I must confess when I read through the dice mechanics of the Ricochet System I got an immediate WTF reaction. It seemed to be a little too clever for it’s own good.
Thus I decided to analyze it statistically. Here is what I got.
Dice Average Variance
1 3.500 1.708
2 5.028 2.048
3 6.296 2.552
4 7.522 3.055
5 8.751 3.477
6 9.975 3.819
7 11.180 4.108
8 12.360 4.370
9 13.513 21.379
10 14.645 23.799
11 15.752 26.341
The Dice column is the number of dice in the dice pool.
The Average column average total you will get from each roll.
The Variance column is the standard deviation of the entire population of totals. Note that the totals are not normally distributed.
Now when you look at the average column you see that is slowly increases in a relatively linear fashion.
Now look at the variance column. It increases slowly as well, but note how it suddenly jumps between 8 and 9 dice. This isn’t a mistake; it is a symptom of the bizarreness of the mechanic.
At 9 dice the system breaks down; by which I mean the random element begins to overwhelm everything else. This is okay when rolling against a difficulty number, but in combat when the difference is used to calculate damage it means that extra dice become irrelevant, and Damage Total becomes king!
I am not sure if this is desirable or not. It's just interesting...
Dice Mechanic Statistics and Analysis
I'm afraid I don't quite understand what you mean by "Variance." Would you mind explaining it to me in slightly simpler terms?
Since I don't quite understand your point, you might wish to take this reply with a grain of salt...
As it stands, it is not common for anyone to chug 9 dice. (In fact, the rules recommend a cap on combat related abilities at around 7 dice)
If by variance, you mean the difference between the lowest possible result and highest possible result (or some average thereof) you have to keep in mind the degree of luck only goes UPWARDS, not down. Once you reach 10 dice, you are never going to roll lower than 6, but it opens up the possibility of incredible totals of 24 or even 36.
Yeah, that's quite a gap, but that's the power of having such an incredible number of dice at your disposal...the power to be absurdly heroic. But even with 10 dice, that's not going to happen OFTEN. As excessive Damage Total successes if we had a FAIR fight, the opponent would have a similar number of Defense dice, which can easily nullify the incredible Damage Total results.
Since I don't quite understand your point, you might wish to take this reply with a grain of salt...
As it stands, it is not common for anyone to chug 9 dice. (In fact, the rules recommend a cap on combat related abilities at around 7 dice)
If by variance, you mean the difference between the lowest possible result and highest possible result (or some average thereof) you have to keep in mind the degree of luck only goes UPWARDS, not down. Once you reach 10 dice, you are never going to roll lower than 6, but it opens up the possibility of incredible totals of 24 or even 36.
Yeah, that's quite a gap, but that's the power of having such an incredible number of dice at your disposal...the power to be absurdly heroic. But even with 10 dice, that's not going to happen OFTEN. As excessive Damage Total successes if we had a FAIR fight, the opponent would have a similar number of Defense dice, which can easily nullify the incredible Damage Total results.
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BrenMan
Variance
Variance is a statistic term which measures how distributed a population is. Here is a link that will explain it a little more:
http://davidmlane.com/hyperstat/A16252.html
http://davidmlane.com/hyperstat/A16252.html
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Brenman
FYI, assuming I am reading the rules correctly, in a ten dice pool:-
The highest possible result is 60 (all ten dice roll a 6).
The lowest possible result is always 2. (all dice roll a 1 except for a single dice that gets a 2). This naturally assumes that the "Automatic failure" of all dice rolling 1 isn't counted as a number.
The point I am trying to make is that, by design or accident, there is strong statistic evidence to claim that the main core dice mechanic of the game breaks once you reach nine dice. The random factor becomes overwhelmingly dominant.
Since a company is using that mechanic as the central system for all its products they should be made aware of it.
There are several options available:
1: Embrace the fact as a feature of the system. It doesn't have to be a bad thing.
2: Introduce ability stacking rules (similar to d20s bonus stacking rules DMG p21) in order to keep dice pools small. Personally I believe some guidelines would be appropriate anyway.
3: Change the dice mechanic.
4: Adjust the current one to alleviate the worst of the wackiness. A simple house rule of you can never add more than 4 dice together may do the trick.
The highest possible result is 60 (all ten dice roll a 6).
The lowest possible result is always 2. (all dice roll a 1 except for a single dice that gets a 2). This naturally assumes that the "Automatic failure" of all dice rolling 1 isn't counted as a number.
The point I am trying to make is that, by design or accident, there is strong statistic evidence to claim that the main core dice mechanic of the game breaks once you reach nine dice. The random factor becomes overwhelmingly dominant.
Since a company is using that mechanic as the central system for all its products they should be made aware of it.
