Original Research Analysis - With Warping Points!

Games Discussion Ars Magica
1

Perhaps the key limit on magi is their warping points, and as Original Research tends to bring out warping points, I present a discussion of OR with WP in mind.

Let us consider a researcher with a +3 Risk Modifier, and with no chance to botch. Let us only consider inventions that can be complete within one season. According to the errata example of TL, his probability for a successful discovery is about 0.5201 (roll of 4; 1,2; 6; 1,3; 7; 8; 1,4; 1,1,2, plus 9; 1,5 minus a 0.11 x 0.19 chance of Complete Failure on these two 12+ results). We can therefore assume that it takes 1.923 seasons to make a discovery.

Stabilization is failed only on a No Benefit or Complete Failure, so the probability to do it is 0.8234 (0; 1; 2; 3; 6; 1,3; 7; 8; 1,4; 1,1;2 plus 9; 1,5; 1,6; 1,7; 1;8; 1,9; 1,10 minus a 0.16 x 0.36 chance of Complete Failure or No Benefit on the two rerolls). We can therefore assume that it takes 1.215 seasons to stabilize a discovery.

During the stabilization season, whether it works or not, you may acquire WP. Unfortunately, there is also a chance for gaining one more simple die (5.5) WP on each season of stabilization due to twilight. I will neglect the other effects of twilight from my analysis, for low Warping Score they are even a boon.

Each year of research one incurs 1 WP due to the longevity potion, so each season one gets 0.25 WP. This applies to both stabilization and invention seasons.

Compiling all this information together, we can deduce the following table:

[code]Mag. Stb-WP Twl-WP Ttl-Stb-WP Ttl-WP SM/WP S/SM Mi-S Ma-S He-S Mi-WP Ma-WP He-WP
1 0 0 0.3 0.78 1.27 3.14 94.14 141.21 188.28 23.54 35.3 47.07
2 0.1 0 0.43 0.91 2.21 1.57 47.07 70.61 94.14 13.59 20.39 27.18
3 0.3 0.55 1.34 1.82 1.65 1.05 31.38 47.07 62.76 18.17 27.26 36.35
4 0.6 1.1 2.37 2.85 1.4 0.78 23.54 35.3 47.07 21.38 32.06 42.75
5 1 1.65 3.52 4 1.25 0.63 18.83 28.24 37.66 24.03 36.04 48.05
6 1.5 2.2 4.8 5.28 1.14 0.52 15.69 23.54 31.38 26.4 39.6 52.8
7 2.1 2.75 6.2 6.68 1.05 0.45 13.45 20.17 26.9 28.62 42.93 57.23
8 2.8 3.3 7.72 8.2 0.98 0.39 11.77 17.65 23.54 30.74 46.1 61.47
9 3.6 3.85 9.36 9.84 0.91 0.35 10.46 15.69 20.92 32.79 49.18 65.58
10 4.5 4.4 11.12 11.6 0.86 0.31 9.41 14.12 18.83 34.79 52.19 69.59

Mag. = Magnitudes of the discovery; assumed to be doable in one season.
Stb-WP = WP due to stabilization directly: the average of (Mag.-simple die).
Twl-WP = The average of 5.5 x Twilight-probability; I assume there is no chance to avoid twilight on 2 or more warping points.
Ttl-Stb-WP = Total amount of WP gained during stabilization: Stb-WP plus Twl-WP plus 0.25 WP from longevity potion, all multiplied by 1.215 seasons.
Ttl-WP = Total WP gained for one stabilized discovery (3.14 seasons): Ttl-Stb-WP plus 0.48 due to lonevity potion during invention.
SM/WP = stabilized magnitudes per warping point.
S/SM = Seasons per stabilized magnitudes.
Mi-S or WP = Seasons or WP requireed for Minor breakthrough.
Ma-S or WP= Seasons or WP required for Major breakthrough.
He-S or WP= Seasons or WP required for Hermetic breakthrough.[/code]

In terms of warping, it is best to work on 2nd magnitude projects. But there is a definite tradeoff for time, which the magus may want to take advantage of.

At any rate even an Hermetic breakthrough should be achievable in 18-94 seasons (4-24 years) of research dedicated towards this goal, with managable levels of Warping gained (as little as 27 WP out of a 275 "maximum"!).

Of course, all these are averages, while the variance I expect would be very large.

For best results, it seems it is best to conduct original research in a mundane aura, as high Lab Totals don't help and a high aura increases the chance of entering twilight. A high Concentration and Vim score would be nice in that regard.

1 Like
2

NO ATTACHMENTS OPTION?!!

Oh well.

If you're interested, the spreadsheet used to generate the above table can be found at
enworld.org/showthread.php?t=168871

Yair

3

Thanks for the link. You introduced to me to yet another site to look into and your table is readable. I find it very interesting. I think what might be most handy about the table is if a GM wanted to explore the idea of an NPC pursueing a break through he could roughly see how long it would take and what effect it would have on the NPC in terms of warping. This is very useful way to built a well rounded character and is much faster than rolling it.

