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general:luck_stats [2013/08/27 23:04] M57 |
general:luck_stats [2017/11/05 10:36] M57 [How Unlucky Is a Luck Stat of -3?] |
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Interpreting Luck Stats requires similar context, but instead of time-frame, you need to know the number of battles fought, and unfortunately, | Interpreting Luck Stats requires similar context, but instead of time-frame, you need to know the number of battles fought, and unfortunately, | ||
+ | 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. | ||
- | Dice probabilities have central tendencies, and WarGear Luck Stats have a central tendency of 0. In theory, the most common luck stat should be 0. | + | In theory, the most common |
- | However, the more rolls made, the more ' | + | Even though there is more ' |
- | * //To balance this effect, it would be necessary to divide the luck stat by the square root of the sum of variances< | + | * //To balance this effect, it would be necessary to divide the luck stat by the square root of the sum of variances< |
==== How " | ==== How " | ||
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 " | + | **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 " |
**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 | + | Given the same number of opportunities, |
- | **Case 3** - Yet, if you were to win that stack of 48 (from Case 2), ending | + | **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' |
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 " | 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 " | ||
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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 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 above examples | + | //(The probabilities given for the " |
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