There are several options available:
1: Embrace the fact as a feature of the system. It doesn't have to be a bad thing.
2: Introduce ability stacking rules (similar to d20s bonus stacking rules DMG p21) in order to keep dice pools small. Personally I believe some guidelines would be appropriate anyway.
3: Change the dice mechanic.
4: Adjust the current one to alleviate the worst of the wackiness. A simple house rule of you can never add more than 4 dice together may do the trick.
I see your point, but the odds of rolling all ones or all sixes with 10 dice is so overwhelmingly bad that it doesn't seem worth considering. If you're lucky enough to roll ten 6s, then, by golly, you should have something to show for it. (IMHO)
I just don't see how it makes the mechanic "break" in any way. As you pointed out, the average goes up smoothly. To me, that's all that matters. Flukes of all ones or all sixes are not going to happen often, if ever, in any gamer's experience when rolling 10 dice.
Bear in mind I'm not trying to shut you out. I'm always glad when folks point out holes in the system. (Heck, it's been a long time since there's been any rule discussion at all here). After all, it can only make it better! I just don't think this is a problem. Maybe that means I chose choice 1? ^_^
And thanks for the chart. I've had difficulty making one of my own for use in similar discussions. It's nice to see one all the way to double digits.
I just don't see how it makes the mechanic "break" in any way. As you pointed out, the average goes up smoothly. To me, that's all that matters. Flukes of all ones or all sixes are not going to happen often, if ever, in any gamer's experience when rolling 10 dice.
Bear in mind I'm not trying to shut you out. I'm always glad when folks point out holes in the system. (Heck, it's been a long time since there's been any rule discussion at all here). After all, it can only make it better! I just don't think this is a problem. Maybe that means I chose choice 1? ^_^
And thanks for the chart. I've had difficulty making one of my own for use in similar discussions. It's nice to see one all the way to double digits.
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Brenman
Perhaps breaks is too harsh a word. The nature of the game does change at "epic" levels when the higher dice totals get more common. When two very powerful characters duke it out instead of getting a long slow fight you are more likely going to get a very quick and bloody one. This is because the dice totals will fluctuate wildly when more dice are involved.
For example if we increase sample character Raine's Defense, Agile, and Quick all to +4 and have our new "Epic Raine" fight her twin Brother Storm.
Epic Raine goes first and attacks with 10 dice attack power move "Raging Thunder slash". The dice roll total is 12. (In a ten dice pool you have a 31% chance of getting exactly a twelve, and you have a 51% chance of getting a 12 or less). Now the Power Move +2 with two lots of extra damage has a DT of 7. Both character have 50 Health, and Endurance of 60 (110 total). But Raine now has only 40 Endurance (due to her power move costing 20 Endurance) so any damage that exceeds 90 takes her out.
Now Storm knows the statistics so he decides: There is no reason for me to not counter attack with the own version of that power move. There is a 20% chance I will take 84 damage, which I can take, a 31% chance we will just parry, but of the remaining there is a 14% chance of getting a 15 (for 105 damage), a 15% chance of getting a 18 (for 126 damage) and a 6% chance of getting 24 (for 166 damage) and a 2% chance of getting a 30 (for 210 damage).
If the duelists fight more conservatively a combat will go more slowly, since the average hit will do either 12, 20, or 24 damage per blow.
For example if we increase sample character Raine's Defense, Agile, and Quick all to +4 and have our new "Epic Raine" fight her twin Brother Storm.
Epic Raine goes first and attacks with 10 dice attack power move "Raging Thunder slash". The dice roll total is 12. (In a ten dice pool you have a 31% chance of getting exactly a twelve, and you have a 51% chance of getting a 12 or less). Now the Power Move +2 with two lots of extra damage has a DT of 7. Both character have 50 Health, and Endurance of 60 (110 total). But Raine now has only 40 Endurance (due to her power move costing 20 Endurance) so any damage that exceeds 90 takes her out.
Now Storm knows the statistics so he decides: There is no reason for me to not counter attack with the own version of that power move. There is a 20% chance I will take 84 damage, which I can take, a 31% chance we will just parry, but of the remaining there is a 14% chance of getting a 15 (for 105 damage), a 15% chance of getting a 18 (for 126 damage) and a 6% chance of getting 24 (for 166 damage) and a 2% chance of getting a 30 (for 210 damage).
If the duelists fight more conservatively a combat will go more slowly, since the average hit will do either 12, 20, or 24 damage per blow.
Of course, such super characters will likely have improved Health and Endurance totals, too. I do see the damage getting quite up there. Counter is a powerful move though, and there's a lot of risk. 20% for near instant death is a fairly big deal, and with a 50% of no effect, losing your next action is nothing to sneeze at either.
