Concentration of power

MichielK

Guest
W16 update

Points-based:
C4: 67.08 (+ 7.35%)
HHI: 12.96% (+ 1.20%)

Village-based:
C4: 64.82% (+ 7.41%)
HHI: 12.20% (+ 2.15%)

Discussion
Due to my vacation it's been a while since I've done an update, and there are some interesting changes in the statistics. A weekly 1% increase in C4 is reasonable, but we went up by more than 7% after 4 weeks.

The obvious cause of this big change is the HRV-LS merger, and I'll isolate that effect below. Obviously there will be other effects (e.g. the demise of PnX), but for now I'll consider those minor.

In my second project for this week, I'm going to have a look at the effect of "non-tribe" tribes. What I mean by this is that I'm going to find out how the stats are influenced by tribes that do not act as normal tribes, e.g. academies (LSHRVa, Shroud, Ad A), solo tribes (Death, ZANE), past tribes (ORC, CND), etc.

Project 1: the effect of the HRV-LS merger

To calculate the effect of the HRV-LS merger, I first need to isolate it first. After all, plenty other things happen in any given week. The method I used is:

1) Take the points totals for today for all tribes
2) Change (LS)HRV and (LS)HRVa back to their point totals for Sep 12.
3) Add ~LS~ back in, also with their point totals for Sep 12.

The new C4 values are 63.65% based on points and 61.47% based on villages. This is a drop of 3.44% and 3.35%, respectively.

Now, is this the only effect? If you subtract the effect of the LSHRV merger from the newest numbers, the past 4 weeks have seen an average weekly change of 0.98% in points-based C4 and 1.02% in village-based C4...

If you subtract this number from the changes mentioned at the start of this thread, the "clean" changes in C4 are 0.98% per week and 1.02% per week. These numbers are almost identical to the regular weekly change, so it's safe to say that the only significant effect influencing our data is the merger.

How big is this effect? If the net effect of the merger is around 3.4%, this corresponds to roughly 3-4 weeks of regular activity. In other words, without the merger we would've reached this result in the middle of October. At first glance, that doesn't seem all that big.

There are a few reasons for this:

1) While a lot of active players moved into HRV, a lot of inactive players got moved into HRVa. This reduces the C4 by about 1%.
2) Our C4 was already quite high (~60%), so a 3-4% increase is a relatively big move forward.
3) I suspect that C4 increases have a tendency to drop over time. After all, at our current rate we'll reach 100% in just 33 weeks, and I seriously doubt that we'll have only 4 tribes left in the world in 7 months. However, there is no way to quantify this until we have a bigger dataset.

In conclusion, the effect of the LSHRV merger seems relatively small at first glance, but is definitely noteworthy because it has basically done about 10% of the "work" needed to bring W16 down to four tribes.

Project 2: the influence of "non-tribes"

One of my personal pet peeves is that the stats posted here could be "polluted" by issues that have nothing to do with the actual concentration of power. For example:

  • Academy tribes make the world seem less concentrated, despite the fact that they are under full control of the parent tribe.
  • Individual players can raise or lower the concentration stats simply by forming their own solo "tribe".
  • Past tribes that are kept active for reasons of history, reputation or OD stats make the world seem less concentrated, despite the fact that they are no longer actively trying to achieve world domination.
The end result of this is that the world seems less concentrated than it actually is. In this project, I want to find out exactly how big this effect is.

Our current (points-based) statistics are a C4 of 67.1% and a HHI of 13.0%. Now, let's get to work:

  • I've added the following tribes to their parents: LSHRVa, Ad A, ~HF²~, and Shroud.
  • I've removed the following tribes: Death, ZANE, TUWF, B.I.G., blowm3, and the other 66 :)icon_eek:) tribes with one member.
  • I've removed the following "historical" tribes: ORC, CND, and BANG!!.
The end result is a C4 of 68.8% and a HHI of 13.6%. Note that the effect of all these changes is about half of the effect caused by the LSHRV merger. In other words, it's pretty big, but not spectacular. I certainly expected it to be bigger.

