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general:luck_stats [2013/08/30 08:46]
M57 [The Most Common Luck Stat Fallacy] 		general:luck_stats [2022/09/15 01:05] (current)
Ozyman [Relevant forum threads]
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 In theory, the most common WarGear luck stat should be 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 sum 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.+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<sup>2</sup> 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, but this is a subject best saved for a separate wiki.//+  * //To balance this effect, it would be necessary to divide the luck stat by the square root of the sum of variances<sup>2</sup> 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, [[General Features:Improved Luck Stats|a proposed WarGear feature]].//
 ==== How "Unlucky" Is a Luck Stat of -3?  ==== ==== How "Unlucky" Is a Luck Stat of -3?  ====
  
 Consider the following cases: 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 -2.76, and most players would agree that you were pretty "unlucky."+**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. **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 enough opportunities, both of these 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.+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), ending 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 very unlucky at all - and you would be right. +**Case 3** - If you were to win that stack of 48 (from Case 2), and ended up with 18 units to spare, you probably wouldn't blink. You might even be tempted to think you had better than average luck. Yet, your Luck stat would be -3 and fall right in the middle of the 15-21 bin of the histogram below.
-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. +
  
 {{ :general:60_v_48_binned.png |}} {{ :general:60_v_48_binned.png |}}
  
-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 above histogram suggests that you will win and end up with between 15 and 28 (Luck Stats from -6 to +7) units more than 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 considered as being anything other than pretty average luck.
  
-//(The probabilities given for the above examples were extracted from various (and typical) samples of 20,000 simulations each using Ozyman's WarGear Simulator.+//(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.
 // //
  
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   * http://www.wargear.net/forum/showthread/2173/Luck_Cumulative_Chart_Wargear_Warfare_1_v_1_games_SquintGnome   * http://www.wargear.net/forum/showthread/2173/Luck_Cumulative_Chart_Wargear_Warfare_1_v_1_games_SquintGnome
   * http://www.wargear.net/forum/showthread/3055p1/How_unlucky   * http://www.wargear.net/forum/showthread/3055p1/How_unlucky
 +  * https://www.wargear.net/forum/showthread/167p1/Ive_seen_enoughthe_RandomLuck_Talk
 +  * https://www.wargear.net/forum/showthread/1324p1/Bad_dice_support_group
 +  * https://www.wargear.net/forum/showthread/3413/Luck_in_Risk
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general/luck_stats.1377866765.txt.gz · Last modified: 2013/10/26 09:33 (external edit)

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