I did have concerns Counter could be abused though, in certain matchups. In playtest games it always seemed to work fine, but it always nagged at me, nonetheless.
I did have concerns Counter could be abused though, in certain matchups. In playtest games it always seemed to work fine, but it always nagged at me, nonetheless.
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Brenman
Agreed, but the increase of Tough/Vitality would be offset by the increase of Power Moves.
I really like the Countering rule. It allows you to capitalise on a poor attack roll of an opponent "aha my opponent has overextended himself giving me an opening" but at a risk "Damn he was only feinting...".
I really like the Countering rule. It allows you to capitalise on a poor attack roll of an opponent "aha my opponent has overextended himself giving me an opening" but at a risk "Damn he was only feinting...".
It reminds me of console RPGs...you go from 200 to 2000 HP and monsters can STILL throttle you in one hit...
And yeah, that was the exact idea for countering. Anime is all about these power struggles (competing energy blasts, dueling of swords), as well as capitalizing on poor moves and all out misses.
I'm glad you like it though. OVA does a lot of surprising things, so it's always on my mind that one facet or another may not hit it off with everyone.
But hey, for every shared Health/Endurance pool people don't like, there's a countering rule they do, hmm? ^_~
And yeah, that was the exact idea for countering. Anime is all about these power struggles (competing energy blasts, dueling of swords), as well as capitalizing on poor moves and all out misses.
I'm glad you like it though. OVA does a lot of surprising things, so it's always on my mind that one facet or another may not hit it off with everyone.
But hey, for every shared Health/Endurance pool people don't like, there's a countering rule they do, hmm? ^_~
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Joe_Mello
- Exalted Amphibian
- Posts: 196
- Joined: Tue Jun 21, 2005 2:50 pm
- Location: Here and There, Now and Then
By the way, being a math major in college, I have to be pedantic and point out that Variance and Standard Deviation are two different things and St Dev is much more widely preferred than Variance
Joe_Mello: Could you make a common sense roll, please, Ryu?
Ryushikaze: With Smart?
Joe_Mello: Sure
*Ryushikaze rolls*
Joe_Mello: SHE'S DEAD!
Ryushikaze: With Smart?
Joe_Mello: Sure
*Ryushikaze rolls*
Joe_Mello: SHE'S DEAD!
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madScientist
Re: Dice Mechanic Statistics and Analysis
System is correct.
BrenMan has replaced (by mistake, I
suppose) standard deviation with
variance for dices 9-11.
Dice Num_of_possible_results Mean Variance Standard_deviation
1 6 min=1 mean=3.50 var=3.50 stdDev=1.87
2 36 min=2 mean=5.06 var=4.11 stdDev=2.03
3 2.2e+002 min=2 mean=6.31 var=6.46 stdDev=2.54
4 1.3e+003 min=3 mean=7.53 var=9.28 stdDev=3.05
5 7.8e+003 min=3 mean=8.75 var=12.06 stdDev=3.47
6 4.7e+004 min=4 mean=9.98 var=14.57 stdDev=3.82
7 2.8e+005 min=4 mean=11.18 var=16.86 stdDev=4.11
8 1.7e+006 min=4 mean=12.36 var=19.08 stdDev=4.37
9 1e+007 min=5 mean=13.51 var=21.37 stdDev=4.62
10 6e+007 min=5 mean=14.65 var=23.79 stdDev=4.88
11 3.6e+008 min=6 mean=15.76 var=26.33 stdDev=5.13
12 2.2e+009 min=6 mean=16.87 var=28.94 stdDev=5.38
13 1.3e+010 min=6 mean=17.97 var=31.56 stdDev=5.62
14 7.8e+010 min=6 mean=19.07 var=34.16 stdDev=5.84
15 4.7e+011 min=7 mean=20.16 var=36.74 stdDev=6.06
16 2.8e+012 min=8 mean=21.24 var=39.31 stdDev=6.27
17 1.7e+013 min=8 mean=22.32 var=41.89 stdDev=6.47
18 1e+014 min=8 mean=23.39 var=44.49 stdDev=6.67
19 6.1e+014 min=9 mean=24.46 var=47.13 stdDev=6.87
20 3.7e+015 min=9 mean=25.52 var=49.82 stdDev=7.06
21 2.2e+016 min=10 mean=26.58 var=52.55 stdDev=7.25
22 1.3e+017 min=10 mean=27.63 var=55.31 stdDev=7.44
23 7.9e+017 min=10 mean=28.69 var=58.11 stdDev=7.62
24 4.7e+018 min=11 mean=29.73 var=60.93 stdDev=7.81
25 2.8e+019 min=12 mean=30.78 var=63.77 stdDev=7.99
26 1.7e+020 min=12 mean=31.83 var=66.62 stdDev=8.16
27 1e+021 min=12 mean=32.87 var=69.48 stdDev=8.34
28 6.1e+021 min=12 mean=33.91 var=72.35 stdDev=8.51
29 3.7e+022 min=12 mean=34.95 var=75.23 stdDev=8.67
30 2.2e+023 min=13 mean=35.99 var=78.12 stdDev=8.84
As you see: no "breakdown"
BrenMan has replaced (by mistake, I
suppose) standard deviation with
variance for dices 9-11.
