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Absol197

Force Points per Force Rating; A Statistics Thread!

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Hey there, friends!  I’ve been working on this off and on for a bit, and I finally buckled down and got all the way to 10, so I wanted to share the mathematical fruit of my mystical labor!

So, oftentimes around here, we find ourselves discussing Force ratings, and in particular, Force points and how common they are.  Typically this is in relation to starting characters, with their Force ratings of 1, but sometimes, especially with masters of the spiritual arts, Force ratings can get rather high.  So, it behooves us to be able to talk precisely about the odds of certain things.  There’s no point in musing on hypothetical examples of play unless they actually have a chance of occurring, and humans (and togruta!) have a nasty habit of assuming the theoretical maximum is not-much-less-likely than the theoretical average.

And it’s with that in mind that I bring this thread to you!  I have calculated the entire range of probabilities for all Force ratings between 1 and 10, for both characters who draw from white pips, and those who draw from black.  I’m presenting them in two specific ways: first, the chance of rolling exactly the specified number of pips.  Secondly, the chance of rolling the specified number of pips or higher with a certain number of Force dice.  While the first chart will be more of use to academics, the second will likely be more use in play.  Determine how many pips you need to pull off the crazy Force stunt you’re attempting, run across to your Force rating, and that’ll give you the general odds that you’ll succeed (without the need of a Destiny Point, importantly).

But first!  I want to discuss something else, which is the average, or statistical mean, of Force points rolled for both Light- and Dark-siders.

 

Average Force Points

So, while the charts below give the odds of rolling a certain number of Force points on any one given roll, another useful metric is the average number of Force points over an arbitrarily high number of rolls.  And here is where the duality of Light and Dark coalesces.

If we take a single Force die and roll it twelve times, averages say it will generate us 16 pips: 8 white, and 8 black.  Yes, the white pips will be clumped together and the black ones spaced out, but the number of both are equal on the die.  This means that, whether you’re a Light-sider or a Dark-sider, your average result on a Force power check will be 2/3 times your Force rating.

So FR 1 = 2/3; FR 2 = 1-1/3; FR 3 = 2; and so on.

As a personal house-rule, I allow all Force users who are neither pressed for time or in any danger to perform any Force powers that don’t require an additional roll using the average number of pips.  Basically a “take 10” for the Force.  For regular skills you don’t generally roll Simple difficulty checks, so I establish that this level of Force use is considered “Simple.”  Of course, if they NEED to jump this building in a limited amount of time, there’s pressure to succeed, or blaster bolts winging by their face, or if they simply want to get more pips o they can activate those Strength upgrades and get the X-Wing out of the swamp, they have to roll as normal.

But now, let’s get into the best part of this thread: CHARTS!

 

Percent Chance for Specific Number of Pips – Light Side

Pips | FR 1 | FR 2 | FR 3 | FR 4 | FR 5 | FR 6 | FR 7 | FR 8 | FR 9 | FR 10 |

00 | 58.33 | 34.03 | 19.85 | 11.58 | 06.75 | 03.94 | 02.30 | 01.34 | 00.78 | 00.46 |

01 | 16.67 | 19.44 | 17.01 | 13.23 | 09.65 | 06.75 | 04.60 | 03.06 | 02.01 | 01.30 |

02 | 25.00 | 31.94 | 30.38 | 25.52 | 19.99 | 14.96 | 10.84 | 07.66 | 05.31 | 03.63 |

03 | 00.00 | 08.33 | 15.05 | 18.09 | 18.12 | 16.31 | 13.70 | 10.94 | 08.43 | 06.30 |

04 | 00.00 | 06.25 | 13.02 | 17.70 | 19.72 | 19.52 | 17.84 | 15.40 | 12.72 | 10.16 |

05 | 00.00 | 00.00 | 03.13 | 07.75 | 12.00 | 14.81 | 15.97 | 15.72 | 14.47 | 12.67 |

06 | 00.00 | 00.00 | 01.56 | 04.69 | 08.45 | 11.86 | 14.27 | 15.45 | 15.48 | 14.62 |

07 | 00.00 | 00.00 | 00.00 | 01.04 | 03.33 | 06.35 | 09.38 | 11.84 | 13.41 | 14.02 |

