#Admit it: PIR buffs itself more than other units

30 messages · Page 1 of 1 (latest)

kindred axle
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Many people know anecdotally that PIR tends to buff itself more than the other units. Recently I raised this matter and we've done some experiments. Bubbles tested PIR with one other unit on board and the buffs seemed random. Berto did another test with nine units on board (pictured). PIR stayed on the board for 34 turns and it buffed itself seven times. Now, does it mean anything?

Using statistics, it is possible to compute the probability of this happening if PIR buffed units truly randomly. For example, with nine units on board, we'd expect PIR to buff itself with 1/9 probability each turn. So what's the probability of PIR buffing itself seven times in 34 turns if it indeed buffed units randomly?

The probability of that happening is less than 3% (calulations below for the interested). In science, people usually consider things significant if that kind of probability (p-value) is less than 5%. It means that Berto found something.

I played two ranked games with PIR and have written down the number of units on board each time (2-8) and whether PIR buffed itself. In 12 turns, it buffed itself 9 times. The probability of that happening if it buffed randomly is 0.0009. It's not 1%, it's about one-tenth of 1%. It's like the probability of finding a $100 bill on the floor in a shopping mall. It just doesn't happen for most people.

Now, if you don't believe me, play PIR (making sure that there are multiple units on board at least sometimes), write down the buffs, and see what you get.

Here's the science for the interested. One can use the Poisson binomial distribution (https://en.wikipedia.org/wiki/Poisson_binomial_distribution) to model the situation. Here's R code which you can run online at https://rdrr.io/snippets:

library(poisbinom)

units_on_board = c(2,4,6,7,8,2,3,3,4,4,3,3)
times_pir_buffed_itself = 9

p_value = 1 - poisbinom::ppoisbinom(times_pir_buffed_itself - 1, 1/units_on_board)
print( p_value )

Just modify units_on_board and times_pir_buffed_itself

berto_pir_experiment.webp
Poisson binomial distribution

In probability theory and statistics, the Poisson binomial distribution is the discrete probability distribution of a sum of independent Bernoulli trials that are not necessarily identically distributed. The concept is named after Siméon Denis Poisson.
In other words, it is the probability distribution of the
number of successes in a collectio...

ripe stirrup
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12 is not sufficient sample size dude

kindred axle
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1939 needs to admit that PIR buffs itself more than expected, whether due to a bug or something else, because Bubbles won't believe it otherwise, citing "small sample size"

ripe stirrup
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Dude

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Its 12 instances

kindred axle
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If the effect is strong, you don't need many samples

ripe stirrup
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Well in 1 of my samples it buffed itself 7 times and the other unit 18 times

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Therefore it's actually bias to other units

visual garden
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What is this suggesting

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1939 should admit to something they haven't even denied?

blazing aspen
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this is the worst post to suggestions yet, including the guy who wanted Amogus in Kards

ripe stirrup
visual garden
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Ok, what does the suggestor want

kindred axle
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I want exactly what I have written in the title

visual garden
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That 1939 admits(?)

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How does that look like

kindred axle
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they release patch notes mentioning that, for example, PIR was bugged, "thank you Edgelord for bringing our attention to this"

visual garden
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Then shouldn't this go into bug reports

ripe stirrup
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If you actually think it's a bug then put it in bug reports and move on

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If you think there's anything deeper to it, then please just keep it to yourself instead of these tinfoil hat posts

kindred axle
smoky pewter
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I'm no statistics pro but if there is indeed something not random about the PIR's buff, then it would be useful to test this a good number of times until you can be sure that this was not a random, albeit extremely unlikely, occurrence right here

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This is probably enough to attract some attention but I doubt it is enough to prove a bias.

kindred axle
ripe stirrup
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Over my 104 instances it was bias to buff the other unit

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Your 12 instances mean jack

kindred axle
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You tested with two units on board. The bias seems to reveal itself when there are more units

ripe stirrup