Dice Num_of_possible_results Mean Variance Standard_deviation
1 6 min=1 mean=3.50 var=3.50 stdDev=1.87
2 36 min=2 mean=5.06 var=4.11 stdDev=2.03
3 2.2e+002 min=2 mean=6.31 var=6.46 stdDev=2.54
4 1.3e+003 min=3 mean=7.53 var=9.28 stdDev=3.05
5 7.8e+003 min=3 mean=8.75 var=12.06 stdDev=3.47
6 4.7e+004 min=4 mean=9.98 var=14.57 stdDev=3.82
7 2.8e+005 min=4 mean=11.18 var=16.86 stdDev=4.11
8 1.7e+006 min=4 mean=12.36 var=19.08 stdDev=4.37
9 1e+007 min=5 mean=13.51 var=21.37 stdDev=4.62
10 6e+007 min=5 mean=14.65 var=23.79 stdDev=4.88
11 3.6e+008 min=6 mean=15.76 var=26.33 stdDev=5.13
12 2.2e+009 min=6 mean=16.87 var=28.94 stdDev=5.38
13 1.3e+010 min=6 mean=17.97 var=31.56 stdDev=5.62
14 7.8e+010 min=6 mean=19.07 var=34.16 stdDev=5.84
15 4.7e+011 min=7 mean=20.16 var=36.74 stdDev=6.06
16 2.8e+012 min=8 mean=21.24 var=39.31 stdDev=6.27
17 1.7e+013 min=8 mean=22.32 var=41.89 stdDev=6.47
18 1e+014 min=8 mean=23.39 var=44.49 stdDev=6.67
19 6.1e+014 min=9 mean=24.46 var=47.13 stdDev=6.87
20 3.7e+015 min=9 mean=25.52 var=49.82 stdDev=7.06
21 2.2e+016 min=10 mean=26.58 var=52.55 stdDev=7.25
22 1.3e+017 min=10 mean=27.63 var=55.31 stdDev=7.44
23 7.9e+017 min=10 mean=28.69 var=58.11 stdDev=7.62
24 4.7e+018 min=11 mean=29.73 var=60.93 stdDev=7.81
25 2.8e+019 min=12 mean=30.78 var=63.77 stdDev=7.99
26 1.7e+020 min=12 mean=31.83 var=66.62 stdDev=8.16
27 1e+021 min=12 mean=32.87 var=69.48 stdDev=8.34
28 6.1e+021 min=12 mean=33.91 var=72.35 stdDev=8.51
29 3.7e+022 min=12 mean=34.95 var=75.23 stdDev=8.67
30 2.2e+023 min=13 mean=35.99 var=78.12 stdDev=8.84
As you see: no "breakdown"
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Tubercular Ox
- Shelled Plebeian
- Posts: 11
- Joined: Mon Mar 23, 2009 7:20 pm
I think my brain just gave a sigh of relief. Knowing that Flight +1 means I can gain altitude a statistically useful amount of time is invaluable.
I'm new, it's a small board, thread necromancy is hard to resist, but I'm trying. However IMO this belongs on the first page. Furthermore, someone in the thread needs to say the word probability for those of us who use the search function but can't remember the difference between that and statistics. I wish I could remember enough prob stat to actually contribute by writing out an expanded probability chart (more detailed than the one Clay put on the board elsewhere), but oh well.
Probability.
PS: I like the die mechanic. How often can you appropriately yell "Yahtzee!" in a role playing game?
I'm new, it's a small board, thread necromancy is hard to resist, but I'm trying. However IMO this belongs on the first page. Furthermore, someone in the thread needs to say the word probability for those of us who use the search function but can't remember the difference between that and statistics. I wish I could remember enough prob stat to actually contribute by writing out an expanded probability chart (more detailed than the one Clay put on the board elsewhere), but oh well.
Probability.
PS: I like the die mechanic. How often can you appropriately yell "Yahtzee!" in a role playing game?
Re: Dice Mechanic Statistics and Analysis
I am bringing this back because it's so useful to me. Now with handy graph:
And with Standard Deviation, if you're into that:
And with Standard Deviation, if you're into that: