Temple of Elemental Evil: Cold rolls from the 20-sided? (5/1/2016)

2016-05-01-ToEE-c
After finishing our first adventure with the Dungeons and Dragons board game, Temple of Elemental Evil, we suspected the hero’s rolls were pretty cold.  Crediting our new session system, we can look back and run the numbers.  Few could be more geek than D&D and 20-sided die stats!

Methodology
We wanted to see how “hot” or “cold” the shooter is.  Median was chosen to better represent the temperature of the hero as exceptionally low and high numbers have little influence of the outcome.  The same method is applied to the roll after added bonuses.  This measures a hero’s individual ability overcomes poorer rolls with better bonuses.

Only one die was used for the entire game and it was the one that came with the game box.  Samples did not include trap disarming or encounter rolls.

Uniformly distributed
Natural rolls: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20
Median: 10.5

If the random generator of the gods were perfectly fair, over time you should expect an even number of outcomes with every possibility.  A uniformly distributed median for natural rolls on a 20-sided die is 10.5.  If you did better than this, you should consider yourself lucky.

How did our heroes do?

Ratshadow
2 for 4, defeating 2
Natural rolls: 2,9,4,10
Bonus: 7,14,9,15
Natural rolls median: 6.5
Median with bonus: 10.5

Alaeros
3 for 4, defeating 2
Natural rolls: 8,10,14,1
Bonus: 18,20,24,6
Natural rolls median: 9.0
Median with bonus: 19

Nymmestra
6 for 8, defeating 6
Natural rolls: 18,9,1,9,16,4,18,10
Bonus: 23,14,6,14,7,9,23,15
Natural rolls median: 9.5
Median with bonus: 14.5

Barrowin
0 for 3, defeating 0
Natural rolls: 4,1,8
Bonus: 10,7,14
Natural rolls median: 4.0
Median with bonus: 10.0

Talon
4 for 4, defeating 4
Natural rolls: 16,10,20,9
Bonus: 24,18,26,6
Natural rolls median: 13.0
Median with bonus: 21.0

Party totals
15 for 23, defeating 14
Natural rolls average median: 9.0
Average median with bonus: 14.0

Group conclusion
As a party, the rolls were cold.  Ratshadow and Barrowin were ice cold while only Talon rolled lucky.  As a group, they benefited with a delta bonus of 5.  Barrowin had a difference of 6 and couldn’t hit once.  Alaeros, thanks to his bonuses, had a advantage of 10.  But it doesn’t help when you roll a “1”.   Nymmestra was the most engaging.  Having hit 6 of 8, she only had a natural roll median and bonus median 0.5 over both group medians, respectfully.

You may begin to ask, “What about the monsters?”  Read the following.

Monsters
7 out of 15
Natural rolls: 17,20,18,7,17,1,9,5,4,4,17,5,14,16,5
Bonus: 21,25,25,14,21,5,13,10,11,9,23,10,19,23,11
Natural rolls median: 9.0
Median with bonus: 14.0

Session conclusion
The monsters had equal luck with the rolls, including after bonuses kicked in.  The difference between the two is armor class.  Three of the five heroes had armor class above 14, putting them out of reach for many attacks.  While the rolls were cold, the rolls were most fair.
Links 404 over time.
Credit to:

http://www.alcula.com/calculators/statistics/median/

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