A Case Study in Probability: In-Set Conversion

[Yomo Kimyata]

Recently I wanted to just verify that the RNG was working as expected, so I converted 1,000 IOs of a six-IO set to one specific IO in the set.  The IOs were all the same level, but not the same type, and I didn't convert them all in one sitting.  The remarkable part is that I tracked how many conversions it took to hit my bogey for each one!  This is remarkable mainly because my attention span is, ooh a squirrel!

 

Anyway, it turned out pretty much as expected if you work off the assumption that the RNG is fair.

 

In 1,000 trials, mean was 5.176 conversions/IO v. expected of 5 conversions/IO.   Median of 4 (only integers counted.  Mathematically it should be 3 point something something.)  StD was 4.388 v. expected of 4.472.  Min of 1 (duh) and a max of 24 (which is far below my personal record).

 

Chance to roll desired outcome
20%
		Cumulative		Expected	Actual
Trials	Probability	Probability		Results	Results
1	0.20000	0.20000		200.000	185
2	0.16000	0.36000		160.000	151
3	0.12800	0.48800		128.000	127
4	0.10240	0.59040		102.400	103
5	0.08192	0.67232		81.920	86
6	0.06554	0.73786		65.536	65
7	0.05243	0.79028		52.429	68
8	0.04194	0.83223		41.943	37
9	0.03355	0.86578		33.554	36
10	0.02684	0.89263		26.844	13
11	0.02147	0.91410		21.475	22
12	0.01718	0.93128		17.180	26
13	0.01374	0.94502		13.744	16
14	0.01100	0.95602		10.995	20
15	0.00880	0.96482		8.796	10
16	0.00704	0.97185		7.037	10
17	0.00563	0.97748		5.629	5
18	0.00450	0.98199		4.504	3
19	0.00360	0.98559		3.603	2
20	0.00288	0.98847		2.882	3
21	0.00231	0.99078		2.306	2
22	0.00184	0.99262		1.845	7
23	0.00148	0.99410		1.476	2
24	0.00118	0.99528		1.181	1
25	0.00094	0.99622		0.944	0

 

For those of you who like graphs:

 

 

I would say, working as intended.  However, there are a few caveats.  I didn't test for this, but it felt like there was some auto-correlation (meaning that a below-median number tended to be followed by a below-median number and vice versa.)  I didn't start with the same IO each time, and I didn't do this all in one batch, so if there is a bias due to a random number seed, I didn't see it.

 

I hope at least one person finds this interesting and/or useful!  If anyone wants the raw data, let me know.  There will be more case studies in the future.

[CrudeVileTerror]

Mmmm . . . nice, neat, and tidy graphs . . . 

*drools*

[Ura Hero]

I have noticed that there seems to be some auto-correlation of some sort as well.  There have been too many times where I have converted to exactly what I converted last for it to be completely random.  My guess is the seed is not so random and that maybe there is some math involved, but I haven't dug around in the code to see.  Wouldn't surprise me to find that it is the same code that has streak breaker in it.

[Yomo Kimyata]

21 hours ago, Ura Hero said:

I have noticed that there seems to be some auto-correlation of some sort as well.  There have been too many times where I have converted to exactly what I converted last for it to be completely random.  My guess is the seed is not so random and that maybe there is some math involved, but I haven't dug around in the code to see.  Wouldn't surprise me to find that it is the same code that has streak breaker in it.

I hope to do some discovery on my next case study on this, assuming you are talking about converting by rarity.  Hopefully, my data sample will be large enough in the next couple of days.

 

One thing though:  it could really be observer bias.  I think we all have good streaks where LotG show up a lot, but then we stop there.  And you may not be consciously tracking if it took three conversions since the last one, or fifty, because when you get in the zone things move quickly.  Just a thought, but I hope to figure out a few things about the mechanics without actually getting into the code.

[Dekordius]

It's as if 5176 converters all cried out in terror and were suddenly silenced.

Edited October 25, 2020 by Dekordius

[Yomo Kimyata]

15,528 actually!

[Dekordius]

You won't get away with this, Darth Yomo!

 

On a serious note, thanks. It's nice to have mathematical confirmation of how converter intensive, on average, in-set conversions are.

 

I also now know why the price of converters has bubbled recently. ;)

Edited October 25, 2020 by Dekordius

[Yomo Kimyata]

51 minutes ago, Dekordius said:

You won't get away with this, Darth Yomo!

 

On a serious note, thanks. It's nice to have mathematical confirmation of how converter intensive, on average, in-set conversions are.

 

I also now know why the price of converters has bubbled recently. 😉

Oh, I’m a bottom feeder when it comes to converters, so that’s certainly not me!

 

I don’t want to summarize what my results “mean” because: 1. It might seem patronizing to people who already know; and 2. I don’t really want more competition.

[Hedgefund]

Just curious, has anyone taken a peek at the code for this?  I know I could and I haven't but if someone else already has, it'd be interesting to hear the findings.

[Yomo Kimyata]

8 minutes ago, Hedgefund said:

Just curious, has anyone taken a peek at the code for this?  I know I could and I haven't but if someone else already has, it'd be interesting to hear the findings.

Code is not my strength unless it's really simple, but I would also appreciate it if someone would take a look!

[tidge]

On 10/24/2020 at 6:54 PM, Yomo Kimyata said:

One thing though:  it could really be observer bias.  I think we all have good streaks where LotG show up a lot, but then we stop there.  And you may not be consciously tracking if it took three conversions since the last one, or fifty, because when you get in the zone things move quickly.  Just a thought, but I hope to figure out a few things about the mechanics without actually getting into the code.

I like to think that I am a potential victim of observer bias (try playing an all AoE character in x8 content and tell me that the RNG is 'fair') but despite many many many rolls of the converter wheel (in sets, out of sets) I don't feel a bias in the converters... for in-set conversions, to me it really does feel like the results are following a Poisson distribution.

[Troo]

24.. the RNG has hate in it's heart.

 

Spoiler

 

Edited October 30, 2020 by Troo