# Boost dice vs Upgrades to produce successes.

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### #1 LethalDose

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Posted 05 September 2012 - 12:51 PM

After a game session with some friends, there were some questions raised about exactly how the dice work.  Given the way the rules are written (e.g. frequency of mechanics and relative cost of talents, upgrades, etc), and the way the dice are described, we expected upgrading dice to be superior to boost dice.  Some quick math so seems to indicate otherwise.  The arguement is built on the following demonstrable facts:

• One boost die has 2 faces with successes, each with one success, i.e. out of six outcomes (each of equal probability) there are two successes.  On average (over many many rolls), we can conclude adding a boost die to a pool will add 1/3 (2/6) successes.
• One Abilitiy die has 4 faces with success, 3 with one, 1 with 2.  On average, an ability die will contribute 5/8 successes to a pool.
• One Proficiency die has 8 faces with successes (or triumph, which count as one success), 2 of which have 2 successes, 1 on the other.  There are 12 sides, and 10 successes amongst them, so each proficiency die will generate, on average 5/6 (10/12) successes.
• Based on this information, upgrading an ability die increases the resultant successes by 5/6 - 5/8 = 20/24 - 15/24 = 5/24 < 6/ 24 = 1/4.

By this math, the addition of one boost die seems to provide 60% more successes (over many many rolls) than upgrading an ability die (1/3 / 5/24 = 8/5 = 1.6). [Note: it is clear that the Proficiency die is superior to the Boost die, but this is not the comparison being made, because there is no way to simply add a proficiency die.  This mechanisms being compared are upgrading vs addition of a boost die]

Where a Proficiency die represents an individuals expertise in a skill, further supported by his attribute, and it resides "On the top" of the spectrum of quality of the positive dice, and a Boost die represents favorable situational/environment conditions, it seems to be problematic that the "upgrading" mechanic, which is presented as being more powerful, is numerically LESS effective at producing successful results than enviromental/situational conditions.

It should be noted that, In the case of there being no ability dice to upgrade and the upgrade adds an ability die, the increase in the average success of the roll caused by the upgrade, 5/8, (1/2 probability of increasing successes rolled), the upgrading mechanic IS acutally superior to the boost die (5/8 - 1/3 = 15/24 - 8/24 = 7/24) by a substantial relative margin (5/8 / 1/3 = 15/8 = 1.875, 87.5% improvement).

This is supported in practice as well.  Instead of rolling these dice over and over, I got into R and wrote some code to simulate dice rolls.  I've included two typical examples of the outcomes below  (all results based on 10000 simulated results, rounded to nearest 0.1%).

Ex 1.  Skill rank 1, Attrib 3, average difficulty.  Pool = YGGPP (1 Yellow Proficiency, 2 Green Ability, and 2 Purple Difficulty dice; I use + for boost dice, and - for setbacks)

• Base probability of success: 65.1% (90% probability interval for net success: [-2, 4])
• Probability of success following upgrade (YYGPP): 69.6% (90% probability interval for net success: [-1, 4])
• Probability of success following a boost die (YGGPP+): 71.1% (90% probability interval for net successes: [-1, 4])

Ex 2. Skill rank 0, Attrib 2, Easy difficulty. Pool = GGP

• Base probability of success: 58.0% (90% probability interval for net success: [-1, 3])
• Probability of success following upgrade (YGP): 65.5% (90% probability interval for net success: [-1, 3])
• Probability of success following a boost die (GGP+): 66.2% (90% probability interval for net successes: [-1, 3])

Ex. 3 Skill rank 3, Attrib 3, Average difficulty.  Pool = YYPP

• Base probability of success: 56.3% (90% probability interval for net success: [-2, 3])
• Probability of success following upgrade (YYGPP): 70.2% (90% probability interval for net success: [-1, 4])
• Probability of success following a boost die (YYPP+): 64.9% (90% probability interval for net successes: [-1, 3])

On the surface I see two problems created by the way this mechanic is working.  First, players will avoid the [typically] higher priced or more difficult to achieve talents that allow upgrading, and prefer talents that provide Boost dice.  Following that, players may be more likely to argue and wheedle for boost dice based on the situation, slowing the game.

Second, players may be reluctant to improve their skills past points where the skill rank matches attribute rank for skills that are "upgraded" by other talents, since upgrading provides a larger boost at this "notches".

From a design standpoint, it seems the goal of "dice upgrade" mechanic should be to provide a very substantial benefit, which should exceed the bonus provided by a Boost die.  Further, the advantage provided by an upgrade should be consistent across spectrum of pools to which it would be applied.  Under the current design, these two goals are not being achieved.

I have not addressed the effect of upgrading difficulty vs the addition of Setback dice, or the effect of upgrading vs boost on advantage production.  This is not due to neglect, it is due to 1) the already considerable length of this post and 2) the fact that the success of the roll does not depend on advantages produced.

Editorial: I LIKE the upgrade system, I think its clever, novel, and well implemented.  There is also some psychological "wieght" that should be added when a green or purple die is upgraded following the expdenditure of a destiny point.  The mechanic should be kept, but the dice need to be tweaked to allow the mechanic to live up to its potential.

-WJL

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### #2 MILLANDSON

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Posted 05 September 2012 - 01:45 PM

Why should it provide a "very substantial" benefit to successes, though? Skills are relatively cheap, and given that you can't spend XP on characteristics, being able to increase skills isn't difficult. Also, what would "very substantial" mean? An increase of 1/2? 2/3?

I think you should also take into account the numbers of advantages (both have 1/2 their sides covering advantages, but proficiency dice have an additional side with 2 advantages) and the ability to get triumphs (which is impossible with either ability or boost dice), which I think makes getting proficiency dice a lot more beneficial.

Also, at this stage, personally, I doubtful that the dice will be getting changed.

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### #3 LethalDose

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Posted 05 September 2012 - 08:40 PM

@Millandson: These are good questions and merit clarifications!

Please remember, that I'm not comparing boost dice to proficiency dice.  I'm comparing the cost and benefit of one game mechanic (adding a boost die to a pool) to the cost and benefit of a different mechanic with a similar intent (upgrading dice in a pool, e.g. replacing an ability die to a proficiency die).

Let's take this apart, shall we?

MILLANDSON said:

Why should it provide a "very substantial" benefit to successes, though?

I think there are two reasons why upgrading should provide more substantial benefits than boost dice: Relative costs, and Fun.

