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

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.

@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:

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:

Upgrades cost:

• 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:

• Advantages, frequent by-products of your rolls and the rolls of your allies
• 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.

Second, players should be feel that upgrading is important, if for no other reason than expending a destiny point, well, should FEEL major. Calling on destiny should FEEL like it has impact. Given the current structure of the dice and effect of an upgrade, I see this mechanic as a failure: A destiny point spent to upgrade an ability die adds about .21 successes, practically 0 advantages (real number is 0.04167), and about an 8% chance to score a triumph (see more below). A destiny point spent to add an ability die is different (adds about .625 successes and .625 advantages) .

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

MILLANDSON said:

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:

Well ****. That's embarassing.

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.

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.

koralas 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.

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

koralas 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.

Also when you start talking about about advantages, you make the claim:

koralas said:

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:

.6666 - .625 ~ 0.04 more advantages per upgrade

A boost provides:

.6666 - 0 = .6666 more advantages per upgrade.

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:

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:

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

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.

You ask:

ynnen said:

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

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?

Timberboar said:

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 ).

@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.

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.

LethalDose said:

So… non-issue. Carry on, then.

*twirls baton and wanders away, whistling*

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.

Quicksilver said:

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

LethalDose said:

LethalDose said:

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:

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:

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 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:

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:

No Skills aren't upgrades, they are Skills, but they factor into how many Ability dice are added to a pool and then subsequently upgraded to Proficiency dice for free based simply on the way the character has been crafted. But you talked about eschewing buying skills beyond the characteristic value, and increasing skill beyond adds dice, yes not part of the upgrade mechanic, but still an important part of this discussion. Especially when talking of using traits to upgrade dice (or downgrade for that matter) as opposed to buying traits that apply Boost. The issue with this is that it is cheaper to buy the skill to upgrade or add dice, there are few traits that allow you to upgrade or downgrade dice (and yes they can be costly in XP as well as spending on the path to get to that particular trait), and while there are more traits that allow the addition of Boost, they are not common, nor are they generally cheap either.

LethalDose said:

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:

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.

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…

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

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.

Take a character with Agility 3, Ranged (Light) 3, firing a Blaster adds three Ability dice to the pool, then upgrades them to three proficiency dice, then add the appropriate difficulty dice, finally the player may opt to spend a Destiny point to add one upgrade, but since there are no ability dice to upgrade, they instead add a new ability die to the pool. If the character has any other method of continuing to upgrade, they can upgrade that die to a proficiency die. Note that you could use the ability/item/whatever to add the die, then spend destiny to upgrade it as well, but that is a little matter, especially if the character doesn't have any method to upgrade in this "step" you can still spend destiny to upgrade a die, in this case adding a die instead. Also, as long as there is Destiny available, the player may always opt to spend it to increase the chance of success. Circumstance will dictate whether a Boost die is added.

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.

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

Hi everyone! A couple other things to consider:

• Proficiency dice have more sides than Ability dice, but both still only have one blank side. This means the odds of rolling a blank are reduced. (This also works with Boost dice, since they have only six sides and two are blank.) Since Proficiency dice also have proportionally more sides with successes, this means you're increasing the odds of generating successes in each roll. While statistically Boost dice may offer a big boost (pun intended) to the probability of success, their probability of also rolling a blank is also increased over all other dice.

• Proficiency dice also have more sides with double results compared to their total number of sides. In a game where you're more limited in your total number of dice, double results can be far more beneficial. Their benefits are also really hard to calculate statistically, and I only say that because I know we had a hard time calculating it.

• The benefits of a Triumph are not easily quantified. Yes, there's a lot in this book that talks about different ways you can spend a Triumph. However, these are just some of the ways Triumphs can be utilized, and GMs and players are encouraged to be creative. Basically, Triumphs (and their Despair counterparts) are intended to be narrative changers. You're in a desperate fire-fight, and you take a wild shot as you run across the room, missing but rolling a Triumph in the process? Hey, you skid to cover next to a barrel of lubricant-oil, and you're pretty sure if you set it on fire, the thick smoke will let you escape the fight unharmed. Just as rolling a despair on that same roll might leave your gun out of ammo. Suddenly you're pinned down, no weapon, and surrender might be the best option.

Just a couple possiblities to consider. Thanks again, everyone. This kind of mathematical analysis is very impressive, and shows a real willingness to go above and beyond in this beta test.

Hey Sam! Thanks for the input on the thread!

First and foremost, if the developers feel the upgrade mechanic is functioning as it should be, then its working as intended, and its fine. I wanted to be sure that the potentially problematic peculiarities in the system were brought to their attention (at this point, they're well documented above).

But for clarity, its obvious that proficiency die IS better than the ability die (and the boost die), but that's not the issue. The question I'm trying to answer is if the improvement (increased reliability, more likely to produce both successes and advantages, possible triumphs, etc) is as effective as intended. This became a question only after seeing the mechanism function and how my play test group responded:

"it doesn't feel right"

As far as the difficulty of producing these estimates, Monte Carlo simulation (randomly generating process results, and observing the pool of results) is a great way to estimate values and effect magnitudes when the underlying process is well understood (as in this case, we have all the necessary probabilities associated with the die faces, and how to interpret them). They aren't hard to produce with a bit of code, which I can make available if you want.

