2d10 for Skill Checks

Blue · Mar 29, 2019

DEFCON 1 said:
Whose play are you talking about?

Considering the fact that this change was for the play at my table (of which you have no idea how often I set DCs at 11, 14, 17, 21 or whatever)... I find it funny that you've been trying to claim my change doesn't work for what I've been trying to accomplish.

Now if you're talking about just the average table... sure your math might be right. But obviously my table isn't average. So why you made the claim in your original post...

...using math for tables which are not mine makes me cock an eyebrow at your claims.

I made a bias for discussion based on D&D 5e, where bounded accuracy keeps things near the middle, which looks like your DCs could support.

If you are also skewing the results so that you need to roll something quite different, then that's your responsibility to mention it just as much as it was your responsibility to mention that you are using 2d10 instead of d20 - because that information is just as crucial to having an informed discussion on a forum. Since you took the time to give us your new DC breakdown I had thought your post was complete with all of the information needed to have a fruitful discussion. I see I was mistaken based on what you left off.

So I stand by everything I've said in a general case. If you have more table variations that you haven't told us, that's not my responsibility to read your mind.

DEFCON 1 · Mar 29, 2019

5ekyu said:
"Considering the fact that this change was for the play at my table (of which you have no idea how often I set DCs at 11, 14, 17, 21 or whatever)... I find it funny that you've been trying to claim my change doesn't work for what I've been trying to accomplish. "

But, by this logic any change you put forth for **discussion** or analysis on an open forum cannot be addressed by others. If we do not have exact and precise knowledge of what you do at your table then we cannot at all evaluate your proposal to roll 2d10.

For all we know, you only ever assign DC 23.

This sounds like the logic a guy gave me once back in a dice debate some decades ago, about how to calculate average damage from various attacks with various attack rolls using d20s.

His "logic" was that his own persona D20 rolled a 14 more than any other number and so he thought it was perfect math process to use the "mode" not the mean or not the distribution of results. So he based all of his proposals based on the d20 rolling 14.

The key part of this then becomes - the difference between 1d20 and 2d10 distribution is that whether +2 is "more" in 1d20 or 2d10 depends on where on the curve you are. So, if we cannot now assume a "common distribution of Dcs" for analysis, we have now been shut out of any analysis - dont have the tools.

So, hey, when we start from a basis of "ignoring anybody else's DCs and only counting whatever i do ay my table that you guys dont know" the only reasonable reply is to not offer any anlaysis since we dont have any info to go on.

So, basically, thats a wrap.

Yes, precisely.

I didn't make my post so that others could fix my faulty math. I put forth my post so as to tell people who would be interested that what I was doing was succeeding in what I was hoping to have occur.

When another person then shows up to claim that oh no... what I am doing to hopefully accomplish what I want is not actually accomplishing what I want... then goes on a long dissertation to illustrate it, but end up illustrating something that *isn't* what I was trying to accomplish... I of course will look at the post funny. What did you expect?

If people want go over the math and see how 2d10 compares to 1d20 for all manner of DCs and rolls for just a general discussion of whether it could work for more people or the average table... hey, go nuts! But just don't try and simultaneously claim that the results for what *I'm* looking for are wrong. Especially if your proofs are for something completely different.

It's the reason why I tried to be very clear in my posts to state what *I* personally was looking to do, and how the results worked *for me*. And if you don't want your comments about it critiqued or looked at askew... just make sure you also be very clear in stating you're taking the convo in a different direction and are going to discuss 2d10 vs 1d20 in general and not about my specific situation.

You do that, and no one will say anything.

DEFCON 1 · Mar 29, 2019

Blue said:
So I stand by everything I've said in a general case. If you have more table variations that you haven't told us, that's not my responsibility to read your mind.

It's also not your responsibility to show up in the thread and try and "fix my math"... but you chose to do it anyway.

But hey, no worries! For a general discussion about 2d10 vs 1d20, your numbers around more middle of the road DCs are probably good fodder for that. If anyone chooses to do a further deep dive on things for their own table, your info might help them.

DND_Reborn · Mar 29, 2019

DEFCON 1 said:
If people want go over the math and see how 2d10 compares to 1d20 for all manner of DCs and rolls for just a general discussion of whether it could work for more people or the average table... hey, go nuts!