The first is due to the relative rarity of chances to apply upgrades compared to the frequency of events or conditions that provide boost dice, and the cost of activating upgrades compared to boosts. Upgrading is definitely less common than boosting, and activating an upgrade usually carries a higher cost than boosting. The reduced frequency of availability for upgrades should make upgrading FEEL special, but if the effect is weaker than a very common effect, the upgrade really just feels inconsequential, not special. In regards to cost, upgrading requires the expenditure of more limited, and therefore more valuable, resources (Destiny points, or talents that charge strain) compared to boosts (which typically require no resources, or require spending maneuvers, which are in MUCH greater supply). Summarized:

• Strain (talent activation,e.g. Dodge & Intimidating), which is typically refreshed at the end of an encounter
• Destiny points, which are refreshed by the GM's use.

Boosts cost:

• Threats, produced by your enemies (hell, they're giving these away)
• Nothing, when boosts are produced by environmental effects.
• Maneuvers (e.g. aim, assist) , replenished fully every round.

The increased cost of activating an upgrade should carry an increased benefit compared to the cheaper option. However, in the current situation, it is the cheaper option which provides greater benefit, which discourages players from using the mechanic.

This kind of weak bonus compared to the weight of invoking it is simply NOT FUN!

MILLANDSON said:

Skills are relatively cheap,

Skill training and the associated expenses aren't the issue here. I do believe there is an an issue there, but that issue merits a separate post.

MILLANDSON said:

and given that you can't spend XP on characteristics, being able to increase skills isn't difficult.

Skill training isn't upgrading. If skill training did upgrade attribute rolls, then Attrib 2, Skill 5 would roll as YYYG (GG, followed by 5 upgrades) not YYGGG, In fact, based on what I've presented, we should be thankful for that.  Also, I assume when you mean XP can't be used to increase characteristics after character creation. Unless I missed a post, you could still use them at character creation to increase attribs.

MILLANDSON said:

Also, what would "very substantial" mean? An increase of 1/2? 2/3?

I can't give you an explicit answer to this because there isn't an absolute value that would qualify, nor do I believe there should be. In this case, I would say it an upgrade would qualify as "very substantial" if it met the following criteria:

1.  The improvement is noteworhty to players, i.e. they should notice the increased value, and should be desired.
2.  The improvement will typically provide a larger benefit than easier or cheaper options
3.  The improvement will typically provide a smaller benefit than more difficult or more expensive options.
4. The improvement will produce roughly consistent improvements regardless of what dice pool it is applied to.

Currently, the upgrade mechanic fails on the first two, and i'm iffy on the third… I'm not sure what I would consider more expensive than a destiny point, and there are no actions (which are more limited than maneuvers) that I can think of that produce these kinds of bonuses.  It fails on the fourth count because of the inconsistency of the upgrade value when applied to pools where attrib rank = skill rank, i.e. no green dice.

MILLANDSON said:

I think you should also take into account the numbers of advantages (both have 1/2 their sides covering advantages, but proficiency dice have an additional side with 2 advantages)

There are several problems here…

First, you are as likely to produce advantages on a Proficiency die than on a boost die. There are 3 sides (out of 6) on a boost die that generate advantages, and 6 sided (out of 12) on a proficiency die, so both dice have a 50% chance of producing one or more advantages. Also, the distribution of the advantages amonst the sides is identical on both dice: 1/3 of the advantage faces produce 2 advantges, and 2/3 produce one. Both dice produce an average of 2/3 advantage per roll (Boost: 4 advantages over 6 sides, Proficency: 8 over 12). The number of sides with or with out a symbol is meaningless; what is important is the proportion of faces that have advantages.

This actually furthers my point as well, because we're not comparing “is a boost die better than a proficiency die”, as I restated above.  We're comparing addition of a boost die to UPGRADING an ability die. Adding a boost die will add 2/3 of an advantage per roll, like it adds 1/3 of a success to a roll, where UPGRADING an ability die will replace a die producing 5/8 advantages per roll with one that produces 2/3.

This is a net gain of 2/3 – 5/8 = 16/24 – 15/24 = 1/24. You produce just over .04 more advantages by rolling a yellow compared to a green. That's such a small change it can be ignored. Its 1/8 the amount of advantages produced by adding a boost die. And again, both ability dice and proficiency dice have a 50% chance to produce at least one advantage.

MILLANDSON said:

and the ability to get triumphs (which is impossible with either ability or boost dice), which I think makes getting proficiency dice a lot more beneficial.

Okay, this argument may have some merit, but its VERY difficult to quantify. But we have to remember, for the triumph to cause the upgrading to be more effective and impressive than a small boost, it has to produce some benefit in excess of the deficits I've already lined out:

First off, lets point out that you have a little more than an 8% chance of scoring a triumph, which also counts as a success (and yes, I accounted for that in my simulations above). So this 8% chance for triumph better be offset by a BIG gain that, by itself, has to offset the problems above. In some cases it can be. But I will tell you that, having seen the faces of my players when the rolled, and got triumph, and still failed… It was the failure that was more important than the triumph.

This serves highlights another point: Getting a triumph on a failure STILL LEADS TO A FAILURE!!!!

Failed attacks with triumphs still miss (and the triumph can't trigger a crit), failed actions with triumphs still fail to achieve the goal of the action.  If your rolls are failing, you are not (or are minimally) advancing the encounter.  You are not downing enemies.  You are not finding clues.  Successes, which drive encounters by achieving goals, are more important than advantages or triumphs. It is not required to roll either of the later to successfully achieve goals in encounters. Period.  They are window dressing and, while they can be used to advance the narrative, they are not neccessary.

It is again that I would make the argument: "In most cases, It is more fun to expend resources to achieve success and smaller bonuses, than it is to achieve failure and bigger bonuses"

In combat, the triumphs, which you have an 8% chance to trigger with an upgrade, can be spent on other upgrades (costs a triumph) OR can add a Boost/setback to an ally/enemy (which costs two advantages or a triumph). Now, based on what I've layed out… I think the boost is the choice that makes sense. And again, notice how its still easier to get the boost: 2 advantages is easier to score than a triumph for sure, especially since it doesn't require proficiency dice.

To sum up, yes, triumphs are great mechanic, but in my opinion, and based on the facts and arguements I have presented here, they do not allow make up for the failings of the upgrade mechanic, and changes need to be made.

