Concentration of power

MichielK

Guest
Hi everyone,

In an earlier thread, I've tried to tackle the problem of TW's lack of victory conditions. One of the issues we came across was that there's no real objective way to determine how power is concentrated in W16.

As you know, I like working with statistics. What you may not know is that I have a degree in economics. In this thread I'm going to try to combine the two...and don't worry, you won't need to know a thing about economics to follow it :)

I've picked two variables that are commonly used in economics to determine market power:
1) C4 ratio, which stands for the total market share of the top 4 companies
2) The Herfindahl-Hirschman Index (HHI), which is a bit more complex
Both variables are expressed as a percentage, and a higher percentage means a higher concentration of power.

I've also decided to ignore tribeless players. This is nothing personal, but it makes data collection a lot quicker :icon_wink:

First, let's look at the C4 ratio:
- C4 (based on points): 58.8%
- C4 (based on villages): 56.4%

A number around 60% indicates that the market is a so-called oligopoly. What this means is that a few tribes (companies) control the majority of the world (market).

Examples of real-life oligopolies are the markets for beer, automobiles, airplanes and cola...everyone can name a few companies that make cola, but most people won't be able to name 20 :icon_wink:

Second, let's look at the HHI:
- HHI (points): 10.52%
- HHI (villages): 9.79%
For the HHI, a percentage above 10% indicates the market is moderately concentrated, while a percentage above 18% indicates the market is heavily concentrated.

If you invert the number, it gives you the amount of equal-sized tribes that would give the same concentration of power. In this case, the world shows the same concentration as a world with 9.5 equally-sized tribes (or 10.2, based on villages).

Both variables show that the power in this world shows moderate concentration, but we're pretty far from being a "monopoly". In other words: while the world isn't won yet, a relatively low number of tribes have a stranglehold on it and new tribes are extremely unlikely to succeed. That sounds about right, doesn't it?

Now, the value of these numbers is obviously not in just doing one analysis and forgetting about it. By doing it on a regular basis, there are a lot of questions you can answer objectively. For example, this is a more objective way of looking at how close we are to the end of the world than through the Countdown thread, since it takes into account not merely the amount of tribes but their relative size.

It can also provide an objective answer to more specific questions. Here are some examples of things we've discussed recently that can be answered with these numbers:
- How big of an impact does Dust (or Coal, or SA) make in the southeast?
- Is the movement of players from BANG to Plight a major world event?
- Will W16 be done earlier than W15?

I'm going to post new numbers at regular intervals and after big events, and provide my own analysis. Hopefully it will spark some debate and give us some facts instead of opinions to use in many discussions. If not, I just wasted 30 minutes on the public forums. Wouldn't be the first time :lol:
 

DeletedUser22370

Guest
You definately know your stuff :)

I look forward to seeing future stats and comparing them.
 

DeletedUser

Guest
Very interesting indeed and I look up for your answer in those questions you wrote at the end.
 

DeletedUser

Guest
This game is designed to not have victory conditions, or victory conditions persay that are easily attainable.

How else would this game stay alive and make money if it was defeated too quickly.

Just like every other game producer, tribal wars takes advantage of the average persons drive to succeed and be the best and on this game, to be the best you need premium. Premium costs money and to keep the money rolling in, you need premium to constantly be purchased. Thus, premium points have shelf lives, the game can be argued to not have a shelf life.

Theoretically the last tribe standing is the winner, but will that happen in any world here?

There are many scenarios that exist in which you can have a single winning tribe. Maybe one tribe is so big that all the other tribes say screw it and give up and quit playing. Bam, theres your winner, close the world.

It's the individual person that makes victory conditions nearly impossible in this game. Take the knight in Monty Python and the Holy Grail. The one who kept getting arms and legs chopped off. he was clearly defeated, yet never gave up. It's the people and the tribes in this game who are clearly (or are clearly going to be) defeated that don't give up.

What does that mean...you have to continue fighting and taking them and with this slow world that could take a loooooooong time.

There needs to be a poll or something with votes compiled on players individual ideas of what constitutes a victory condition in a world setting.

Then, based off the best and most logical answers, poll them and come up with a bonafide answer to go by.

removing all barbs would help, making for player on player attacks only. Putting a time limit on the entire world would certainly have a clear winner, but then no more premium and no more income...

it's a catch 22.
 