Don't worry, the "Dissertation on the Comparative Distributions of Skill Checks Systems: An Examination of the Merits and Flaws of 2d10 versus d20" will be coming if I have the time and inclination to write it over the weekend.

5ekyu · Mar 29, 2019

dnd4vr said:
LOL! Sorry I didn't give you my "Dissertation on the Comparative Distributions of Skill Checks Systems: An Examination of the Merits and Flaws of 2d10 versus d20." My point was to simply present a couple examples expounding the differences between the two for a moderate DC 10 and a difficult DC 20. Which was exactly what I accomplished.

Of course they don't, that is obvious.

So you want to example the range of DC's over the range of likely applicable modifiers? That's fine, but that wasn't my intent as I felt such an over-analysis was unwarranted. I misunderstood your comment earlier, so apology accepted and I hope you will accept mine.

That is very true, but just as often everyone in a party will be involved in a check (such as perception). Other times the best person might not be there.

I feel the DCs were appropriate, even if the total modifiers weren't typical for PCs.

Here, however, you are doing the wrong comparison. I wasn't comparing the difference between 2d10 and d20 directly, I am comparing the two variants by showing the relative increase comparing someone with no modifier to someone with low modifier.

Using the 2d10 variant: For a DC 12, no modifier has a 45% of success. A +3 modifier has a 72% chance for success. That is a 60% relative increase.
Using the d20 model: For a DC 12, no modifier has a 45% of success again. A +3 modifier has a 60% chance for success. That is a 33.3% relative increase.

The point is that the 2d10 variant makes it so having a modifier will greatly increase the relative likelihood of success. You seem to be focusing on the +3 modifiers using the two systems, I'm focusing on comparing two levels of modifiers to each other and then looking at the comparison of the systems.

Perhaps your point is better illustrated with a "moderate" DC 12 and more reasonable PC-type modifiers, say +5 and + 10 (someone with proficiency and some ability versus someone with more proficiency, greater ability and/or expertise):

Using the 2d10 variant: For a DC 12, +5 modifier has a 85% of success. A +10 modifier has a 100% chance for success. That is a 17.6% relative increase.
Using the d20 model: For a DC 12, +5 modifier has only a 70% of success. A +10 modifier has a 95% chance for success. That is a 35.7% relative increase.

So, here the d20 model shows the character with the greater modifier total is more likely to succeed than the lower modifier compared to the 2d10 system. Now, that isn't to say the d20 system itself is more likely, just that the relative comparison of +5 to +10 is.

Was that more in line with your point?

"The point is that the 2d10 variant makes it so having a modifier will greatly increase the relative likelihood of success. You seem to be focusing on the +3 modifiers using the two systems, I'm focusing on comparing two levels of modifiers to each other and then looking at the comparison of the systems."

But it doesn't not consistently across the spectrum. It really depends on where you are on the curve.

Take the original example at the higher Dc range - copied below - and look at say 100 rolls...

For a d20 system the 100 rolls with +3 succeeds 20 times in 100 and the guy with +0 succeeeds only 5. thats 15 more successes. The success was increased by 15 more times in 100 tries.

At the same time, in a 2d10 the success expected went up from 1 in 100 to about 10 in 100 - which means 9 more successes. The modiefier mattered *less* in terms of the basic question of "mow many more times do i succeed.

To put it in a very basic way - lets say i off you two deals and you can only choose one:
A you can hand me $1 bill and i will give you a $10 bill back.
B you can hand me a $20 bill and i will give you a $100 dollar bill back.

Now, sure, one can get into the 1000% gain from the 4! deal vs the %500 gain from the $20 deal but when it comes to how much money you got at the end (your "likelihood of success at buying stuff") nobody is gonna look at the % and take that deal over the one that gives you more money.

So, in terms of "real value" the 2d10 in that case "lowers" the value of the +3 modifier, makes it matter less.

Thats the problem inherent with pyraminds or curves, the "value" of a shift is subjective and often not in ways that make sense.

i mean, wouldn;t you normally think that "more skill" would matter more at the harder tasks than the middle of the road ones?

***
Original d20 version

A character with a +3 needs 17 or higher for DC 20, or 20% chance of success, a character with +0 needs a 20, only 5%. So, that +3 modifier increases the likelihood of success by 300%.