Let's see, anything else?  Oh, right!

MILLANDSON said:

Also, at this stage, personally, I doubtful that the dice will be getting changed.

I'm assuming you believe that the dice aren't gonna be changed because they're probably already minted, and changing the dice would cause a huge amount of waste due to the invalidation of already created product.

Well, I respect your opinion on this, but I STRONGLY disagree.  Support for my different position is below:

At the in-flight report where Edge of the Empire was announced, the presenter (wish I could remember his name) spent about 20-30 minutes discussing and describing FFG's process of producing games, from R&D, to Production, to Distribution, and how beta testing fit into the picture.

When a beta is created, its on an extremely limited run, hence only 5,000 copies of the book in print, and sh*tty sticker dice. The beta phase is expected to take weeks to months (around 1-3 months was presented), only then followed by large-scale production of widgets, and distribution, which, combined,  take about 6-12 weeks.  So, if we're looking at an "Early 2013" release of this game, the absolute soonest FFG would start production would be early October, and that's 3 month lead to a 1.Jan launch.  That would be a month before any meaningful number of dice would be produced.  And let's face it, "Early 2013" really means before 30.Jun.2013, so production is unlikely to start until after the new year.

So what would be involved in changing the dice at this point? 2 things:

1. Updating their printable sticker sheet (don't have to print any themselves, since the book is distributed and sold out)
2. Patching the dice roller app.

Neither is anywhere near insurmountable.

And besides, the point of a beta is to find the problems and fix them, regardless of wherever they are; And it'd be a pretty sh*tty beta if the devs aren't willing to tweak the event generators that run… pretty much the entire game.

Hope that cleared things up.

-WJL

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### #4 LethalDose

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Posted 05 September 2012 - 08:43 PM

Well ****.  That's embarassing.

"All models are wrong, but some models are useful."  - George E. P. Box

### #5 koralas

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Posted 06 September 2012 - 01:28 AM

Ah, I had a great post typed up and must have accidentally hit the touch pad on my laptop while typing and reaching for the backspace key.  It must have clicked in the background of the page which then the backspace key works like the "back button" in the browser, grrr!!!!

I will paraphrase the most important points I was making.

Chance of getting a success from an Ability die:  4/8 (50%)

Chance of getting a success from a Proficiency die:  8/12 (66%)

Chance of getting a success from a Boost die:  2/6 (33%)

Chance of getting a non-success from an Ability Die:  4/8 (50%)

Chance of getting a non-success from a Proficiency Die:  8/12 (33%)

Chance of getting a non-success from a Boost die:  4/6 (66%)

Chance of getting a blank from an Ability die:  1/8 (12%)

Chance of getting a blank from a Proficiency die:  1/12 (8%)

Chance of getting a blank from a Boost die:  2/6 (33%)

Chance of getting an advantage from an Ability die:  4/8 (50%)

Chance of getting an advantage from a Proficiency die (counting a triumph as an Advantage):  7/12 (58%)

Chance of getting an advantage from a Boost die:  3/6 (50%)

Chance of getting both a Success and Advantage from an Ability die:  1/8 (12%)

Chance of getting both a Success and Advantage from a Proficiency die (counting a Triumph as both an Advantage and Success):  4/12 (33%)

Chance of getting both a Success and Advantage from a Boost die:  1/6 (16%)

So yes, the boost die is an additional 33% chance to gain a success, while the upgrade is only a 16% increase in the chance to gain a success, the boost die could be considered more valuable.  But with the boost die has a 66% chance of not providing a success increase, while the Proficiency die changes the chance of generating a non-success result from an ability die from 50% to 33%, that is a huge improvement over the basic die.

Also, you have to factor in the Advantages and Triumph when judging the comparative worth of the dice.  As the numbers above show, the upgrade is simply better than a boost die.  Also, as long as you have a skill, you can always upgrade a die for free, something external to the character (except for traits) must be in effect to get a boost die.

Don't make the mistake I started to, and think of Destiny as Fate/Hero points.  This is a pool that will dwindle, but always be replenished, within a session, the players start with an advantage, but as they spend the points, the GM gets them to spend, but when the GM spends them the players get them back…  Destiny is not individual for each player, but a pool that is determined each game session.  Destiny is the will of the universe, the Force, or however you want to view it, it is simply a resource to be used, not something that helps to define a character.

### #6 ynnen

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Posted 06 September 2012 - 04:46 AM

Design-wise, there is another important factor in determining the relative value between any two options presented: where the addition or subtraction of value comes from.

Do the players have direct control over it? Is it subject strictly to GM fiat? Is control purely luck-based due to previous die rolls and results?

As such, a player-empowered resource is evaluated differently than a luck-powered or GM-powered resource.

### #7 LethalDose

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Posted 06 September 2012 - 05:18 AM

koralas said:

Ah, I had a great post typed up and must have accidentally hit the touch pad on my laptop while typing and reaching for the backspace key.  It must have clicked in the background of the page which then the backspace key works like the "back button" in the browser, grrr!!!!

I will paraphrase the most important points I was making.

Chance of getting a success from an Ability die:  4/8 (50%)

Chance of getting a success from a Proficiency die:  8/12 (66%)

Chance of getting a success from a Boost die:  2/6 (33%)

Chance of getting a non-success from an Ability Die:  4/8 (50%)

Chance of getting a non-success from a Proficiency Die:  8/12 (33%)

Chance of getting a non-success from a Boost die:  4/6 (66%)

Chance of getting a blank from an Ability die:  1/8 (12%)

Chance of getting a blank from a Proficiency die:  1/12 (8%)

Chance of getting a blank from a Boost die:  2/6 (33%)

Chance of getting an advantage from an Ability die:  4/8 (50%)

Chance of getting an advantage from a Proficiency die (counting a triumph as an Advantage):  7/12 (58%)

Chance of getting an advantage from a Boost die:  3/6 (50%)

Chance of getting both a Success and Advantage from an Ability die:  1/8 (12%)

Chance of getting both a Success and Advantage from a Proficiency die (counting a Triumph as both an Advantage and Success):  4/12 (33%)

Chance of getting both a Success and Advantage from a Boost die:  1/6 (16%)

So yes, the boost die is an additional 33% chance to gain a success, while the upgrade is only a 16% increase in the chance to gain a success, the boost die could be considered more valuable.  But with the boost die has a 66% chance of not providing a success increase, while the Proficiency die changes the chance of generating a non-success result from an ability die from 50% to 33%, that is a huge improvement over the basic die.

