate on how you accumulated some of your statistics? For example, what is "External Nobling" and how is it different from everything aside from Internal Nobling and Overnobling? It seems like everything else, from the tier system to barb ennoblement, would be encompassed in External Nobling. Great work! :D

I believe "External Nobling" is taking non-barbarian villages outside the tribe. "Internal Nobling" would then be taking non-barbarian villages inside the tribe. "Overnobling" is sending too many nobles and self-converting. This would obviously be separate and distinct from Internal Nobling.
 

DeletedUser

Guest
I believe "External Nobling" is taking non-barbarian villages outside the tribe. "Internal Nobling" would then be taking non-barbarian villages inside the tribe. "Overnobling" is sending too many nobles and self-converting. This would obviously be separate and distinct from Internal Nobling.

I agree with this.
 

DeletedUser

Guest
I believe "External Nobling" is taking non-barbarian villages outside the tribe. "Internal Nobling" would then be taking non-barbarian villages inside the tribe. "Overnobling" is sending too many nobles and self-converting. This would obviously be separate and distinct from Internal Nobling.
This is what I figured, but then wouldn't this mean that, for example, villages nobled from a Tier 1 tribe would be counted in both the Tier 1 category AND External Nobling? Thus those villages would be counted twice. If this is the case, there should be two separate pie charts for each tier: one chart showing just internal and external nobling, and one chart showing everything else minus those two categories?
 

DeletedUser

Guest
Then modify "External Nobling" to being non-barb players outside any tribe.
 

DeletedUser

Guest
I believe "External Nobling" is taking non-barbarian villages outside the tribe. "Internal Nobling" would then be taking non-barbarian villages inside the tribe. "Overnobling" is sending too many nobles and self-converting. This would obviously be separate and distinct from Internal Nobling.
Well we still have to wait on MK to clear this up, but I still think its my reasoning. Like Shadow said, if it were your reasoning Savik, then the nobles would be counted twice. Mine was the only one I could come up with that might be seperated into a completely different section.

u6 - there's also already a percentage for tribeless players.
 

MichielK

Guest
Woops, looks like I caused some confusion with my categories :icon_eek:

First off, note that it does not say internal/external nobling, but internal/external eating. These are villages that are free to take (or should be free to take).

Internal eating is taking villages from tribemates, e.g.one C² taking a village from another C² member.

External eating is taking villages from a tribe that's under control of your tribe, such as an academy or inactives repository. BANG-TKR, LSHRV-LSHRVa and Plight-Ni fall in this category.

Each conquer can only be in one category, so there is no doublecounting. If BANG takes a village from TKR, it only counts as external eating and is not included as a tier 2 conquer as well. This way, the tier 1-3 conquers indicate "war" conquers only.

Sorry for the confusion!

EDIT: Nearly forgot: overnobling is nobling villages that already belong to you personally (e.g. Jurasu taking a village from Jurasu).
 
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