08 | 00.00 | 00.00 | 00.00 | 00.39 | 01.57 | 03.59 | 06.11 | 08.70 | 10.91 | 12.47 |

09 | 00.00 | 00.00 | 00.00 | 00.00 | 00.33 | 01.28 | 02.93 | 05.08 | 07.37 | 09.47 |

10 | 00.00 | 00.00 | 00.00 | 00.00 | 00.10 | 00.50 | 01.40 | 02.84 | 04.68 | 06.68 |

11 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.10 | 00.46 | 01.24 | 02.46 | 04.06 |

12 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.02 | 00.16 | 00.52 | 01.22 | 02.29 |

13 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.03 | 00.16 | 00.49 | 01.10 |

14 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.01 | 00.05 | 00.18 | 00.49 |

15 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.01 | 00.05 | 00.18 |

16 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.01 | 00.06 |

17 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.02 |

18 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

19 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

20 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

 

Percent Chance for Specific Number of Pips – Dark Side

Pips | FR 1 | FR 2 | FR 3 | FR 4 | FR 5 | FR 6 | FR 7 | FR 8 | FR 9 | FR 10 |

00 | 41.67 | 17.36 | 07.23 | 03.01 | 01.26 | 00.52 | 00.22 | 00.09 | 00.04 | 00.02 |

01 | 50.00 | 41.67 | 26.04 | 14.47 | 07.54 | 03.77 | 01.83 | 00.87 | 00.41 | 00.19 |

02 | 08.33 | 31.94 | 35.59 | 28.45 | 19.34 | 11.93 | 06.90 | 03.81 | 02.03 | 01.05 |

03 | 00.00 | 08.33 | 22.92 | 29.51 | 27.73 | 21.85 | 15.38 | 10.01 | 06.15 | 03.61 |

04 | 00.00 | 00.69 | 07.12 | 17.39 | 24.37 | 25.63 | 22.60 | 17.68 | 12.69 | 08.53 |

05 | 00.00 | 00.00 | 01.04 | 05.90 | 13.61 | 20.17 | 23.04 | 22.18 | 18.92 | 14.74 |

06 | 00.00 | 00.00 | 00.06 | 01.14 | 04.87 | 10.87 | 16.75 | 20.38 | 21.06 | 19.29 |

07 | 00.00 | 00.00 | 00.00 | 00.12 | 01.11 | 04.03 | 08.80 | 13.96 | 17.86 | 19.55 |

08 | 00.00 | 00.00 | 00.00 | 00.00 | 00.15 | 01.03 | 03.35 | 07.19 | 11.67 | 15.55 |

09 | 00.00 | 00.00 | 00.00 | 00.00 | 00.01 | 00.17 | 00.92 | 02.79 | 05.92 | 09.79 |

10 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.02 | 00.18 | 00.82 | 02.33 | 04.91 |

11 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.02 | 00.18 | 00.71 | 01.96 |

12 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.03 | 00.17 | 00.62 |

13 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.03 | 00.16 |

14 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.03 |

15 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

16 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

17 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

18 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

19 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

20 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

 

So, what do we get from these?  Well, first, we can note that, as Force rating increases, the chance for getting a maximum result drops precipitously.  Even for Light-siders, who are better at getting those bursts of inspiration, high-pip results occur less than 1% of the time.  Dark-siders have an especially hard time getting their maximum, or even a higher-than average, roll.

On the other hand, we can see that the Dark side lives up to its “quicker, easier” reputation.  Dark siders, once they get to Force rating 3, have a negligible chance of rolling no pips.  What’s more, their results cluster strongly around the average, meaning that they can trust that when they thrust their hand forward, they can have confidence in how much oomph! their Force push is going to have.  Light-siders, on the other hand, can have trouble maintaining their poise and center in stressful situations, leading to some inconsistencies in their abilities under strain.

Okay, next up is the chance for minimum pips.