Also, you have to factor in the Advantages and Triumph when judging the comparative worth of the dice.  As the numbers above show, the upgrade is simply better than a boost die.  Also, as long as you have a skill, you can always upgrade a die for free, something external to the character (except for traits) must be in effect to get a boost die.

Don't make the mistake I started to, and think of Destiny as Fate/Hero points.  This is a pool that will dwindle, but always be replenished, within a session, the players start with an advantage, but as they spend the points, the GM gets them to spend, but when the GM spends them the players get them back…  Destiny is not individual for each player, but a pool that is determined each game session.  Destiny is the will of the universe, the Force, or however you want to view it, it is simply a resource to be used, not something that helps to define a character.

Well, lets try to get some numbers straight, first.  Probably the most important is difference is that I'm discussing the average NUMBER of symbols that are produced by a die roll, while the numbers you've provided numbers only address the probability of producing ANY symbols of a type.  Since different faces produce different values of symbols (success, advantages), the likelihood of those events must be weighted by the the different results for the comparisons to have value.

Next, I see at least one problem in your numbers:

koralas said:

Chance of getting an advantage from a Proficiency die (counting a triumph as an Advantage):  7/12 (58%)

Triumphs don't count as an advantage, only a success. They may be spent in ways similar to multiple advantages, but in your argument you can't count them both as a source of advantage generation AND as some big boost because a single triumph result can't be spent in both ways.

koralas said:

Also, you have to factor in the Advantages and Triumph when judging the comparative worth of the dice. As the numbers above show, the upgrade is simply better than a boost die.

You're confusing "upgrade" with "proficiency die".  And its not the just probability of getting any advantage that you should be concerned with. And your numbers don't support your claim.  By YOUR numbers (which are wrong), the upgrade provides:

58% - 50% = 8% increased probability of getting an advantage. (If you corrected your numbers, this would become .5-.5 = 0)

A boost provides:

50% - 0% = 50% increased probability of getting an advantage.

The numbers that matter are the number of average success gained by a boost or upgrade.  An upgrade provides:

A boost provides:

If you want to say that triumphs are simply "super advantages", even if I count a triumph as 4 advantages (which would increase the number of advantages on a proficiency die to 12), it doesn't win this comparison!

12/12 = 1.0 [alternatively, this can be written: 0(5/12) + 1(4/12) + 2(2/12) + 4(1/12) = 0/12 + 4/12 + 4/12 + 4/12 = 12/12 = 1]

1.0 - .625 = .375 net additional advantages for an upgrade!  That's just a little more than half (.375/.667 = 56.3%) of the bonus of getting a boost die.

koralas said:

As I've said before, skills aren't upgrades.  Not talking about the value of training skills, only the costs and benefits of activating the "upgrade" mechanic here.

koralas said:

something external to the character (except for traits) must be in effect to get a boost die.

This isn't true, for reasons beyond what you provide in your own quote.  Maneuvers can be spent and don't require "something external to the character [to]  be in effect to get a boost die."

koralas said:

Don't make the mistake I started to, and think of Destiny as Fate/Hero points. This is a pool that will dwindle, but always be replenished, within a session, the players start with an advantage, but as they spend the points, the GM gets them to spend, but when the GM spends them the players get them back… Destiny is not individual for each player, but a pool that is determined each game session. Destiny is the will of the universe, the Force, or however you want to view it, it is simply a resource to be used, not something that helps to define a character.

I think what you're trying to argue in this paragraph is that destiny points either aren't special and/or aren't limited.  If they aren't supposed to be special… I don't understand what the intent of the mechanic is then.  Calling on destiny to aid you in your time of need… seems like it should carry some weight.  And if you are trying to argue that they aren't limited, I would have to ask: Do you really think that destiny points are as common as and have equivalent value to maneuvers?

-WJL

"All models are wrong, but some models are useful."  - George E. P. Box

### #8 LethalDose

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Posted 06 September 2012 - 05:48 AM

Ah! Yes! Thanks for your attention to this thread, ynnen.  I'm interested to hear your perspective on this.

You referred to player-empowered vs GM-powered resources.  I assume this refers to destiny points (and when and how to use them) and talent selection as being player-empowered resources and conditional modifiers based on environment as being GM-powered resources.  Also, "upgrading" can be seen as a player-empowered resource, and receiving a Boost die is a GM resource

However, I think based on the availability of boost dice via some talents and maneuvers (primarily "aim" and "aid an ally" for combat skills), the boost die isn't a purely GM controlled mechanic.

ynnen said:

Do the players have direct control over it?

And yes, with these talents and maneuvers they do, in and out of combat.  It is also possible for the players to enhance the narrative, by spending destiny points, to create situations in which they could gain boost dice for environmental bonuses.  I understand that this IS controllable via GM fiat; the players don't have sole control over the environment, but it is another example of how they ARE able to activate the mechanic independent of the GM.  This means that players have both Boost dice and Upgrading available as mechanical options they can activate.

I guess my big question here is that, given the numbers I've provided and logic I've constructed, is the upgrade mechanic really working as intended?

I'm asking is because, during play, it seemed to be a pretty lackluster option.

Again, thanks for you time and hard work, Jay!  Its a great game, just needs some tweaks.

-WJL

"All models are wrong, but some models are useful."  - George E. P. Box

### #9 Timberboar

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Posted 06 September 2012 - 07:55 AM

While only tangential to the point of this thread, I find it somewhat distressing that the character in Example 1 (Attribute 3, Skill 1) has a significantly higher base chance of success than the character in Example 3 (Attribute 3, Skill 3).

Surely that can't be working as intended?

### #10 Callidon

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Posted 06 September 2012 - 08:30 AM

Timberboar said:

While only tangential to the point of this thread, I find it somewhat distressing that the character in Example 1 (Attribute 3, Skill 1) has a significantly higher base chance of success than the character in Example 3 (Attribute 3, Skill 3).

Surely that can't be working as intended?

It seems fine to me.  The proficiency dice have an increased chance of rolling a success over the ability dice.  In Example 1, the player rolls 2 ability dice and 1 proficiency die.  In Example 3, the player rolls 3 proficiency dice.  Not sure how that equates to a decreased chance of success when you are rolling the same number of dice with improved chances of success (57% vs 66% chance of a success popping up in Ex 1 vs Ex 3).