I've done the same thing for the data from Aug 24. The starting C4 and HHI are 59.7% and 10.8%, and here's what I did:

  • Added to their parents: HRVa, Ad A, Shroud
  • Removed single-member tribes: ZANE, TUWF, Death, AOL, Damw., and the other 83 :)icon_eek:!) single-member tribes
  • Removed historical tribes: ORC, CND, BANG!!
The final C4 is 61.1% and the final HHI is 11.4%. This is an even smaller increase than we could achieve with the current tribes (mainly due to the emergence of LSHRVa at rank 11).

It's safe to conclude that the data pollution caused by the three effects mentioned above is minor. Looks like our data is a fair representation :icon_biggrin:
 

MichielK

Guest
W16 update

Points-based:
C4: 67.99 (+ 0.91%)
HHI: 13.32% (+ 0.36%)

Village-based:
C4: 65.80% (+ 0.99%)
HHI: 12.57% (+ 0.37%)

Discussion
With the LSHRV merger over, the stats are right back to normal. From a CoP point of view, it's been a pretty dull week...go figure :icon_wink:

No projects this week (I'm busy!), though I will post some additional stats to show how concentrated the world has become:

  • Market share of top 10 tribes:
    • Points: 91% (+ 1.1%)
    • Villages: 89% (+ 1.2%)
  • Membership statistics:
    • Tribes with more than 10 members: 27
    • Tribes with more than 20 members: 18
    • Tribes with more than 10 members over 100K: 14
    • Tribes with more than 20 members over 100K: 9
    • Solo tribes: 64
  • Combined size of tribes:
    • Outside top 10: 64 million points (slightly larger than BANG)
    • Outside top 20: 25 million points (slightly smaller than Ad Inf)
  • Players large enough to be a top 20 tribe: 80 (!)
 

DeletedUser22370

Guest
yeah... scary isn't it, to think that if axl/spank made a solo tribe they would be #12?
 

MichielK

Guest
foofong1 said:
That's my favourite statistic :)
Click to expand...

Mine too. If any of these stats shows clearly how concentrated W16 is becoming, it's that one.

We're up to 85 "top 20" players already. I expect this number to go up quickly since several tribes in ranks 11-20 are losing ground, while most players in the top 200 are still going up.
 

MichielK

Guest
W16 update

Points-based:
C4: 68.81 (+ 0.82%)
HHI: 13.63% (+ 0.31%)

Village-based:
C4: 66.71% (+ 0.91%)
HHI: 12.90% (+ 0.33%)

By popular demand:
Number of players that could be a top 20 tribe: 99 (+19)
Number of players that could be a top 15 tribe: 27

Discussion
Once again, a pretty standard week as far as CoP goes. Only noteworthy stat is that for the first time ever, the top 4 tribes own more than 2/3 of the villages in W16.

Again no project this week...get used to it, I've got work to do :lol:
 

DeletedUser

Guest
MichielK said:
Again no project this week...get used to it, I've got work to do :lol:
Click to expand...

What do you mean with "work"? RL work? Work for us, yes! Go do some project. :icon_wink:

You're doing a great job here and I'm loving it. Keep it up!
 

MichielK

Guest
Geobram said:
What do you mean with "work"? RL work? Work for us, yes! Go do some project. :icon_wink:

You're doing a great job here and I'm loving it. Keep it up!
Click to expand...

It's one part TW work, one part RL work, and one part lack of inspiration..."statistician's block" :icon_eek:
 

MichielK

Guest
W16 update

Points-based:
C4: 71.11% (+ 2.30%)
HHI: 14.36% (+0.73%)

Village-based:
C4: 69.02% (+2.31%)
HHI: 13.62% (+0.72%)

By popular demand:
Number of players that could be a top 20 tribe: 82 (-17)
Number of players that could be a top 15 tribe: 25 (-2)

Discussion
Well, this week is definitely not business as usual. Both C4 and HHI went up by about 2-2.5 times as much as they normally do.

Unfortuately, I cannot make a direct comparison with the data from last week, since that got lost when my old computer died. However, the biggest effect is a game of musical chairs that happened in the Northeast, with an additional minor effect from a dying tribe in the Northwest.

Project 1: where did the weekly increase come from?

Top tribe Plight and their academy Ni have been swapping members all week. A total of 6 members left Plight for Ni, while 8 members made the reverse move. In total, Ni gained 2.6 million points worth of new members, while Plight gained a whopping 12.5 million.

The net effect of this is 10 million points moving into a top 4 tribe and out of a non-top 4 tribe. This is responsible for a C4 increase of over 1.5%.

Another noteworthy event that affected the concentration of power is the beginning of the end for Ad Inf. In the past week, they lost 2.5 million points, including more than 60 villages to BANG, more than 30 villages to TKR, a 500K+ member to LSHRVa :)icon_eek:), and 4 members to the great gray empire.

The losses to TKR and LSHRVa (both also tribes outside the top 4) will not affect C4, but the barbs and losses to BANG will. While the effect is much smaller than the Plight-Ni move mentioned above, it is still over 0.3%...in any other week this would be major.

Project 2: conquers analysis

In this project, I'll try to make some predictions on where our concentration of power is going, and the effect this will have on the world.

First, let's divide the tribes in W16 into four groups and look at their net conquers:

The top 4

1 C² + 149
2 Plight + 310
3 LSHRV + 86
4 BANG! + 139

The top 4 tribes combine for 684 conquers this week, despite the fact that two of the tribes are engaged in a war with eachother (note that a conquer of C² against LSHRV or vice versa means zero net conquers for the top 4).

The rest of the top 15

5 TKR + 73
6 Ad Inf - 60
7 Ni! + 13
8 Dust + 18
9 *MK* + 5
10 Coal + 7
11 LSHRVa - 23
12 ATE + 8
13 cocane + 9
14 ~HF~ + 9
15 -S-A- + 3

The other 11 tribes in the top 15 combined for 62 conquers. This is a mere 9% of what the top 4 tribes did, and the average village size is smaller too.

Also note that TKR is essentially saving this group (statwise, that is :lol:). Their performance is really closer to that of a top 4 tribe than to the group they're in now.

The rest of the world

I hope you'll forgive me for not calculating the net gain of every individual tribe outside the top 15 (there's 114 of them!). Instead, I'm going to estimate their values.

They have a combined size of 28.8 million, which is roughly equal to the size of Ad Inf or Ni....both tribes who have lost size this week. To err on the side of caution, let's give the remaining tribes the same conquers as TKR (which is 25% larger): 85.

However, these tribes are losing villages as well, e.g.:
AoFA: 36 losses
ORC: 18 losses
~HF²~: 18 losses
H2O: 18 losses
DmgInc: 14 losses

Considering these losses, I think it's more than fair (in fact, it's wildly conservative) to state that the tribes outside the top 15 made zero net gain or loss this week.

Comparing the data

So, what are we looking at here? On the one hand, we have the top 4 tribes responsible for 684 net conquers, while on the other hand we have the rest of the world responsible for 62 net conquers. The top 4 are outnobling the rest of the world combined by 11 to 1. Since the current size ratio is about 2.5 to 1, this means that the C4 ratio has only one place to go: up.

Note that these numbers were calculated using very conservative assumptions. In reality, the smaller tribes will lose villages on a net basis, their conquers will be smaller, and their members are more likely to go barb. If there was a convenient way to calculate these effects, the numbers would look far better for the top 4.
 

DeletedUser

Guest
Finally decided to stop being lazy and give us a project, eh? :lol:

Thanks for this MK. As always, was very interesting to read. You did worry me for a minute when I saw Plight had more than twice our conquers before I read the part about conquers between LSHRV and C2 against each other didn't count.

I really would like to know about that LSHRVa player up in the northwest though. I noticed that a few days ago when I saw green dots up there in the map. Anyone care to explain?
 

DeletedUser

Guest
Jurasu said:
Finally decided to stop being lazy and give us a project, eh? :lol:

Thanks for this MK. As always, was very interesting to read. You did worry me for a minute when I saw Plight had more than twice our conquers before I read the part about conquers between LSHRV and C2 against each other didn't count.

I really would like to know about that LSHRVa player up in the northwest though. I noticed that a few days ago when I saw green dots up there in the map. Anyone care to explain?
Click to expand...

From the last 7 daysRank Tribe Conquered Villages
1 Plight 334
2 C² 195

With the ennoblements, it's still quite a gap :lol:.
 

DeletedUser

Guest
Look at the continental dominance maps. For C2, most of the continents not shared with another tribe in the top 5, and even some that are above 90% dominance. But if you look at Plight and the continents they dominate that aren't shared with other top tribes, many only have 60 or 70% dominance, even with Ni! added in to some. They don't even have K9 yet. So they still have more nobling prospects, many of which are rather easy left-overs from PnX, while beside a few remaining small rim players, our only source of targets is a the rank 3 tribe in the world. So it can only be expected that Plight will be out nobling us, and probably for quite a while.
 

DeletedUser

Guest
You were outnobling them prior to the war on a constant basis :icon_wink:.
 

DeletedUser

Guest
Of course. We were in the process of preparing for a war. Eating up as many of our inactives as we could, furthering our control on the rim, cleaning out solo players who had grown quite large in the core (Albatross for example). Now we are left with few targets who aren't LSHRV.

Also add on to the fact that our nukes are occupied with either A. Traveling to an LSHRV village, B. Returning from an LSHRV village, or C. Rebuilding after hitting an LSHRV village. We are using our offenses elsewhere using them on whatever remains as a target in our territory.
 

DeletedUser

Guest
I think neither of us is arguing the same point. In fact, I don't think we even disagreed anywhere :lol:.

Back on topic:

Much appreciated work MK. Always nice to see how the world is progressing on a statistic scale.
 

DeletedUser

Guest
No, we weren't arguing anything. You're too smart for that Orel. You know I'd win :icon_wink:

Rather, we were discussing how Plight was playing a rather leading role in this larger increase in power concentration despite the fact that they are rank 2, rather than C2 which is rank 1.
 

DeletedUser

Guest
So yeah...Plight is playing a leading role.

All done :lol:.

And I don't necessarily think you'd win, but I think that after gaining a bit of maturity on my part we're unlikely to ever directly disagree on anything, given similar reasoning and both of us knowing what arguments to avoid.
 

MichielK

Guest
Jurasu said:
Finally decided to stop being lazy and give us a project, eh? :lol:

Thanks for this MK. As always, was very interesting to read. You did worry me for a minute when I saw Plight had more than twice our conquers before I read the part about conquers between LSHRV and C2 against each other didn't count.
Click to expand...

That's not what I said. Let me reprhase:

If C² takes a LSHRV village, that's +1 for C² and -1 for LSHRV, creating a net result for the top 4 of zero. It does not mean it's not being counted at all.

The gap in conquers between Plight and the rest of the world does exist. The only factor that artificially inflates this gap is the fact that Plight moves inactives to Ni before/during eating, while tribes like C² and BANG keep them within the tribe. This means that if Plight eats a (Ni) inactive, it counts as +1, while for C² and BANG it counts as zero (+1 - 1).

This policy increases Plight's net nobling rate by about 40-50 villages a week. Even after subtracting those, there's still a serious gap. After all, Plight has more and easier targets than the rest of the top 4...the stats should reflect that.
 

DeletedUser

Guest
I disagree:

Side 1:
Tribes: Plight
Players:

Side 2:
Tribes: Ni!
Players:

Timeframe: Forever

Total conquers against opposite side:

Side 1: 62
Side 2: 24
Difference: 38

image.php


Points value of total conquers against opposite side:

Side 1: 604,047
Side 2: 224,483
Difference: 379,564

image.php



Plight has rarely nobled Ni! villages, so how can you say this boosts their stats?
 
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