 

Percent Chance for Minimum Number of Pips – Light Side

Pips | FR 1 | FR 2 | FR 3 | FR 4 | FR 5 | FR 6 | FR 7 | FR 8 | FR 9 | FR 10 |

01+ | 41.67 | 65.97 | 80.15 | 88.42 | 93.25 | 96.06 | 97.70 | 98.66 | 99.22 | 99.54 |

02+ | 25.00 | 46.53 | 63.14 | 75.19 | 83.60 | 89.31 | 93.10 | 95.59 | 97.21 | 98.24 |

03+ | 00.00 | 14.58 | 32.75 | 49.67 | 63.61 | 74.35 | 82.27 | 87.93 | 91.89 | 94.61 |

04+ | 00.00 | 06.25 | 17.71 | 31.57 | 45.49 | 58.04 | 68.57 | 76.99 | 83.46 | 88.30 |

05+ | 00.00 | 00.00 | 04.69 | 13.87 | 25.77 | 38.52 | 50.73 | 61.59 | 70.74 | 78.15 |

06+ | 00.00 | 00.00 | 01.56 | 06.12 | 13.78 | 23.70 | 34.76 | 45.87 | 56.27 | 65.48 |

07+ | 00.00 | 00.00 | 00.00 | 01.43 | 05.32 | 11.84 | 20.49 | 30.43 | 40.79 | 50.86 |

08+ | 00.00 | 00.00 | 00.00 | 00.39 | 02.00 | 05.50 | 11.11 | 18.58 | 27.38 | 36.84 |

09+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.42 | 01.91 | 04.99 | 09.89 | 16.47 | 24.37 |

10+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.10 | 00.63 | 02.06 | 04.81 | 09.10 | 14.90 |

11+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.12 | 00.65 | 01.97 | 04.42 | 08.21 |

12+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.02 | 00.19 | 00.73 | 01.96 | 04.15 |

13+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.03 | 00.22 | 00.74 | 01.86 |

14+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.01 | 00.06 | 00.25 | 00.76 |

15+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.01 | 00.07 | 00.27 |

16+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.02 | 00.08 |

17+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.02 |

18+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

19+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

20+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

 

Percent Chance for Minimum Number of Pips – Dark Side

Pips | FR 1 | FR 2 | FR 3 | FR 4 | FR 5 | FR 6 | FR 7 | FR 8 | FR 9 | FR 10 |

01+ | 58.33 | 82.64 | 92.77 | 96.99 | 98.74 | 99.48 | 99.78 | 99.91 | 99.96 | 99.98 |

02+ | 08.33 | 40.97 | 66.72 | 82.52 | 91.21 | 95.71 | 97.95 | 99.04 | 99.55 | 99.79 |

03+ | 00.00 | 09.03 | 31.13 | 54.07 | 71.87 | 83.78 | 91.05 | 95.23 | 97.52 | 98.74 |

04+ | 00.00 | 00.69 | 08.22 | 24.55 | 44.14 | 61.93 | 75.67 | 85.22 | 91.37 | 95.13 |

05+ | 00.00 | 00.00 | 01.10 | 07.16 | 19.77 | 36.29 | 53.07 | 67.53 | 78.68 | 86.60 |

06+ | 00.00 | 00.00 | 00.06 | 01.26 | 06.15 | 16.12 | 30.03 | 45.35 | 59.76 | 71.86 |

07+ | 00.00 | 00.00 | 00.00 | 00.12 | 01.28 | 05.25 | 13.28 | 24.97 | 38.71 | 52.57 |

08+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.17 | 01.22 | 04.48 | 11.01 | 20.85 | 33.02 |

09+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.01 | 00.20 | 01.13 | 03.82 | 09.17 | 17.47 |

10+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.02 | 00.21 | 01.02 | 03.25 | 07.68 |

11+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.03 | 00.21 | 00.92 | 02.77 |

12+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.03 | 00.20 | 00.81 |

13+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.03 | 00.19 |

14+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.04 |

15+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.01 |

16+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

17+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

18+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

19+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

20+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

 

Okay, there we go!  Whew!  Lots of awesome charts :) !

So!  I hope these are helpful!  Any questions, comments, whatever?  Let me know!  I’m glad to help!