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### #11 LethalDose

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Posted 06 September 2012 - 08:44 AM

@Timberboar: Thanks for catching that, Ex 3. has a typo I missed.  It should be  (The Die code for the roll, YYPP, is correct.)  All of the other dice pool codes are also correct.

A player rolling vs the same difficulty with Attrib and skill ranked 3 (YYYPP) has a 74.4% chance of success (based on 50k rolls), which exceeds the YGGPP stated above.

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### #12 LethalDose

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Posted 06 September 2012 - 08:57 AM

I don't what the issues is with my typing lately.  Ex 3 Above should read "It should be skill 2 attrib 2" instead of 3 and 3.  all dice pool codes are correct.

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### #13 Timberboar

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Posted 06 September 2012 - 09:31 AM

LethalDose said:

I don't what the issues is with my typing lately.  Ex 3 Above should read "It should be skill 2 attrib 2" instead of 3 and 3.  all dice pool codes are correct.

So… non-issue.  Carry on, then.

*twirls baton and wanders away, whistling*

### #14 Quicksilver

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Posted 06 September 2012 - 09:48 AM

While I will not debate your math, there is little here to recommend a solution. Adding more successes to the proficiency dice or reducing successes on ability dice would make skills far more effective than they are now, thereby trading one problem for another. Reducing the number of successes on boost dice also creates a major problem, preventing the GMs from having an effective way to adjust rolls for positive circumstances.

When it comes to destiny points specifically, I personally think that a static bonus is better than a die change anyway, and would recommend that a destiny point be able to 'buy' a success, advantage, failure or threat on a roll of the spender's choice. This allows destiny to be the thing that pushes close calls over the edge, rather than the thing that might help.

90% of the time I'm posting without access to rulebooks.  Unless I say otherwise, assume everything is I.I.R.C.

### #15 LethalDose

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Posted 06 September 2012 - 11:26 AM

Quicksilver said:

While I will not debate your math, there is little here to recommend a solution. Adding more successes to the proficiency dice or reducing successes on ability dice would make skills far more effective than they are now, thereby trading one problem for another. Reducing the number of successes on boost dice also creates a major problem, preventing the GMs from having an effective way to adjust rolls for positive circumstances.

When it comes to destiny points specifically, I personally think that a static bonus is better than a die change anyway, and would recommend that a destiny point be able to 'buy' a success, advantage, failure or threat on a roll of the spender's choice. This allows destiny to be the thing that pushes close calls over the edge, rather than the thing that might help.

You're absolutely right, Quicksilver, I've done nothing here to recommend a solution for the identified problem.

The purpose of this thread was to draw attention to the issue using solid evidence, and hear a variety of opinions about it.  Before any solutions would be considered, it has to be clear there actually IS a problem.

I'm hoping the thread will stimulate ideas to fix the problem.  I have ideas on how to fix it, (one of which you touched on above, but is slightly more involved) but don't think there's a point to offering solutions to such a core mechanic until we understand the problem better.

Honestly, understanding the problem better requires a dev's perspective in addition to the evidence I've presented.  And if ynnen comes back and states "working as intended, we like the numbers where they are", well, there's the solution.

-WJL

"All models are wrong, but some models are useful."  - George E. P. Box

### #16 koralas

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Posted 06 September 2012 - 12:21 PM

LethalDose said:

koralas said:

Ah, I had a great post typed up and must have accidentally hit the touch pad on my laptop while typing and reaching for the backspace key.  It must have clicked in the background of the page which then the backspace key works like the "back button" in the browser, grrr!!!!

I will paraphrase the most important points I was making.

Chance of getting a success from an Ability die:  4/8 (50%)

Chance of getting a success from a Proficiency die:  8/12 (66%)

Chance of getting a success from a Boost die:  2/6 (33%)

Chance of getting a non-success from an Ability Die:  4/8 (50%)

Chance of getting a non-success from a Proficiency Die:  8/12 (33%)

Chance of getting a non-success from a Boost die:  4/6 (66%)

Chance of getting a blank from an Ability die:  1/8 (12%)

Chance of getting a blank from a Proficiency die:  1/12 (8%)

Chance of getting a blank from a Boost die:  2/6 (33%)

Chance of getting an advantage from an Ability die:  4/8 (50%)

Chance of getting an advantage from a Proficiency die (counting a triumph as an Advantage):  7/12 (58%)

Chance of getting an advantage from a Boost die:  3/6 (50%)

Chance of getting both a Success and Advantage from an Ability die:  1/8 (12%)

Chance of getting both a Success and Advantage from a Proficiency die (counting a Triumph as both an Advantage and Success):  4/12 (33%)

Chance of getting both a Success and Advantage from a Boost die:  1/6 (16%)

So yes, the boost die is an additional 33% chance to gain a success, while the upgrade is only a 16% increase in the chance to gain a success, the boost die could be considered more valuable.  But with the boost die has a 66% chance of not providing a success increase, while the Proficiency die changes the chance of generating a non-success result from an ability die from 50% to 33%, that is a huge improvement over the basic die.

Also, you have to factor in the Advantages and Triumph when judging the comparative worth of the dice.  As the numbers above show, the upgrade is simply better than a boost die.  Also, as long as you have a skill, you can always upgrade a die for free, something external to the character (except for traits) must be in effect to get a boost die.

Don't make the mistake I started to, and think of Destiny as Fate/Hero points.  This is a pool that will dwindle, but always be replenished, within a session, the players start with an advantage, but as they spend the points, the GM gets them to spend, but when the GM spends them the players get them back…  Destiny is not individual for each player, but a pool that is determined each game session.  Destiny is the will of the universe, the Force, or however you want to view it, it is simply a resource to be used, not something that helps to define a character.

Well, lets try to get some numbers straight, first.  Probably the most important is difference is that I'm discussing the average NUMBER of symbols that are produced by a die roll, while the numbers you've provided numbers only address the probability of producing ANY symbols of a type.  Since different faces produce different values of symbols (success, advantages), the likelihood of those events must be weighted by the the different results for the comparisons to have value.

Next, I see at least one problem in your numbers:

koralas said:

Chance of getting an advantage from a Proficiency die (counting a triumph as an Advantage):  7/12 (58%)

Triumphs don't count as an advantage, only a success. They may be spent in ways similar to multiple advantages, but in your argument you can't count them both as a source of advantage generation AND as some big boost because a single triumph result can't be spent in both ways.

koralas said:

Also, you have to factor in the Advantages and Triumph when judging the comparative worth of the dice. As the numbers above show, the upgrade is simply better than a boost die.