Also if characters want to pursue research in game and by the book, they can get an idea of what sort of dedication is needed from the get-go rather than investing a few seasons, getting frustrated, then begging the Gm to give them the fantastic results now! I appreciate this.

4

Yes doing your research in a mundane aura does seem to be the logical result of the rules which seems wrong to me. I also am not sure I like the warping point build up as a mechanic: still the rules are the rules. Thanks to Yair for the fascinating analysis.

5

This is wonderful. Thank you so much.

6

This is really cool.

Did you figure in the potential of rolling a Discoverys on the follow up Rolls for rolling higher on your initial roll. You know 1,6; 1,7; 1,8... 1,1,3; 1,1,4... 1,1,1...
I think you get some weird irrational fractally repeating decimal if you continue to figure Discovery and No Benefit or Complete Failure results with iterative re-rolls. My gut says it might raise the potential for a discovery by 4-5% but I totally lack the math skills to figure it out.

I discovered Google's Blockly https://blockly-demo.appspot.com/static/apps/index.html and of course one of the first things I programmed was a stress die roller. Which I then turned into a vis study simulator. They produced some interesting Data and I've considered attempting programs that simulate twilight comprehension and Original Research.

7

Thanks :slight_smile:

It's been a long time, I don't really remember. The math derivation is up there, but I'll have to check the rules again (remember the Errata! It changes things) to delve into it. To my best recollection, I just summed up the result for up to 3 re-rolls, figuring that more re-rollls are so unlikely that they won't significantly alter the statistics.

I've considered simulating Original Research, but the math turned out to be so simple I just created a table instead.

Yair

8

I did some calculations using infinite series YR7, here's my final post in a thread, but you may find the whole thread informative. My final result was P(Discovery) ~ 0.585

https://forum.atlas-games.com/t/revised-calculations-for-original-research/5738/43

I was actually thinking about doing something like this. My intuitive thought was magnitude 2 effects would be the most beneficial for a trade off between warping and speed.

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9

I've sketched a couple of tables and seem to be getting it, but I'm still planning on trying to write a simulator. Mostly I'm just playing around with figuring how to code. But part of me wants to make a simulator to see how other variables would effect things. Like the Exciting Experimentation flaw from MoH. Or some house rules like allowing the luck virtue to modify rolls, or an aura aligned in some way to favor experimentation.

My first real attempt a coding is here https://blockly-demo.appspot.com/static/apps/code/index.html#8tascn (I think) so I'm a long way off. Not exactly user friendly but I think it's accurately simulating learning from vis.

10

That looks like an impressive bit of analysis. I wouldn't be surprised if you're right (and hence I'm slightly wrong in my numbers). :slight_smile: I'm afraid I don't have the time to follow up on this at the moment.

Yes, this is my conclusion as well.

That's a cute website/tool.

Yes, simulation would let you play with these variables. I just wanted to get an idea on how best to do Original Research, and how long that would actually take. For that my analysis was enough, I feel, but it can certainly be improved :slight_smile:

Yair

11

YR7

Looking at your previous quote

The reason I have ~ 0.585 vs your 0.5201 isD that I used the infinite series estimation factoring in rerolls. In practice for small sample sizes, the observed P(^Discovery^) will be closer to 0.50 than it will be to 0.585.

12

You know, looking at this again my estimate of 0.585 is too high.

Using the errata, one makes a stress die roll, and in addition to accepting result of the experimentation, can add or subtract the risk modifier again. So, we know that the +3 is the best one to take since we can use add any number from 0 to 6 to the stress die roll in order to get a discover.

So, it goes like this:

roll a 4 with a probability of 0.11. Result is 7, "no benefit" and can add +3 again for discovery.

roll a 5 with a probability of 0.1 Result is 8 "complete failure" which according to my interpretation, is literally a complete failure and you do not get a discovery.

roll a 6 with a probability of 0.11. Result is 9, "something else or story" and can add +1 again for discovery.

roll a 7 with a probability of 0.1 Result of 10 is a discovery.

roll a 8 with a probability of 0.111 Result of 11 is modified effect. Can add -1 again for discovery.

roll a 9 with a probability of 0.1 result is 12 - reroll twice, can add -2 again for discovery.

roll a 10 with a probability of 0.01 result is 13 - can add -3 again for discovery.

Now, it seems that our base P(Discovery) = 0.541

Now on this result of reroll twice, we must accept the results, which means on a result of 12 or 13 we can still get a botch of failure that will destroy the discovery. I am explicitly assuming a botch or failure nullifies any other result. I am assuming that further "discoveries" are from the normal table of discovery results, not an original discovery used for pushing the bounds of hermetic magic. I am also assuming that a result of a failure or botch stops the endless rolling.

Assuming 4 botch dice due to doing the research in no aura at all.

First we need to look at this in terms of a single roll per the two rerolls:

P( reroll on discovery chart with +3 modifier) = P(roll a 9+ on a stress die) = which is: P(9)+ P(1,6 to 10) + P(1,1,(3 to 10))+P(1,1,1 (anything)) = 0.1+0.05+0.008+0.001=0.159 = P(R)

P(failure or botch)=0.134 = P(BF)

P(not a failure, botch or reroll) = 1-0.134-0.159 = 0.707 = P(something) = P(S)

So, per reroll we are concerned with a botch or fail since that will invalidate our original discovery.

