Regarding balance -

[Dicke Bertha]

...
[Regarding balance ... we currently calculate a balance for each scenario that has results in WARS. Of course, the more reports, the more accurate this "balance" figure. However, most scenarios have so few reports that the balance figure really can't be considered statistically significant. Ideally, we would factor in balance, but I can't think of a legitimate way to do so. Maybe if WARS has more than say 10 reports for a scenario we would then adjust the battle points in some way by the balance but even that would be iffy.]


:whist: Guess what, it's me again. :cheeky:

Sorry for drifting off course a little:

On the balance thing; I checked some scenarios of interest on the WARS. I wonder how the balance attributes are set; look at one example:

Slightly SOVIET (11 reports)

18% (2) - SOVIET Overwhelming Victory
9% (1) - SOVIET Substantial Victory
18% (2) - SOVIET Marginal Victory
36% (4) - Draw
18% (2) - AXIS Marginal Victory

Comparing the apples with apples I find a 1:1 ratio between marginal victories. Then the same total amount of draws, (ratio there within 1:1:1) then 150% more Soviet substantial or overwhelming wins than either of Soviet or German wins, or draws, and indeed of those 150%, 67% are overwhelming. Yet, the scenario is slightly unbalanced in Soviet favour? (I find 'slightly' slighty underestimating).

Qué? :crosseye: You know us schmucks can ask a hundred questions more, than you wise may be able to answer! :D

Edit: maybe I should add for clarity; I view a draw as a zero; thus I see the Soviets winning (all three categories) 5:2 over the Germans. That is a 250% factor. Draw is not a player, only the Germans and the Soviets are... ?

[CyberRanger]

Raw Norm Games
+3 +1.00 2 2.00
+2 +0.67 1 0.67
+1 +0.33 2 0.67
+0 +0.00 4 0.00
-1 -0.33 2 -0.67
-2 -0.67 0 0.00
-3 -1.00 0 0.00
11 2.67 Score - > 2.67/11=0.24
Slightly Side 1



With:

Strongly >= .34
Slightly >= .1 < .34 Slightly
< .1 Balanced

Draws are very important. Ideally, in a well balanced scenario, equally skilled players should get a draw. Need to hit the sack .. more explanation tomorrow. Note that in the example above, two more side 1 OV's will move the rating to "strongly".

[Dicke Bertha]

It doesn't look that unlogical... :) Since I haven't looked into numerical analysis or math-stat in a long time, erm :o , could you just explain how the deviation value ranges (0-0,1), (0,1-0,34) and (0,34-1) were chosen... Thanks!

[Reepicheep]

We did a bit of statistical analysis and tried a number of different figures when we came up with the ranges to which to apply the different victory levels tags to. Remember that we're using W.A.R.S. for a number of different game systems, so we had to consider the fact that different games have different possible outcomes we need to take into account.

On a three outcomes game (Side 1 wins, Draw, Side 2 wins), the levels we chose equate to outcomes for Side 1 of:

>= 0.34 equates to Side 1 winning 67%+ of the time
>= 0.10 < 0.34 equates to Side 1 winning between 55% to 66% of the time
< 0.1 equates to Side 1 winning less than 55% of the time.

After some discussion, intuitively these values felt right to us. If one side can win 2/3 of the time, the scenario is pretty strongly in their favor. 55-65% is a definite edge to one side, but it's only slightly favouring them. Anything from 50-55% is showing a scenario that's pretty balanced to all intents and purposes. Obviously they're still slightly arbitrary cutoff points, but a point does have to be drawn somewhere when interpreting the raw numerical data.

Another factor in consideration was the impact on games like TOAW which have as many as three different levels of victory. If just one game was recorded which results in a "marginal victory" (the lowest of the three victory levels), the result will come out at 0.33 which equates to a "slightly" rating. If the 0.34 cut off for "strongly" were set any lower, it would produce the unusual result of a single "marginal victory" report rating the scenario as "strongly" favoring that side! Setting it at 0.34 requires at least one "substanital" or "overwhelming" victory to occur to merit that scenario being given the "strongly" rating.

Hope this helps explain some of the factors that went into our decision.

[Dicke Bertha]

Thanks Reepicheep, this is interesting. So I understand the ranges are "arbitrarily" set (albeit well thought-out) and not specifically according to some statistical formula. And also the WARS system does not allow for additional "levels" of balance.(?)

Otherwise, for the WARS TOAW, maybe having "levels" of balance; Overwhelmingly, Substantially, Marginally unbalanced... according to the game victory principle would allow for greater "accuracy" and intuitive feel? I guess I'll need to look at how TOAW decides the various victory/loss levels, is it static/linear (always a fixed relation of total points) or dynamic/designer set (I suppose the former, given the existance of The Victory Calculator Add-on program). I will look at some more scenario balance reports and experiment a little with the equations.

Thanks again! :clap:

[CyberRanger]

In TOAW, the victory levels are based on a set equation. The point to remember is that WARS supports multiple games that each have different levels of victory. The "balance" is a way to try to give a simple (althought admittedly subjective) measure of which side one would expect to win a contest.

Because the "balance" is subjective, we made a point to maintain much more detailed %'s showing the exact breakdown of game reports for each scenario. Each player can use these as he wishes to determine how balanced he feels a scenario is.