You're confusing "upgrade" with "proficiency die".  And its not the just probability of getting any advantage that you should be concerned with. And your numbers don't support your claim.  By YOUR numbers (which are wrong), the upgrade provides:

58% - 50% = 8% increased probability of getting an advantage. (If you corrected your numbers, this would become .5-.5 = 0)

A boost provides:

50% - 0% = 50% increased probability of getting an advantage.

The numbers that matter are the number of average success gained by a boost or upgrade.  An upgrade provides:

A boost provides:

If you want to say that triumphs are simply "super advantages", even if I count a triumph as 4 advantages (which would increase the number of advantages on a proficiency die to 12), it doesn't win this comparison!

12/12 = 1.0 [alternatively, this can be written: 0(5/12) + 1(4/12) + 2(2/12) + 4(1/12) = 0/12 + 4/12 + 4/12 + 4/12 = 12/12 = 1]

1.0 - .625 = .375 net additional advantages for an upgrade!  That's just a little more than half (.375/.667 = 56.3%) of the bonus of getting a boost die.

koralas said:

As I've said before, skills aren't upgrades.  Not talking about the value of training skills, only the costs and benefits of activating the "upgrade" mechanic here.

koralas said:

something external to the character (except for traits) must be in effect to get a boost die.

This isn't true, for reasons beyond what you provide in your own quote.  Maneuvers can be spent and don't require "something external to the character [to]  be in effect to get a boost die."

koralas said:

Don't make the mistake I started to, and think of Destiny as Fate/Hero points. This is a pool that will dwindle, but always be replenished, within a session, the players start with an advantage, but as they spend the points, the GM gets them to spend, but when the GM spends them the players get them back… Destiny is not individual for each player, but a pool that is determined each game session. Destiny is the will of the universe, the Force, or however you want to view it, it is simply a resource to be used, not something that helps to define a character.

I think what you're trying to argue in this paragraph is that destiny points either aren't special and/or aren't limited.  If they aren't supposed to be special… I don't understand what the intent of the mechanic is then.  Calling on destiny to aid you in your time of need… seems like it should carry some weight.  And if you are trying to argue that they aren't limited, I would have to ask: Do you really think that destiny points are as common as and have equivalent value to maneuvers?

-WJL

LethalDose said:

Well, lets try to get some numbers straight, first.  Probably the most important is difference is that I'm discussing the average NUMBER of symbols that are produced by a die roll, while the numbers you've provided numbers only address the probability of producing ANY symbols of a type.  Since different faces produce different values of symbols (success, advantages), the likelihood of those events must be weighted by the the different results for the comparisons to have value.

OK, I'm sure you will break out some long formula, but often breaking things down to a its most simple view makes it easier to understand.  You increase your chance of rolling an advantage by 16% when you upgrade an ability die to a proficiency die.  You also increase your chance to roll a double success from 1/8 (12%) on the ability die, to 2/12 (1/6 or 16%).  So yes, adding a boost die gives you a success on 2/6 (33%) of the time, so it is double the increase of upgrading a die, regardless of how you upgrade that die.  But unless you have a trait, there is nothing from the core of the character that will add boost dice, that is done through external effects.

Remember when crafting your dice pool you compare the Skill level with the Characteristic score, and take the higher of those numbers to create a pool of Ability dice.  You then take the lower of those numbers and upgrade Ability dice to Proficiency dice based on that number (Page 16).  You can then use Destiny to upgrade additional Ability dice to Proficiency dice (Page 18), finally you can even increase the size of the dice pool through spending additional Destiny as upgrades and then actually upgrading the Ability die that was just added.

LethalDose said:

Triumphs don't count as an advantage, only a success. They may be spent in ways similar to multiple advantages, but in your argument you can't count them both as a source of advantage generation AND as some big boost because a single triumph result can't be spent in both ways.

They certainly do count as Advantages, or as I put it "super advantages", in that a Triumph provides a success, but it also provides an unlimited pool of Advantage when activating a single special ability; that is a single Triumph will activate one special effect of a weapon or score a critical wound regardless of the number of Advantages it would normally require.  Further, while Advantages can be used to remove Strain, Triumph instead can remove wounds, some effects require a Triumph, and the GM or scenario may call out other uses for Triumph in the narrative (Page 20).

LethalDose said:

koralas said:

Also, you have to factor in the Advantages and Triumph when judging the comparative worth of the dice. As the numbers above show, the upgrade is simply better than a boost die.

You're confusing "upgrade" with "proficiency die".  And its not the just probability of getting any advantage that you should be concerned with. And your numbers don't support your claim.  By YOUR numbers (which are wrong), the upgrade provides:

58% - 50% = 8% increased probability of getting an advantage. (If you corrected your numbers, this would become .5-.5 = 0)

A boost provides:

50% - 0% = 50% increased probability of getting an advantage.

As I noted above, Proficiency dice are Ability dice that have been upgraded, regardless of this was done because of a Skill/Characteristic combo, or Destiny, the rule book calls the mechanic of replacing them as an upgrade.  Thus, the 58% chance of gaining an Advantage on the Proficiency die stands.  Yes, this is an 8% difference, where you have a 50% chance of generating an Advantage with a Boost die, but again Boost are most commonly added via external influences, and you still have the 33% chance of gaining NOTHING from a Boost die.

LethalDose said:

The numbers that matter are the number of average success gained by a boost or upgrade.  An upgrade provides:

A boost provides:

The problem here is applying a straight statistical analysis to something with a heavy Random factor.  Roll a 6 sided die 6 times, you are not guaranteed of rolling each number.  Now obviously the more rolls you apply, the more likely you are to come to a statistic showing that each result of the die came up nearly 16% of the time, but in a game we are not sitting down continuously rolling dice and taking an average number to apply.  We take the result of each INDIVIDUAL die roll, and on an individual roll, long range statistical analysis means nothing.  It is still a 1 in 6 chance of getting any particular result on any given roll.

LethalDose said:

If you want to say that triumphs are simply "super advantages", even if I count a triumph as 4 advantages (which would increase the number of advantages on a proficiency die to 12), it doesn't win this comparison!