New 2d10 variant

A character with a +3 needs 17 or higher for DC 20, or 10% chance of success, a character with +0 needs a 20, only 1%. So, that +3 modifier increases the likelihood of success by 900%.
***

Blue · Mar 29, 2019

DEFCON 1 said:
It's also not your responsibility to show up in the thread and try and "fix my math"... but you chose to do it anyway.

Umm, you posted something on a forum. That is inplicitly inviting comments and discussion.

You also stated your goal.

I was commenting that your math and your goal did not match. I did so in a helpful way and provided the numbers for people to check. This is useful not just for you, but for others reading your post and considering doing a similar change.

Someone else posted an example and I said why I thought it wasn't the right numbers to choose so everyone could talk about a more appropriate one.

Both of those seem not just correct behavior on a discussion board, but positively good neighborly.

If you don't want people commenting on what you post, then perhaps the correct action is not to post it in a public forum in the first place.

5ekyu · Mar 29, 2019

Blue said:
Umm, you posted something on a forum. That is inplicitly inviting comments and discussion.

You also stated your goal.

I was commenting that your math and your goal did not match. I did so in a helpful way and provided the numbers for people to check. This is useful not just for you, but for others reading your post and considering doing a similar change.

Someone else posted an example and I said why I thought it wasn't the right numbers to choose so everyone could talk about a more appropriate one.

Both of those seem not just correct behavior on a discussion board, but positively good neighborly.

If you don't want people commenting on what you post, then perhaps the correct action is not to post it in a public forum in the first place.

Hey, you know, maybe there should be a solitaire post section. Folks who just want to share something and not get any comments on it could post there.

Or at least a turn-off comments feature like FB or YouTube have.

DND_Reborn · Mar 30, 2019

(under revision for further analysis... please stand by.)

DND_Reborn · Mar 30, 2019

dnd4vr said:
Don't worry, the "Dissertation on the Comparative Distributions of Skill Checks Systems: An Examination of the Merits and Flaws of 2d10 versus d20" will be coming if I have the time and inclination to write it over the weekend.

While not quite a dissertation, these are the results of the analysis of a d20 system to a 2d10 system with the following parameters:

DC's ranged from 5 to 30
Low modifier ranged from -1 to +10
High modifier ranged from current Low modifier to +11

The d20 column indicates the number of scenarios when the d20 system resulted in a greater relative chance of success for a High modifier probability over a Low modifier probability (column 1).
The 2d10 column indicates when the 2d10 variant results in a greater relative chance of success for a High modifier probability over a Low modifier probability.
The chart shows the distributions of each system (column 2).
The even column shows the points where the two systems are equivalent and offer no increased relative chance of success between the two modifiers (column 3).
If the DC was higher than 20 + High modifier, a result of N/A was given (column 4).
If the DC was higher than 20 + Low modifier, a result of INF was given (column 5).

The intersection in the chart shows when the DC is 12 or lower, the d20 system works better overall for having a Higher modifier increasing the relative chance of success over a Lower modifier.
For a DC above 12 the 2d10 variant results in Higher modifiers having a more impactful chance of success over a Lower modifier.

Thus, to the OP, DEFCON 1, if your typical DC's are above 12 (which I believe is true for many tables as many DC's are 8 + proficiency bonus + modifier, usually 8 + 2 + 2, making 12 often a minimum, not typical) then your system should indeed allow for a greater modifier to be more impactful relative to a lower modifier.

For what it is worth, ignoring the non-NA, non-INF results, the d20 system is better a total of 34.2% of the time and 65.8% of the results the 2d10 system performs better or as well (i.e. even).

Of course, this involves a range of modifiers, but the overall general case holds true. This also does not examine the actual increased values in relative likelihood of success, only comparing which system results in a greater value, even if the improvement is minor. I won't be analyzing that deeply into it as I don't believe it will add much value to the study.

Have fun DEFCON 1, I am glad the system works to your satisfaction!

Saeviomagy · Apr 1, 2019

dnd4vr said:
Have fun DEFCON 1, I am glad the system works to your satisfaction!

My only comment there would be that your low modifier range goes too high, and your high modifier range far too high. Without certain class specific powers (which I would consider to warrant a special case), the biggest modifier you're going to have is +11, and even a +5 represents proficient and with an unusually high attribute. I think if your high/low ranges are from -1 to +5 and +6 to +11, you'll find that the point where the current skill system differentiates between high and low skill totals falls to DCs of about 5... which the book strongly hints at not bothering with.