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Power Shift, a statistical analysis
https://www.swmgamers.com/forums/viewtopic.php?f=3&t=846		 Page 1 of 1
Author:  lt_murgen [ Wed Oct 17, 2007 1:26 pm ]
Post subject:  Power Shift, a statistical analysis
I’ve decided to take an objective look at power creep amongst the sets. By objective, I mean using the available numbers, and presenting them without any filtering. OK, well without significant filtering.

What I did was take a look at uniques and non-uniques by set. I divided their Hitpoint, attack value, and defense value by their cost. The results are summarized in the following charts:

A= Qty
B= Average Hit----points per point of cost
C= Standard Deviation of Hit----point per point of cost

Note- for those of you unfamiliar with statistics, a standard deviation is a way of explaining the spread of data based on a normal bell curve. One standard deviation on either side of the mean contains 66% of all values. Two standard deviations contain 95% of all values.

------------------non-unique------------------------uniques--------------
-------------A--------B-----------C------------A---------B-------------C----
[1] RS---------36-----2.433-----0.750---------24------3.070------0.815
[2] CS---------38-----2.401-----0.879---------22------3.078------0.626
[3] ROTS----35------1.994-----0.817---------25------2.922------0.693
[4]UNIV-------36-----2.461-----0.887---------24------2.619------0.836
[5] COTF----35------2.563-----1.172---------25------2.758------0.672
[6] BH---------35------2.178-----0.721--------25------2.243------0.470
[7] A&E-------37------2.348-----0.812--------23------2.807------1.023


Now, with these statistics, we can attempt a Z-test. A Z-test compares one mean to another, judging whether there is significant statistical variation between them. It is essentially the number of standard deviations you would have to take the population set out to encompass the sample set mean.

For non-uniques:
From [1] to [2] = 0.17. Not statistically significant shift
From [2] to [3] = 2.05. Satistically significant shift
From [3] to [4] = 2.30. Statistically significant shift
From [4] to [5] = 0.41. Not statistically significant shift
From [5] to [6] = 1.64. Potentially significant shift
From [6] to [7] = 0.94. Potentially significant shift

For Uniques:
From [1] to [2] = 0.04. Not statistically significant shift
From [2] to [3] = 0.81. Potentially significant shift
From [3] to [4] = 1.38. Potentially significant shift
From [4] to [5] = 0.64. Not statistically significant shift
From [5] to [6] = 3.14. Statistically significant shift
From [6] to [7] = -2.42 Statisticallysignificant shift

From this, I can develop the following general ideas:

For non-uniques, the revenge of the sith set was an anomaly, with many pieces getting less hit points for their cost values than the previous sets. We could assume that they compensated during the next two sets. But for bounty hunters and Alliance and Empire, there appears to be another set of corrections.

For Uniques, we see a similar set of shifts. For revenge of the sith, the uniques got more hitpoints for their cost than previous sets did. There appears to be a deliberate correction for the next two sets. But bounty hunters represents a significant decrease, followed by another correction on Alliance and empire.

I’ll follow the same process for attack values and defense values as time permits.
Author:  Bail Ohmar [ Wed Oct 17, 2007 4:59 pm ]
Post subject: 
What formula did you use to include Marketing? :D

Seriously though, newer pieces must be either new characters that people want, be better than previous sets or boost characters from previous sets. Otherwise the sets would only appeal to the collectors and not the Gamers. You have to give the buyer a reason to buy your new product, and in CCG & CMG it's by making the new product better. The side-effect being that this gets translated as 'Power-Creep,' but I just see it as Marketing. 8)
Author:  Lord_Nihl [ Wed Oct 17, 2007 5:08 pm ]
Post subject: 
What does this help do?

We can identify which pieces should be used or not used.
Author:  lt_murgen [ Thu Oct 18, 2007 10:12 am ]
Post subject: 
Actually, all I was attempting to do is try to amalyze the shifts in hit-points per cost.

I found it interesting that the sets were changed one way with Revenge of the Sith, then countered in future sets.

I make no judgements whether this is a good or bad thing.
Author:  NickName [ Thu Oct 18, 2007 3:37 pm ]
Post subject: 
The downside of this kind of analysis is that cost isn't directly related to HP so it's hard to judge anything by it because if a set has a high proportion of SAs or other stats contributing to the cost in the set then that throws off the calculation of HP for the set.

It doesn't tell you much of anything about "powercreep". For example, a glass canon type figure registers as a lot lower in your calculation than a solid statistical figure with minimal offense at the same price. But which is more powerful? It could be either. Does a higher or lower number equal powercreep? There's no way to know.
Author:  exarkun_sithmaster [ Thu Oct 18, 2007 6:51 pm ]
Post subject: 
Sorry. Lt. you lost me a standard deivation. I was never very good at math in school. :( However it looks cool.
Author:  headache62 [ Thu Oct 18, 2007 8:06 pm ]
Post subject: 
I made a chart comparing the Points, HP, Def, Att, and Dam for each figure from each set - but I can't figure out how to get it into a jpg to post.

It really surprised me to see the results.
Author:  adder [ Sat Oct 20, 2007 9:35 pm ]
Post subject: 
headache62 wrote:
I made a chart comparing the Points, HP, Def, Att, and Dam for each figure from each set - but I can't figure out how to get it into a jpg to post.


You could take a screenshot and then crop it down, that's what I do
Author:  headache62 [ Sun Oct 21, 2007 12:47 pm ]
Post subject: 
Good Idea - Ive got the JPEG now, but I don't have a hosting site to post it. Anyone have any ideas?
Author:  NickName [ Sun Oct 21, 2007 7:50 pm ]
Post subject: 
free image hosting:

http://www.imageshack.us
Author:  punxnbutter [ Sun Oct 21, 2007 10:00 pm ]
Post subject: 
yea imageshack is the way to go; it's free and very easy to use
Author:  headache62 [ Mon Oct 22, 2007 7:10 pm ]
Post subject: 
Here it is:
Image


The most variation is in HP, with Huge Sets (BH, Universe) and Champions of the Force Leading the way.

The least variation is in Def.

Bear in mind, this does not take into account SAs that increase attack and damage like Opportunist.
Author:  headache62 [ Mon Oct 22, 2007 7:52 pm ]
Post subject: 
Agreed, but you can also learn a lot from the base stats - like A&E is almost a "reset" in terms of basic stats.

It will be interesting to see how FU stacks against the rest.

I would add FPs to it, but so many characters now have Renewal that the stats would not reflect Force accurately.
Author:  punxnbutter [ Mon Oct 22, 2007 7:52 pm ]
Post subject: 
Opportunist and mobile for tons of new figs is power creep
Author:  LoboStele [ Tue Oct 23, 2007 8:06 am ]
Post subject: 
But is it really power creep if those same figures with Opportunist and Mobile are balanced in other ways? I mean, sure, Han Scoundrel, Lord Vader, Lando Dashing Scoundrel all have a lot of attack power, but they each die pretty quick when they start getting hit. In contract, Vader JH or Vader Imperial Commander aren't as powerfully offensive, but they take a lot longer to kill.

Power creep/shift has to be looked at as a whole figure, not just how much damage they can do, or how much HP they have, in comparison to older pieces.

I think until someone in the community determines what the formula is for costing minis, we will never truly know whether we're seeing power creep or power shift. It's just so hard to tell. The graphs and statistics stuff is pretty cool though. ;)
Author:  lt_murgen [ Tue Oct 23, 2007 8:14 am ]
Post subject: 
True- SAs throw any statistical calculations into question.
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