12/12 = 1.0 [alternatively, this can be written: 0(5/12) + 1(4/12) + 2(2/12) + 4(1/12) = 0/12 + 4/12 + 4/12 + 4/12 = 12/12 = 1]

1.0 - .625 = .375 net additional advantages for an upgrade!  That's just a little more than half (.375/.667 = 56.3%) of the bonus of getting a boost die.

See notes on Triumph above.  And, uhm, what????  (not sure quite what you are trying to show in the formula, nor what the numbers you are applying are derived from.  Go back to the note above about statistical analysis, it is only valid give a large enough pool of die rolls, not on individual rolls, or even a small group of rolls.

LethalDose said:

koralas said:

As I've said before, skills aren't upgrades.  Not talking about the value of training skills, only the costs and benefits of activating the "upgrade" mechanic here.

LethalDose said:

koralas said:

something external to the character (except for traits) must be in effect to get a boost die.

This isn't true, for reasons beyond what you provide in your own quote.  Maneuvers can be spent and don't require "something external to the character [to]  be in effect to get a boost die."

Actually a Maneuver is external to the character, it is not something that makes up the character, but rather a specific action being chosen, aiming, assisting another character, etc.

LethalDose said:

koralas said:

Don't make the mistake I started to, and think of Destiny as Fate/Hero points. This is a pool that will dwindle, but always be replenished, within a session, the players start with an advantage, but as they spend the points, the GM gets them to spend, but when the GM spends them the players get them back… Destiny is not individual for each player, but a pool that is determined each game session. Destiny is the will of the universe, the Force, or however you want to view it, it is simply a resource to be used, not something that helps to define a character.

I think what you're trying to argue in this paragraph is that destiny points either aren't special and/or aren't limited.  If they aren't supposed to be special… I don't understand what the intent of the mechanic is then.  Calling on destiny to aid you in your time of need… seems like it should carry some weight.  And if you are trying to argue that they aren't limited, I would have to ask: Do you really think that destiny points are as common as and have equivalent value to maneuvers?

Destiny points are special, but only somewhat limited in availability as the pool will wax and wan during the course of a gaming session.  The next session they will be completely replaced with yet another pool of perhaps a different size.  They are special but they aren't the Fate/Hero points of other game systems.  Destiny is the universe/Force interacting in behalf of or opposition to the actions being taken.  Each individual piece of this resource is indeed better than a Maneuver in that it takes nothing to activate it other than spending the point.  In instances when there are no Manuevers, pieces of gear, or other things that will assist in a task, or even to add onto those that do, you can spend Destiny to provide additional chances at success through the upgrade mechanic.  Especially if you continue the upgrade Mechanic to increase the size of the dice pool.  So in that way they are better than Maneuvers.

### #17 LethalDose

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Posted 07 September 2012 - 07:14 PM

Well, first, I'm not going to quote anymore, that's obviously just creating a mess of the thread and making this illegible.

Second, you seem to think my method is inappropriate, as you put it "applying a straight statistical analysis to something with a heavy Random factor".

Simply put, No. You're wrong.

One of the foundations of inferential statistics is that, given an appropriate sample size, the probability of success on a single trial can be estimated as equivalent the proportion of successful trials in a sample.  Further, this estimate stabilizes as the number of trials sampled increases, which is why I performed 10,000 simulations (or more, in the later instances) for each die pool.  As an example, If you asked 100 people if they liked the color blue, and 60 of them said yes, and then asked another person if they liked the color blue, you could infer that person would have a 60% chance of liking the color blue.  That forms part of the basis of the analysis I'm performing here.

As a brief explanation to my calculations, the probability of an even may also be estimated in simple cases by finding the average of the results weighted by frequency.  In simpler terms, the expected value of a die roll is equal to the probability of each face being rolled multiplied by the value of that face.  As an example, the expected result of a typical d6 is calculated as 1 (the value of the first face) multiplied (wieghted) by 1/6 (the probability of a 1), plus the 2 times 1/6, etc.  Expressed below (I REALLY hope this formula isn't to long for you…):

1(1/6) + 2(1/6) + 3(1/6) + 4(1/6) + 5(1/6) + 6(1/6) = 1/6 + 2/6 + 3/6 + 4/6 + 5/6+ 6/6 = 21/6 = 3.5

Similarly, we could throw a d6 thousands of times, and find the average roll.  The larger the sample (the increased number of die throws), the closer we would expect to be to the REAL expected value (although its unlikely we would hit it exactly).  Note also that, even though this would provided expected value of a dice throw, the actual result of 3.5 is impossible to observe.  But that doesn't mean that information is not valid.

Hopefully now you will understand, based on equations that were beyond you, how I concluded a roll of the proficiency die produces an average of 2/3 of an advantage per roll (or produce 1 advantage per roll, if you count a triumph as 4 advantages).

I don't know how else to assure that the method being applied is correct.  If you need FURTHER evidence that this how to find the expected values of random processes, I will have to refer you to statistical resources.  I recommend one of the following book chapters:

• Rousas, G. Chapter 2.  The Concept of Probability and Basic Results, in "An Introduction to Probability and Statistical Inference". ISBN10 0-12-599020-0
• Hogg, RV & EA Tanis. Chapter 1. Probability, in "Probability and Statistical Inference". 7 Ed. ISBN 1- 0-13-146413-2

Also on a quick scan, Essentials of Inferential Statistics (Asadoorian, MO, et al, 4th ed) appears sufficient, and is available for free on google books.  However, I have not personally used this text.

Third, I should have been more explicit about the intended scope of this discussion about the value of the upgrading dice.  The intended purpose was to compare the 2 primary ways a die pool may be modified as described in the 3rd step (and ONLY the third step) of "Modifying Dice Pool" on pg 17 of the Beta text.

You were right, it does refer to "upgrading" ability dice to account for skills.

It was not my intention to discuss the value of skill training here, and the only time I mention skill training was in reference to the peculiar nature of an upgrade to produce ~ 3 times greater benefit when applied to a pool w/o ability dice.  I can see how you got confused, my bad.  Let me state, in no uncertain terms, my opinion on training:

TRAINING IS GOOD.  DO IT.

Fourth, you have raised some good points regarding this discussion, primarily

• There is a 1/3 chance of getting no result on a boost die, but upgrading G --> Y decreases the probability of no result by about 1/24.  This may have some effect on the variance (unpredictability) of the results, but, because the expected number of successes produced has already accounted for the blank sides, it there is no effect on the point estimate.  I suspect this is offset when consideration is given to the removal of the green die… more room for analysis though.
• There are situations where destiny points may be invoked when maneuvers may not.