However, some of you may be wondering…what’s next for this thread?  Is it just a post with no real future?  No, of course not!  I was thinking we could use this space to discuss the ramifications, both mechanical, narrative, and in-universe, of this structure.  Also, I’ll be adding new charts occasionally.  The next one I’m working on is a “grey pip” chart, showing the chances of getting however many pips regardless of color, such as you might want if you’re okay with spending a Destiny Point, or if you’re using a house-rule that allows you to use both pip colors at the same time, for whatever reason.

Also, I stopped at 10 because that’s currently the highest Force rating a character who doesn’t go outside of their career can go.  A Consular with all 7 ranks of Force Rating in the Consular specs, and both Force-Sensitive specs, can get to a Force rating of 10.  I’m assuming that the Mystic will be able to get their, too, but we’ll have to wait and see on that :( …  But!  I find it very unlikely that there won’t be another Force-Sensitive universal in Dawn of Rebellion, and technically high-powered vergences (and the Bardottan Sphere) can increase one’s Force rating temporarily, so adding extra columns will eventually be a thing :) .  And if you want to help with the adding of extra columns, I can post the equation I used to calculate these for you.

But for now, I hope you all enjoy, and that you find this helpful in guiding both your discussions, character building, and tactics!

Edited by Absol197

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10 minutes ago, Shlambate said:

Well was this spawned from our conversation ages ago? Impressive... most Impressive.

A little bit.  I'd already calculated 1 through 5 by hand by the time we'd had that discussion, but getting above that required exponentially more work to do by hand, and I hadn't found the key that let me simplify it yet.  That key was factorials, like we were discussing in the Trends thread :) .  I've been slowly working my way up to ten for the past two weeks, simplifying my equation as I went and double- and triple-checking my work to make sure it's accurate.

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@Absol197 have you got that as a spreadsheet- I’d like to work out the difference between each rating (I could obviously do this by hand, but that’s a ton a great data) - so it’s possible to see the improvement you are going to get by buying the next FP quickly (and don’t want to ask you to do it)

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11 minutes ago, Random Bystander said:

@Absol197 have you got that as a spreadsheet- I’d like to work out the difference between each rating (I could obviously do this by hand, but that’s a ton a great data) - so it’s possible to see the improvement you are going to get by buying the next FP quickly (and don’t want to ask you to do it)

Hmm...I do have it in a spreadsheet, but not one I can easily get online.  I can't upload it from where it's at...

But if you're basically just wanting the change in value, that's not too hard.  Did you want it for the specific pips, minimum pips, or both?  If both, which would you want first?  I can whack up some ugly charts, then correct them a little later. 

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10 minutes ago, GroggyGolem said:

I'm just curious why there's an entry for rolling 0 pips on a Force Die when there's no blank sides.

Because if you're only drawing from Light Side pips, if you roll all black you've rolled 0 pips of your color :) .  Sure, you can spend a Destiny Point, some strain, and take Conflict to use those black pips, but you might not be able/might not want/can't afford to do so.  These tables are measuring no-cost pips only.  That's why they're split between Light- and Dark-side tables.  If i was just counting pips, that wouldn't matter. 

As I said, a third set of tables is coming for all pips regardless of color. 

Edited by Absol197

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23 minutes ago, Absol197 said:

Hmm...I do have it in a spreadsheet, but not one I can easily get online.  I can't upload it from where it's at...

But if you're basically just wanting the change in value, that's not too hard.  Did you want it for the specific pips, minimum pips, or both?  If both, which would you want first?  I can whack up some ugly charts, then correct them a little later. 

If you don’t mind it would rock - it’s more for the second set of charts so it’s easy to see if someone goes up a FP the expected improvement they can get

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14 minutes ago, Random Bystander said:

If you don’t mind it would rock - it’s more for the second set of charts so it’s easy to see if someone goes up a FP the expected improvement they can get

Sure thing!  It's not that complex.  I'll run the calc and post some (really ugly) charts soon, and then I'll make 'em pretty tonight :) .

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You ask, I deliver!

EDIT:  And I've fixed the formatting, so now it looks nice(r)!

