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general:luck_stats

Clicking on the Luck Stats link on the Game View page of a game will bring up a page with dice distribution tables. Premium members additionally receive “Luck Stats”. Luck Stats are also available to Premium members on the Player page via a pop-out window via the link in the breadcrumb area. The Dice distribution tables should be self-explanatory. This wiki focuses on the “Luck Stats” feature.

A positive Luck Stat indicates that, statistically speaking, the player should have lost that amount of armies when attacking/defending; this person would be “lucky”. A negative value indicates the player would 'normally' have won that amount of armies when attacking/defending; this person would be “unlucky”.

*The number of attacking/defending dice, dice settings, and border modifiers are all considered in the luck calculation.*

There is an expected number of armies you should win (or lose) with “average rolling”. Luck stats tells you how many armies above (+) or below (-) this average you have after rolling. Consider the following table of the probabilities when both attack and defending dice are 6-sided.

Table of Expected Wins | Expected Wins |
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Dice | A-0 D-2 | A-0 D-1 | A-1 D-1 | A-1 D-0 | A-2 D-0 | Attacker |
---|---|---|---|---|---|---|

1 - 1 | 0.58 | 0.42 | 0.42 |
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1 - 2 | 0.75 | 0.26 | 0.26 |
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2 - 1 | 0.42 | 0.58 | 0.58 |
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2 - 2 | 0.45 | 0.32 | 0.23 | 0.78 |
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3 - 1 | 0.34 | 0.66 | 0.66 |
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3 - 2 | 0.293 | 0.336 | 0.372 | 1.08 |

Luck stats are calculated by finding the difference between what you '**expect**' to win and what you '**actually**' win. Examples (all with 3v2 dice)..

Let's say we roll once, winning 2 (and losing 0).

We **expected** to win 1.08 units, but we **actually** won 2 units.

(Actual) - (Expected) = 2 - 1.08 = +0.92 luck stat.

Roll 10 times, winning 9 and losing 11

We **expect** to win 1.08 x 10 = 10.8 units but we **actually** won 9 units.

(Actual) - (Expected) = 9 - 10.8 = -1.8 luck stat.

The total - or average of all luck is always 0. When one player is 'lucky' (neutral counts as a player), some other player must be 'unlucky.'

In each column the large number in bold is the total number of kills or deaths. The number in parentheses breaks it down by specifying how many of those deaths were from attacking and defending dice. In the above chart..

- M57 recorded 460 Kills, 266 of which were with attack dice and 194 with defending dice.
- M57 suffered 469 Deaths, 194 of which were with attack dice and 275 with defending dice.
- M57 ended up with a total luck stat of +0.13, +4.67 while using attack dice and -4.54 while using defending dice.
- Looking at the Total luck row, we can see that generally speaking, defending dice were 'luckier' than attack dice.

While the luck Stat number you have in a game may tell you how far your number of kills or deaths are from the expected average, it is incorrect to assume that a certain number always indicates how lucky your rolls are.

Luck Stats are cumulative; they simply add up. Interpreting them needs context. If you were told that a company made a $10,000 dollar profit, you would not have a good idea of how profitable that company really is until you found out about the time-frame involved. Is that $10,000 per day, per month, or per year ..or perhaps over the entire life-span of the company?

Interpreting Luck Stats requires similar context, but instead of time-frame, you need to know the number of battles fought, and unfortunately, unlike our company, comparing two luck stats is not just a simple matter of dividing them by their respective number of battles. Whereas most economic models would have companies making more money as time passes, dice probabilities have central tendencies, and WarGear Luck Stats have a central tendency of 0.

In theory, the most common WarGear luck stat should be 0. Even though there is more 'opportunity' for deviation from that central tendency (of 0) as more rolls are made, the sums of most samples (groups of rolls) will remain close to the central tendency. As a result, the value derived from dividing the Luck Stat by the number of battles will approach 0 as the number of battles increases.

*To balance this effect, it would be necessary to divide the luck stat by the square root of the sum of variances*^{2}from all battles, and then use tables to determine a Z-score and/or a standard deviation, and then perhaps from there determine a percentile score, a proposed WarGear feature.

Consider the following cases:

**Case 1** - If you were to roll 3v2 dice 3 times, losing all of your rolls for a total of 6 units lost, your Luck Stat would be -3.24, and most players would agree that you were pretty “unlucky.”

**Case 2** - If you were to attack a stack of 48 units with a stack of 60 and not be able to win (depleting your stack in the process), your Luck Stat would very likely fall somewhere between -19 and -22.

Given the same number of opportunities, both of the above events will happen about 4% of the time. Clearly, a Luck Stat of -3 can be just as *unlikely*, and therefore just as unlucky as Luck Stat of -21.

**Case 3** - Yet, if you were to win that stack of 48 (from Case 2), and end up with 18 units to spare and a luck stat of -3, you probably wouldn't blink. In fact, you probably wouldn't consider it unlucky at all - and you would be right.
Whereas after winning you are likely to end up with exactly 18 units ~3.7% of the time, you are only likely to end up with the “central tendency” of 21 units only ~4.1% of the time, and a good 30% of the time you will end up winning with somewhere between 18 and 25 units left over.

The above histogram suggests that you will win and end up with between 15 and 28 (Luck Stats from -6 to +7) units about half the time when attacking a stack of 48 units with a stack of 60 units. In fact, to end up with an overall Luck Stat of -3 in this type of battle scenario could hardly be seen as being anything other than pretty average luck.

*(The probabilities given for the “cases” used in this discussion were derived from various (and typical) samples of 20,000 simulations each using Ozyman's WarGear Simulator.
*

general/luck_stats.txt · Last modified: 2017/11/05 10:36 by M57