Fifth, I selected the "add the boost die" mechanic as a comparison primarily because it was the mechanic most comparable to the upgrade in the modification of the die pool step.  The two mechanics are in no way exclusionary, but SOME kind of comparison is needed to judge a mechanics relative power and value.  If there is another game concept it should be compared to, I'd be more than happy to run the numbers.

However, I added a second post for the clincher, because its really the take home point of ALL of this…

"All models are wrong, but some models are useful."  - George E. P. Box

### #18 LethalDose

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Posted 07 September 2012 - 07:26 PM

Finally, if "breaking things down to a its most simple view makes it easier to understand.", fine, here are the simplest facts:

• Adding a boost die will, on average, add 1/3 of a success and 2/3 of an advantage to the roll.
• Upgrading an ability die will, on average, add 5/24 successes, 1/24 of an advantage, and 1/12 of a triumph to the roll.

OR if you prefer (and you seem to), count a triumph as advantages *(again, I'll give you 4.  "Unlimited" is just stupid and misleading) …

• Upgrading a boost die will, on average, add 5/24 of a success and 3/8 of an advantage to the roll.

These results have empirical support, from both play experience and simulated data.

If you see these results and still feel upgrades are superior to boosts, and the upgrade mechanic is functioning as it should be, that's fine. It's clear I can present all the evidence and logic and not convince you.  That's okay, you get your opinion.

However, what I see concerns me, because it means a fun mechanic isn't functioning as well as it could be.  There's room for improvement and I'd like to see it be as fun as possible in the final game.

-WJL

"All models are wrong, but some models are useful."  - George E. P. Box

### #19 koralas

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Posted 08 September 2012 - 03:38 AM

Yeah, the quoting mechanism is leaving something to be desired.

I think you either missed my point on the application of statistical analysis in this instance, or I didn't explain it well.  When it comes to something like a die roll, given a large enough pool, the analysis will prove out to show that given number on a d6 will be achieved ~16% of the time, or the average result will be achieved.  However, when playing a game, you are not concerned with the result of 10,000 dice rolls, but the probability of any given individual roll.  Take for instance the old 3d6 rolling for attributes, there is a bell curve showing the likely result based on the pool of dice being rolled.  This is a perfectly valid use of statistical analysis to predict the probability of an outcome.  Rolling an individual die three times to aggregate into the same, single outcome will result in the same bell curve.  Rolling an individual die on a single roll results in a flat line with an equal probability of any side being rolled.

That said, back to the mechanic…

Upgrading the dice to proficiency works very well.  You take a die with a lower probability of success and replace it with one with a higher probability of success.  Perhaps it doesn't increase the probability of success as much as adding a Boost die, but think back on that; it is a difference between changing an existing die and adding a die.  Though, don't forget that through the upgrade mechanic you can also add ability dice to a pool when there are no ability dice left in the pool to upgrade and you still have an upgrade opportunity.

Finally, you are really focusing on using Destiny to provide the upgrade.  You feel that it doesn't provide enough of a increase in probability of success, obviously I feel the opposite.  Make Destiny a static pool that dwindles and requires extraordinary measures to renew, then sure a larger increase in the chance of success would be warranted.  However, dramatically increasing the probability of success on a die through the expenditure of renewable resource is something I would take away from the anticipation of success/failure of an outcome.

### #20 LethalDose

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Posted 11 September 2012 - 02:21 PM

This ins't ONLY about using destiny points.  Thats just probably the most common situation.  Invoking destiny is just one example of the ways that rolls can be upgraded in stage three of building a dice pool. Talents (which take XPs to get and strain to activate) are another important way (in fact, the ONLY other way I can find).  Examples include the Dodge, True Aim, and Intimidating talents, which, with this information, look like pretty poor talent options given the effects they produce, EXCEPT in some peculiar situations, that you have drawn attention to.

I agree that, given the current dice rules, adding a positive die universally trumps other mechanics.  The example you cite (upgrading YYY) is a VERY specific instance where the upgrade mechanic produces an effect vastly disproportionate to the effect created by applications of the same mechanic in different instances (anytime skill rank does not equal attribute rank).

This is a problem with the mechanic.  It was one of my original complaints.  Thank you for highlighting it.

It is my opinion that a mechanic should, at least roughly, produce consistent results when applied to different situations.

This makes the effect of invoking the mechanism more predictable, intuitive, easier to understand, and reduces the frequency with which players feel they wasted actions or resources.  It also reduces players trying to "game the system", micromanaging rolls and advancement choices to stay within these "sweet spots" where activating the mechanism is vastly more profitable.

In your example, if a player increases his ranged skill once, suddenly upgrading becomes a **** option because it barely improves their likelihood of success, where as before it made a big difference.  For your example, the probabilities to succeed at a Hard check are:

• Pool 1: YYY: 62.9% success rate, mean of -.26 advantages (32.6% chance of net advantages, with an average of 1.71 advantages when net advantages occur), and about 1/4 rolls scores a triumph
• Pool 2: YYYG: 73.2% success rate, mean of .37 advantages (46.4% chance of net advantages, with an average of 2.00 advantages when net advantages are rolled), and about 1/4 rolls still gets a triumph
• Pool 3: YYYY:  76.8% success rate, mean of .41 advantages (47.3% chance of net advantages, with an average of 2.02 advantages when it occurs), and about 1/3 rolls produces a triumph.

The first upgrade provides a MASSIVE net benefit (> 10% increase in success probability, more than an additional 1/2 advantage/roll, 14% more likely to get advantages) vs the second upgrade produces almost nothing (<4% increase in success probability, and almost no change in the advantages, about 8% increase in chance to get a triumph).  All these numbers are based on 50k simulations and consistent with previous results.

This phenomenon (adding a green die >> replacing a green die with a yellow one) is repeatable across the possible die pools. Also, if the starting pool were YYG, the first upgrade would be worth ****, and the second one would be amazing.  So, my question to you is this:

What reasonable justification can you offer to explain why the same mechanic SHOULD produce such radically different results when applied to two very similar die pools (Pool 1 differs from pool 2 by a single rank of training)?

-WJL

"All models are wrong, but some models are useful."  - George E. P. Box

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