 

Increased Chance for Minimum Pips at New Force Rating – Light Side

Pips | FR 2 | FR 3 | FR 4 | FR 5 | FR 6 | FR 7 | FR 8 | FR 9 | FR 10 |

01+ | 24.31 | 14.18 | 08.27 | 04.82 | 02.81 | 01.64 | 00.96 | 00.56 | 00.33 |

02+ | 21.53 | 16.61 | 12.05 | 08.41 | 05.71 | 03.80 | 02.49 | 01.61 | 01.03 |

03+ | 14.58 | 18.17 | 16.91 | 13.94 | 10.74 | 07.92 | 05.66 | 03.96 | 02.72 |

04+ | 06.25 | 11.46 | 13.86 | 13.92 | 12.55 | 10.54 | 08.42 | 06.48 | 04.84 |

05+ | 00.00 | 04.69 | 09.19 | 11.90 | 12.75 | 12.21 | 10.86 | 09.15 | 07.41 |

06+ | 00.00 | 01.56 | 04.56 | 07.66 | 09.93 | 11.05 | 11.12 | 10.40 | 09.21 |

07+ | 00.00 | 00.00 | 01.43 | 03.89 | 06.52 | 08.64 | 09.94 | 10.36 | 10.07 |

08+ | 00.00 | 00.00 | 00.39 | 01.61 | 03.50 | 05.61 | 07.48 | 08.80 | 09.46 |

09+ | 00.00 | 00.00 | 00.00 | 00.42 | 01.49 | 03.08 | 04.89 | 06.59 | 07.90 |

10+ | 00.00 | 00.00 | 00.00 | 00.10 | 00.53 | 01.43 | 02.75 | 04.29 | 05.80 |

11+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.12 | 00.53 | 01.32 | 02.45 | 03.79 |

12+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.02 | 00.17 | 00.54 | 01.22 | 02.20 |

13+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.03 | 00.18 | 00.53 | 01.12 |

14+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.01 | 00.05 | 00.20 | 00.51 |

15+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.01 | 00.06 | 00.20 |

16+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.02 | 00.07 |

17+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.02 |

18+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

19+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

20+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

 

Increased Chance for Minimum Pips at New Force Rating – Dark Side

Pips | FR 2 | FR 3 | FR 4 | FR 5 | FR 6 | FR 7 | FR 8 | FR 9 | FR 10 |

01+ | 24.31 | 10.13 | 04.22 | 01.76 | 00.73 | 00.31 | 00.13 | 00.05 | 00.02 |

02+ | 32.64 | 25.75 | 15.79 | 08.69 | 04.50 | 02.24 | 01.09 | 00.52 | 00.24 |

03+ | 09.03 | 22.11 | 22.93 | 17.80 | 11.91 | 07.27 | 04.18 | 02.29 | 01.22 |

04+ | 00.69 | 07.52 | 16.33 | 19.59 | 17.79 | 13.74 | 09.55 | 06.16 | 03.76 |

05+ | 00.00 | 01.10 | 06.06 | 12.60 | 16.53 | 16.77 | 14.47 | 11.15 | 07.92 |

06+ | 00.00 | 00.06 | 01.20 | 04.89 | 09.97 | 13.90 | 15.32 | 14.41 | 12.09 |

07+ | 00.00 | 00.00 | 00.12 | 01.16 | 03.98 | 08.02 | 11.69 | 13.74 | 13.86 |

08+ | 00.00 | 00.00 | 00.00 | 00.16 | 01.05 | 03.26 | 06.53 | 09.84 | 12.17 |

09+ | 00.00 | 00.00 | 00.00 | 00.01 | 00.18 | 00.93 | 02.69 | 05.36 | 08.30 |

10+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.02 | 00.19 | 00.82 | 02.23 | 04.43 |

11+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.03 | 00.18 | 00.71 | 01.86 |

12+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.03 | 00.17 | 00.61 |

13+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.03 | 00.16 |

14+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.03 |

15+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

16+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

17+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

18+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

19+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

20+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

 

Edited by Absol197

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It's possible I did by accident!  I'm not actually a trained mathematician, I just like numbers, and I play around with it until I get everything to work.

The basic formula I used is as follows, and you can tell me if I was using binomials to do it :) .