MichielK

Guest
Here's a nice preview of the kind of posts I have in mind :)

What is the difference between W1 and W16?

The oldest world currently running on TW is world 1. According to TW Stats, they currently have 605 players left in 61 tribes (and only 24 of those have points). That's less than a third of what we have here on W16, so at first glance they appear to be much further on the road to the end of their world.

However, is this true? How far ahead are they?

To answer that, let's have a look at the concentration stats of both worlds:
C4: W1 = 79.8%, W16 = 58.8%
HHI: W1 = 20.0%, W16 = 10.5%
As expected, their concentration stats are a lot higher. This indicates that they are a lot closer to a "monopoly"...a situation where one tribe controls the world.

Here's the really interesting question though: what would we need to do to "catch up" with this ancient world?

I'll focus on C4 first since that's easiest to calculate. The first thing I'll do is borrow the phrase "junior partner" from Seagryfn and apply it in an extreme scenario: I'm going to add each junior partner to their senior partner. While I doubt all of these will end up in a merger, this is one possible long-term effect of such a partnership (and in the case of C² and BFL, it's happening right now).

This means that Ni joins Plight, LS (and HRVa) join HRV, TKR joins BANG and the remainder of BFL joins C². Our C4 now becomes 74.3%, an increase of 15.5%. Just like that, we've closed most of the gap to W1.

The next step is to fast-forward some of the current wars and conflicts. I'm going to cut the size of Ad Inf (and Ad A), PnX, Dust (and Shroud) and Coal in half.

Out of the points lost, I'm going to assume that half are nobled (so added to HRV-LS, Plight-Ni and BANG-TKR), and the other half consists of players quitting. Our C4 is now 80.3%, and we've passed W1!

HHI works a bit differently, and is only at 16.6%. The way HHI works, it benefits mainly from tribes disappearing completely. In other words, it's cleanup time!

Let's fast-forward a bit more in the wars and conclude them. The attacking tribes take the remainder of Ad Inf/Ad A, PnX, Dust/Shroud and Coal. While some players may quit and disappear, it's safe to assume that the winning tribes will help themselves to those barbs as well. This brings our HHI to 19.3%, which is very close to W1. The remaining gap can be closed pretty quickly by removing a few of the tribes with 3 or less players in it.

So, to answer the original question, here is the difference between W1 and W16:

- Junior partners need to join their senior partners
- Current wars need to be concluded (partially)

I'll leave it up to you to give an estimate of how likely you think these events are or how quickly you see this happening, but IMO we're not talking years here, nor are we talking huge stretches of the imagination.
 

DeletedUser

Guest
Aren't tribe member limits a bit of a factor in all these merges?
 

MichielK

Guest
Aren't tribe member limits a bit of a factor in all these merges?

Of course they are, but so are the intentions of the tribes involved, future wars, etc.

I'm not predicting the future here, or making any statement about whether or not these mergers will occur. What I did was give a possible example of how we could end up in the same situation as W1, and it's tough to argue that these events are completely impossible :icon_wink:

In an economic sense, you could even argue that given the fact that the tribes involved have acted towards common goals and fought common enemies for quite a while now, they are the same entity as far as control and power is concerned. Only reason I didn't do that is because someone will derail the whole thread with a huge discussion on how "MK just called you tribe X's academy!" :icon_confused:

There are other routes to get there, of course. Open warfare is one of them, rim cleanup is another. If PnX, Ad Inf/Ad A, Dust/Shroud and Coal are completely destroyed, you're already at a C4 of 73%...one or two mergers would do the trick then.
 

DeletedUser

Guest
They should incremently give world and troop speed increases periodically. Such as 1 year from opening the world speed increases by .5 and the troop speed by whatever that equals out to be....then 6 months from that another small increase...that would certainly bring life back into some inactives and the world.
 

DeletedUser

Guest
MichielK,

Are your results for HHI posted using the normalized equation? If so, would I be correct in assuming you took N to be tribes with points (as any number of tribes without points would combine to nothing) or did you use some construct for determining tribes that are counted?
 

MichielK

Guest
MichielK,

Are your results for HHI posted using the normalized equation? If so, would I be correct in assuming you took N to be tribes with points (as any number of tribes without points would combine to nothing) or did you use some construct for determining tribes that are counted?

