Dice roll statistics

Because math is fun, I decided to make a full statistical analysis of the dice roll system...

I'm going to roll several times, and see how many of the numbers are immense triumphs, Pyrrhic victories, stalemates or failures.

For obvious reasons, this does not account for modifiers (advantages, disadvantages, etc.) The results are shown as four numbers, with the first being number of immense triumphs, second being number of Pyrrhic victories, and so on.

Test #1: 1, 2, 5, 2

Test #2: 2, 2, 2, 4

Test #3: 4, 3, 0, 3

Test #4: 2, 5, 1, 2

Test #5: 3, 3, 2, 2

Test #6: 0, 4, 3, 3

Test #7: 3, 4, 1, 2

Test #8: 2, 2, 1, 5

Test #9: 1, 4, 2, 3

Test #10: 4, 2, 2, 2

Test #11: 4, 1, 2, 3

Test #12: 1, 2, 1, 6 (oof)

Test #13: 1, 2, 5, 2

Test #14: 3, 1, 4, 2

Test #15: 4, 3, 2, 1 (nice)

Test #16: 4, 4, 1, 1 (also nice)

Test #17: 2, 3, 2, 3

Test #18: 2, 0, 6, 2

Test #19: 2, 3, 2, 3

Test #20: 1, 2, 5, 1

Test #21: 2, 4, 3, 1

Test #22: 2, 4, 3, 1

Test #23: 1, 5, 1, 3

Test #24: 3, 4, 2, 1

Test #25: 1, 8, 1, 0

Alright, now that we're done testing, let's take a look at the data.

55 total Immense Triumphs

77 total Pyrrhic Victories

59 total Stalemates

55 total Failures

To calculate averages, I'll divide each of these by 25.

Average Immense Triumphs: 2.2

Average Pyrrhic Victories: 3.08

Average Stalemates: 2.36

Average Failures: 2.2

Of course, this is just an average number, and we'll see some exceptions; for instance, in the trials we saw a set of 1, 8, 1, 0, which is, of course, an outlier in the data set.

Now, for a graph:

Number of Immense Triumphs in 10 rolls

And more statistical data that certainly is not necessary, but I just like math:

Average Immense Triumphs: 2.2

Median Immense Triumphs: 2

Standard Deviation of Immense Triumphs: 1.19 (rounded)

Part 2: Total Dice Roll Values

1. 138
2. 140
3. 128
4. 124
5. 99
6. 109
7. 76
8. 122
9. 115
10. 97
11. 68
12. 79
13. 98
14. 155
15. 84
16. 90
17. 130
18. 70
19. 88
20. 141
21. 102
22. 110
23. 114
24. 83
25. 108

Now I'll calculate the average total dice roll and average roll for a single die:

Average total roll for ten dice: 106.72

Average roll for one die: 11 (10.672 rounded)

This reveals that the average roll, according to this data set, would be considered a Pyrrhic Victory.

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Conclusions:

Why do we need this data?

We don't. I just like statistics, and when I noticed stuff about the probability of getting a certain number of rolls over 10, I just randomly felt like putting together a statistical report about the dice roll system. Use this data to prove whatever point you want, but please don't turn this into an entire argument in the replies. I just did this because I like math.

The math was fun, but you know what wasn't? Putting this together on mobile... and having to recalculate everything when I somehow managed to FORGET ABOUT TEST 18. Like, I didn't even do one, and then I was putting it into a graphing software which told me that I had to have the same number of x and y values, and then I looked back and THERE WAS NO EIGHTEENTH TEST and then I had to do it and recalculate my averages.

Disclaimer: I used a calculator for some of it (I'm not taking credit for solving the average total value myself)...