((((7A1*2B1*3C1)*(F!/(A1!*B1!*C1!))) + … + ((7AN*2BN*3CN)*(F!/(AN!*BN!*CN!))))/12F)*100

"F" is the Force rating I'm calculating, the variable that's not here, "P," is the current number of pips that I'm calculating for.  "A," "B," and "C" are the number of 0 results, 1 results, and 2 results needed for that particular sub factor so that A+B+C = F, and B+2C = P.  "N" is a variable related to how many combinations of A, B, and C are possible to satisfy the previous two rules.

 

EDIT:  Oh, this is specifically for the Light side charts.  The Dark side charts are:

((((5A1*6B1*1C1)*(F!/(A1!*B1!*C1!))) + … + ((5AN*6BN*1CN)*(F!/(AN!*BN!*CN!))))/12F)*100

I realize this is somewhat of a brute-force method, but I don't know enough math to do it any other way.

Edited by Absol197

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First thanks for all the efforts ;)

In our games we have a houserule for "really avanced force users" (not necessarelly Jedi but something near). We are aware that you can succumb to dark side and Flip a Destiny point to exchange pips (paying also strain cost and earning Conflict? Not sure) but we still created something to empower a bit force using characters.

Force Focus/Mastery/Insert cool name here XD (Incidental, Out of turn): Let you exchange FP (LS ↔ DS) paying 1 Strain per pip limited by Ranks on Discipline.

In movies or TV Shows high skilled Force users doesn't seem to fail checks (just when confronting another one) and apparently without falling to the Dark Side. Some scenes we watch can be explained as a "cinematic moment" or a "really lucky roll", but when it happens so usually we considered to create this option (not Talent) as one possible idea. Maybe you can consider a 3+ FR or just a "scenic Master grade" of Force Domain, not sure, but seems to work pretty fine.

It's a really overpowered option in general cases, but for high level games and characters like the ones on my games (More than 2600XP) is not so powerful as it seems.

 

Edited by Josep Maria

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This is what is referred to as a Multinomial distribution. When rolling the dice you have your three outcomes: 0, 1, and 2, each with their own probability. This is a special case of a multinomial distribution though because your results are fungible. What I mean by that is when you roll 2 dice, an outcome of 2 on one of the dice produces equivalent results to rolling a 1 on both of the dice. Because of this property, it may be easier to do future calculations of this as the sum of two binomial distributions, which is just a multinomial distribution with only 2 outcomes. The two binomial distributions could be set up a couple ways, but the most intuitive would probably be: Did I roll a 1 or not, and did I roll a 2 or not on any specific die. So your two binomials have potential results of (1,0) and (2,0). The probability of having K results/success (that side is up) in N trials (number of dice) for any binomial is n!/[(n-k)!*k!]*p^k*(1-p)^n-k. This first term involving the factorials is referred to as "n choose k". You use that calculation to get your probabilities for rolling how ever many successes, but then you have to add them together. For instance if you wanted to see the probability of getting 5 points on 7 dice, you could get that by either rolling five 1s, three 1s and one 2, or by rolling two 2s and one 1. The probability for this would be P(five 1s) + P(three 1s)*P(one 2) + P(one 1)*P(two 2s). This formula would be read as "the probability of getting fives 1s or getting three 1s and one 2 or getting one 1 and two 2s." The five probabilities needed in this formula are all calculated by the equation above. The number of combinations goes up at every even number, start at 1 for 1, 2 for 2, 3 for 4, etc, ending with 6 ways you can roll a 10.

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I knew there had to be a simpler way of doing this!  Thanks for your help, it's much appreciated :) .  I'll give it a shot next time!

But the real reason I'm back is to gift you all the "Grey" charts!  These are the same as the charts in the OP, except they don't take into account pip color, and are just counting the number of pips rolled. 

This will be useful for those who need to (or are planning on) spending a Destiny Point to draw from both colors, or those who are using a house-rule that allows you to do so at no (or reduced) cost.

I hope you enjoy!  As always, questions, comments, and requests are welcome!