I didn't use the normalized equation, and you touched upon the reason: is a tribe with 0 points still a tribe? It's a matter of definition, and I decided to avoid it by using the non-normalized HHI.

Btw, the normalized equation actually makes the differences much closer. The HHI for W16 would drop 0.5%, while the HHI for W1 drops by 3.5%.
 

MichielK

Guest
They should incremently give world and troop speed increases periodically. Such as 1 year from opening the world speed increases by .5 and the troop speed by whatever that equals out to be....then 6 months from that another small increase...that would certainly bring life back into some inactives and the world.

If that was true, it would chase away a lot of the players who chose to play W16 because of the low speed. You can't change the rules midway through the game, IMO.

We're heading off-topic though...
 

DeletedUser

Guest
I believe that the normalized equation would be more valid. However using the normalized equation makes differentiation a bit more complicated. My thinking is that one could construct a system of equations and their corresponding first-order derivatives to determine how the HHI would change based on the pace of current wars. I think that would be an interesting statistic and discussion in itself.

It would allow us to quantitatively discuss how the destruction of one tribe at the hands of another affects the rate at which the world reaches the "end game".
 

DeletedUser

Guest
While this thread seriously stresses my knowledge of statistics, it shows that we are actually more concentrated that I had originally though. However the assumption you are making MK is that the large tribes that currently exist will remain unified in the future. As we just saw with Bang!? breaking apart, this may not always be the case.
 

DeletedUser

Guest
Cant wait to hear the answers. Very interesting (I didnt get half of it because of my age but still, lol)
 

MichielK

Guest
I believe that the normalized equation would be more valid. However using the normalized equation makes differentiation a bit more complicated. My thinking is that one could construct a system of equations and their corresponding first-order derivatives to determine how the HHI would change based on the pace of current wars. I think that would be an interesting statistic and discussion in itself.

It would allow us to quantitatively discuss how the destruction of one tribe at the hands of another affects the rate at which the world reaches the "end game".

We could, but the whole idea behind this thread for me is to make the statistics accessible for as many people as possible. It's not about the numbers, it's about the "story" that the numbers tell us :)
 

MichielK

Guest
While this thread seriously stresses my knowledge of statistics, it shows that we are actually more concentrated that I had originally though. However the assumption you are making MK is that the large tribes that currently exist will remain unified in the future. As we just saw with Bang!? breaking apart, this may not always be the case.

The effect of the people moving from BANG to Plight on C4 was zero and the effect on HHI was minor. People changed places, but the overall concentration of the world hardly changed.

Think about it this way: do the smaller tribes in W16 now have a far better (or worse) chance of growing big? Do the bigger tribes not involved (HRV and C²) now have a much better (or worse) chance of staying big? I think the answer to both questions is no, and that's what the stats reflect as well.

It would be different if a tribe collapsed into multiple parts, and that is pretty rare. I can only remember one example of that happening (Plight's "civil war"), and that's quite a long time ago.
 

DeletedUser

Guest
We could, but the whole idea behind this thread for me is to make the statistics accessible for as many people as possible. It's not about the numbers, it's about the "story" that the numbers tell us :)

Well of course it is about the "story". That said, it is often the case that forum posters will tell stories based on individual bias and feelings and not something quantitative in nature. I think lots of forum posters falsely believe that anything not quantitative is qualitative. There is of course a third option -- false. I think recent claims made by members of Ad Inf suggest that there are a large number of subscribers to theories that fall into that third category.

Using numbers to quantitatively support a story with quantitative descriptions, theories, and conclusions is really the best way to illustrate a scenario or situation. That is why, within TKR, I try to accumulate data for dissemination as a numerical basis for conclusion. It's not necessarily important that all readers understand the numbers. In fact, they only need to understand the story. But the numbers provide statistical support for the story and helps to convince skeptics that the story is accurate.

Regarding my thoughts on the HHI, certainly knowing the HHI is meaningful and important. But it is of greater interest to me to know how changing one piece of the world changes the HHI. For starters, knowing the effects of specific events on the HHI would be good for strategy planning.
 

DeletedUser

Guest
Well, i'm not an economics man myself, but i did enjoy reading what you wrote - bravo!

This was actually very interesting and enlightening and i am keen to read more on this, so, keep it coming!
 

DeletedUser

Guest
Well statistics and maths related stuff is not my favourite subject but this thread is quite fascinating.
 
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