And there is a problem with reporting results as the probabilty of success and then number advantages separately, because these values are not independent. This means the more advantages you roll, the less likely you are to succeed at the task at hand. However, it is extremely difficult to represent these results and relationships simultaneously, even with graphics (which I can't figure out how to post here) or without logisitic regression models (which I doubt anyone here would understand, its just a specialized tool my field uses). The issue of so many advantages has been brought up in the Dice Mechanic Thread.

Finally, the Beta is the only time that systemic changes can be made to solve these problems (if they are problems). I hardly see this as going "above and beyond" in a beta; its the least the testers can do to give the best input possible to ensure the best possible product. I think this game looks to be the best Star Wars game produce in over 15 years. I want it to be as great as possible.

-WJL

I have little to add really, the statistical analysis is nice, and by the way: logistic regression is fiddly but entertaining. Had fun with that earlier this year.

As for perspectives on this issue. In my experience my players rarely think twice about these things, more "good" dice is better either way (if its a d6 or d12 makes no difference, although a d12 is bigger and therefore - as with anything american - better ). And yes, I see the issue you talk about and I can understand that for some this could be considered a problem, yet people still play the lottery (I even do that sometimes, when I feel "lucky" ) . And while I have no solution to this issue, changing the dice is perhaps a bit late as some has mentioned, although it could be done I assume, but how would that impact this? My probability math skills are lacking, so I won't try to meddle with dice and faces.

On the other hand I am kind of interested in the solutions you have thought of, if any.

Yeah, the other thing to bear in mind is that it's not necessarily the probability of getting a single success or advantage that matters for any given roll, but more the probability of getting any particular outcome . There are some outcomes that are not possible (triumph) with just ability + boost, and some that may not increase in probability (double success, which isn't present on the boost die, but I suppose is simulated by one success on the ability die + one success on the boost die). Then again, the only way to get three successes (even if a vanishingly small chance) is with ability + boost, so it does seem a bit wonky there…

I don't have the time (or really the statistical background) to work out the exact odds, but I suspect that if you're after more successes or advantages - rather than just a higher chance of at least one success or advantage - then you're better off with upgrading rather than boosting.

@ Jegergryte

I appreciate the feedback, but man… I feel this

Jegergryte said:

is a wicked pandora's box I'm very hesitant to open, because of the following:

• Small changes here can lead to a myriad of unintentional consequences
• I think there are other dice mechanic issues which need to be addressed simultaneously (too many advantages produced, difficulties seem harsher than titles imply)
• The desired magnitude of the effect is ultimately up to the devs.
• Offering specific solutions invariably leads to the destruction of the thread, via bickering about details.

But, to tempt fate, I'll try offer some response to your direct question. To painted in incredibly broad strokes, my solution would consist of one or more the following:

1. Widen the gap between a proficiency die and an ability die (main reason for this thread)
2. Reduce the symbols on both ability and difficulty dice (serves #1 and other mechanic issues above)
3. Remove at least one advantage from boost die
4. Remove artificial [imperfect] symmetry between Ability/Difficulty dice and Challenge/Proficiency dice

As a note, I will absolutely not respond to any criticism or discussion re: any of specific points above in this thread because its not the point of this thread.

Number 1 could be accomplished by making the ability dice "worse" (remove symbols, add blank faces, addressed in 2), which i think would nicely deal with the "sweet spot" problem I've identified. However, this solution necessitates a change in the difficulty die configuration, despite what I offer in #4, and could worsen the difficulty issue I think exists (but haven't posted about yet). It also causes a problem of 'nerfing' skill training, as Quicksilver pointed out earlier in this thread (an issue I had NOT considered). Maybe the proficiency die needs to be made "better" instead, not sure. Number 3 I think moves to address the issue of producing too many advantages (my players had trouble figuring out what all those successes meant on a failed roll), but also shifts the value of the comparison point. I asked for alternative comparisons, and none have yet materialized.

I never meant to imply the boost die was too powerful because of this comparison, I just needed a point of reference with established and demonstrable costs. The main thrust of the thread was to provide an objective, evidence-based evaluation of the upgrade mechanic. In light of the evidence and how the mechanic is presented, I think it under-performs.

I took a look at the configuration of the WHFRPG dice, and based on my limited experience throwing those, I can say I like the asymmetry between the "good" and "bad" dice, the empirical success probability, and the frequency with which boons (aka advantages) are produced better than what I've seen in Star Wars. I think there is value in understanding how decisions were made regarding the configuration of those dice, before stating how these dice 'should' look. The same mind conceived both sets, I just don't have the insight on how Jay's goals and ideas evolved from there to here, or if the new dice met those new goals.

-WJL