 

Percent Chance for Specific Number of Pips – Grey

Pips | FR 1 | FR 2 | FR 3 | FR 4 | FR 5 | FR 6 | FR 7 | FR 8 | FR 9 | FR 10 |

01 | 66.67 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

02 | 33.33 | 44.44 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

03 | 00.00 | 44.44 | 29.63 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

04 | 00.00 | 11.11 | 44.44 | 19.75 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

05 | 00.00 | 00.00 | 22.22 | 39.51 | 13.17 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

06 | 00.00 | 00.00 | 03.70 | 29.63 | 32.92 | 08.78 | 00.00 | 00.00 | 00.00 | 00.00 |

07 | 00.00 | 00.00 | 00.00 | 09.88 | 32.92 | 26.34 | 05.85 | 00.00 | 00.00 | 00.00 |

08 | 00.00 | 00.00 | 00.00 | 01.23 | 16.46 | 32.92 | 20.48 | 03.90 | 00.00 | 00.00 |

09 | 00.00 | 00.00 | 00.00 | 00.00 | 04.12 | 21.95 | 30.73 | 15.61 | 02.60 | 00.00 |

10 | 00.00 | 00.00 | 00.00 | 00.00 | 00.41 | 08.23 | 25.61 | 27.31 | 11.71 | 01.73 |

11 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 01.65 | 12.80 | 27.31 | 23.41 | 08.67 |

12 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.14 | 03.84 | 17.07 | 27.31 | 19.51 |

13 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.64 | 06.83 | 20.48 | 26.01 |

14 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.05 | 01.71 | 10.24 | 22.76 |

15 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.24 | 03.41 | 13.66 |

16 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.02 | 00.73 | 05.69 |

17 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.09 | 01.63 |

18 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.01 | 00.30 |

19 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.03 |

20 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

 

Percent Chance for Minimum Number of Pips – Grey

 Pips | FR 1 | FR 2 | FR 3 | FR 4 | FR 5 | FR 6 | FR 7 | FR 8 | FR 9 | FR 10 |

01+ | 100.0 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

02+ | 33.33 | 100.0 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

03+ | 00.00 | 55.56 | 100.0 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

04+ | 00.00 | 11.11 | 70.37 | 100.0 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

05+ | 00.00 | 00.00 | 25.93 | 80.25 | 100.0 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

06+ | 00.00 | 00.00 | 03.70 | 40.74 | 86.83 | 100.0 | 00.00 | 00.00 | 00.00 | 00.00 |

07+ | 00.00 | 00.00 | 00.00 | 11.11 | 53.91 | 91.22 | 100.0 | 00.00 | 00.00 | 00.00 |

08+ | 00.00 | 00.00 | 00.00 | 01.23 | 20.99 | 64.88 | 94.15 | 100.0 | 00.00 | 00.00 |

09+ | 00.00 | 00.00 | 00.00 | 00.00 | 04.53 | 31.96 | 73.66 | 96.10 | 100.0 | 00.00 |

10+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.41 | 10.01 | 42.94 | 80.49 | 97.40 | 100.0 |

11+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 01.78 | 17.33 | 53.18 | 85.69 | 98.27 |

12+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.14 | 04.53 | 25.86 | 62.28 | 89.60 |

13+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.69 | 08.79 | 34.97 | 70.09 |

14+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.05 | 01.97 | 14.48 | 44.07 |

15+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.26 | 04.24 | 21.31 |

16+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.02 | 00.83 | 07.66 |

17+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.10 | 01.97 |

18+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.01 | 00.34 |

19+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.04 |

20+ | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 |

 

 

Edited by Absol197

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On 1/18/2018 at 5:45 AM, Josep Maria said:

First thanks for all the efforts ;)

In our games we have a houserule for "really avanced force users" (not necessarelly Jedi but something near). We are aware that you can succumb to dark side and Flip a Destiny point to exchange pips (paying also strain cost and earning Conflict? Not sure) but we still created something to empower a bit force using characters.

Force Focus/Mastery/Insert cool name here XD (Incidental, Out of turn): Let you exchange FP (LS ↔ DS) paying 1 Strain per pip limited by Ranks on Discipline.

In movies or TV Shows high skilled Force users doesn't seem to fail checks (just when confronting another one) and apparently without falling to the Dark Side. Some scenes we watch can be explained as a "cinematic moment" or a "really lucky roll", but when it happens so usually we considered to create this option (not Talent) as one possible idea. Maybe you can consider a 3+ FR or just a "scenic Master grade" of Force Domain, not sure, but seems to work pretty fine.