P(Botch or Fail including all rerolls) = P(BF)+P(S)*P(BF)+P(S)P(R)(P(BF)+P(S)*P(BF)+P(S)P(R)(P(BF)+P(S)*P(BF)+P(S)P(R)(P(BF)+P(S)*P(BF)+P(S)P(R)....

=P(BF)(1+P(S))/(1-P(S)P(R))=(0.134(1+0.707))/(1-0.707*0.159)=0.2577

So, we have D= 0.541 - 0.2577*0.11=0.5127.

Using my previous formula of D/(1-(nr+r)) = P(Discovery) given , n =0.2660, r=0.059 then the net P(Discovery) = 0.554

YR7 after looking at what you did, I think it sort of works, but underestimates the variability of the process. i.e. A random number of boxes with a random number of objects inside is a stochastic probability (I think) and can be trickier than at first thought.

I'll be playing around with this on a spreadsheet and see what I can get.

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13

And if you lower or eliminate the risk of botch with lab saftey? How does that effect it.

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14

Assuming with safety you reduce the chance of a botch to 0, you only have a 0.1 chance of Failure.

P(S) from above = 1- 0.1 -.159 = 0.741

=P(BF)(1+P(S))/(1-P(S)P(R))=(0.1(1+0.741))/(1-0.741*0.159)=0.1974

So P(n)=1-.541-.059-.1 = 0.3

P(D) = .541

(0.541 - 0.11*0.1974)/(1-(nr+r))=0.5612

Assuming I've done everything right (usually I haven't I'm endlessly picking over my stuff in finer detail so, if you reread later the numbers might be different.) The old probability with 4 botch dice is .5127

So your odds improve by .5612/.554 -1 = .0130 or 1.3%

I think. The effect isn't that high. But say, we have a +3 experiment done in a +5 aura, so 9 botch dice...The net chance of discovery only drops to 0.5477

If we increase to a +10 magic aura, so 14 botch dice, the net chance of discovery drops only to 0.544. We're talking

Note fiddling with the number of botch while small on the effect of discovery, will also affect the chance of stabilization and losing one's work. You can on a bad enough disaster roll lose all of your work. This does become quite high in a +10 aura, 7.7% chance of losing however many season's worth of work to get the discovery in the first place is not inconsiderable.

15

The variabikity will surely be high. I noted so in my original post. My purpose, however, was just to get a scale of what making a breakthrough entails.

For the record - I wouldm't allow OR in my game rifgt now. Stories are better generated by integrating hedge, ancient or rival magic IMO.

16

I agree in principle - but would remark, that OR can be necessary to complete research started by integration.

Cheers

17

Part of the problem is that OR is too easy, as written. We have a poor idea of why the Order has not produced more breakthroughs, unless we figure out how hermetic magic was less effective than before. In another thread someone was talking about lowering the difficulty of all spells to 1 before parameters. Implying that say, in the past hermetic magic cast the same spells at higher levels. It would be IMO a Major discovery to lower the difficulty of just one TeFo combination - and I would require all five combinations done for an Art before it could properly understood and distributed across the Order.

18

Part of the problem is that OR is too easy, as written. We have a poor idea of why the Order has not produced more breakthroughs, unless we figure out how hermetic magic was less effective than before. In another thread someone was talking about lowering the difficulty of all spells to 1 before parameters. Implying that say, in the past hermetic magic cast the same spells at higher levels. It would be IMO a Major discovery to lower the difficulty of just one TeFo combination - and I would require all five combinations done for an Art before it could properly understood and distributed across the Order.

19

What's the definition of Easy?
It takes a fair amount of time. It causes a fair amount of warping. Not every magus is going to be interested in pursuing research because of the warping. That is unless I'm reading the table improperly. 2nd magnitude effects used to discover a minor breakthrough would grant 13.59 wp, right? And it takes 47 seasons, which is nearly 12 years. Like the theoretical maximum lab total of a magus, you can easily add half again as much time to the discover when you factor in other things that pull him away from invention, so 18 years for a minor breakthrough is not at all unreasonable. Right?
Am I missing or misreading something?

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20

Agreed.

I also don't like other aspects of the rules, however, especially that Intelligence and Inventive Genius don't add directly to it. It would also probably be cooler to reward higher-magnitude spells, high Arts, and high auras. I once tried to come up with alternative rules for OR; I'm not sure how well that succeeded. I fear they only made OR easier :blush:

Not every magus, certainly, but enough for things to start to get weird. You have an entire House (well, half a House) devoted to this kind of thing, after all. And other magi, from other Houses, will surely join the fray. Given the long Hermetic history, and the number of magus-years devoted to OR this entails, I think we should have lots of Discoveries. By these rules. Which raises all the troubles Heaven's Thunder Hammer raised.

Yair