It's a really overpowered option in general cases, but for high level games and characters like the ones on my games (More than 2600XP) is not so powerful as it seems.

 

seems unnecessary since you already can do this with a destiny flip and strain...you just get conflict. Skilled force users likely get some conflict. You are making assumptions on the mechanics based on no info. We don't know what the die roll was or if they took conflict flipped DP or anything.

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Yep I'm aware that is just an assumption, but in general cases I use to create things more "player friendly". But yes, still considering it because Conflict rules doesn't necessarrely means that you "fall to the dark side" just that you can be "tempted" by it rolling a d100. 

So probably you are right, that's because we haven't fully implmented it yet.

After watching the tables of pip probability I'm still trying to discover how probable is for a FR6 character with a pair of full power trees ahieve the desired results.

By the way, thanks ;) 

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I don't know about your games, but I have recently implemented a house rule in my game that removes the destiny point cost from using opposite flavor pips.  The reasoning for this is I have found over the games I've played in and GM'ed, I have found players more often than not getting caught up in the meta of "Do I spend community resource X to make my roll not suck..." instead of answering the pertinent question of "Would my character in this situation willing tap into the dark side given their background and the situation...."   I don't like the idea of a community resource dictating action on a player, and taking agency away from that player to make decisions for their character that make sense. I'll post what the results are of this rule change once my groups have had a few sessions.  

 

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Hey all!

I wanted to bump this back up in case people needed to reference it, and also to ask if there was anything else related that they wanted to see.  Since I don't have anything else to oogle over at the moment, I might as well run numbers...

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On 20/01/2018 at 12:24 PM, TrystramK said:

I don't know about your games, but I have recently implemented a house rule in my game that removes the destiny point cost from using opposite flavor pips.  The reasoning for this is I have found over the games I've played in and GM'ed, I have found players more often than not getting caught up in the meta of "Do I spend community resource X to make my roll not suck..." instead of answering the pertinent question of "Would my character in this situation willing tap into the dark side given their background and the situation...."   I don't like the idea of a community resource dictating action on a player, and taking agency away from that player to make decisions for their character that make sense. I'll post what the results are of this rule change once my groups have had a few sessions.  

 

We tried that with a previous suggestion of not requiring it to use DS pips , however when you do that you then give lightsiders a significant advantage. They can then guarantee that they can pull off a force ability when it counts without significantly hurting their ability to stay lightside. Doing it both ways has the same effect on everyone, although I like the idea, you should increase the strain cost to compensate, meaning that they cant keep that amount of strain use up for long.

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4 hours ago, syrath said:

We tried that with a previous suggestion of not requiring it to use DS pips , however when you do that you then give lightsiders a significant advantage. They can then guarantee that they can pull off a force ability when it counts without significantly hurting their ability to stay lightside. Doing it both ways has the same effect on everyone, although I like the idea, you should increase the strain cost to compensate, meaning that they cant keep that amount of strain use up for long.

Yeah, I took the destiny cost away from force checks entirely, both ways.  The DP mechanic has no bearing on their ability to stay lightside.  If I were to double anything "to compensate", it would be conflict.  Strain I don't see as being much of an issue as the dark side wants you to use its cookies, until you realize they were laced with dark side drugs the entire time and now you are addicted. 

I'm not sure how this makes lightsabers any more silly than they already are though?  Unless you are just calling F&D characters lightsabers :P

So far in the games I've run, it's been quite successful in letting players leverage their powers. on a consistent basis, and also makes certain abilities less volatile in their utility.  It also has netted larger conflict pools at the end of games.

 

 

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On 3/4/2018 at 2:55 AM, Absol197 said:

Hey all!

I wanted to bump this back up in case people needed to reference it, and also to ask if there was anything else related that they wanted to see.  Since I don't have anything else to oogle over at the moment, I might as well run numbers...

I just referred to it today when telling a player that the roll they made (Heal Mastery to bring back a fallen ally last session) was a 6.25% chance (rolled 4 light points on FR2.)

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