Diversity Formula + Jan to April diversity stats

eric the espeon

maybe I just misunderstood
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Background reading: X-Act's threads here, here, here, here, and here.

The early measures were reasonably good within a metagame, but either had some other flaw or had to include the total number of Pokemon, rendering the numbers generated not very useful for comparing diversity across tiers. The most recent estimate of diversity (the last "here") relies on the cumulative usage following an exponential distribution very closely to be accurate, which has been shown to not always be the case, and will never take into account all of the little kinks in the usage graph since it only uses one data point (at 5/6 total cumulative usage).

It's always seemed like using all of the usage data (like the graphs here), rather than a specific point should be more accurate since even if the trend was extremely predictable and relied almost entirely on a single constant which could be taken as a measure of diversity, there would always be quirks in the stats. After doing some research I came across something called Simpson's Diversity Index which is commonly used for measuring the diversity of species in a real ecosystem, and can be applied almost directly to Pokemon usage stats. Basically, you take the % usage of each Pokemon (not the % per team which Doug's stats give directly, the actual share of usage), square it, then just take the sum of all the squared usages away from one.

This measure does not need a constant for metagame size added in artificially, so comparisons across metagames with different numbers of Pokemon are entirely valid. It should not run into problems with extremely large metagames or small ones, or rely on data perfectly fitting any pre-determined trend.

Anyway, what most of you will be more interested in:
Higher value = more diverse, one would be perfectly diverse, 0 would be the least diverse possible.
Code:
		April		March		February	January
OU		0.982237088	0.982308722	0.981674694	0.980915579		
OU Lead		0.97101384	0.97198333	0.971747105	0.969492976		
UU		0.986095532	0.985346613	0.98657257	0.985764676		
UU Lead		0.967771738	0.963061923	0.964481434	0.956267244		
Ubers		0.96793781	0.966426838	0.963107316	0.961904362		
Ubers Lead	0.933500605	0.927127416	0.920775591	0.904700124
Any surprises there? Explanations for the larger shifts? Is it interesting enough to be worth generating stats over longer timescales, or even graphs of comparative diversity?

Still working on the big pokestats sheet, which depending on interest may or may not include diversity numbers from the start of shoddy stats to now.
 
0.904 to 0.933 is a good increase, I like seeing variety in Ubers leads, because everybody knows how original Deoxys-S is...
 
I'm surprised that there's so little change in UU's diversity, what with the introduction and banning of the ducks and subsequent "rise in diversity" noted by many players.

Interesting read.
 
It's good to see that diversity as a whole is going up through all of the tiers here. It can't go up forever, though, so I'm just wondering at what point and when people start settling into more standard pokemon...well, more so, that is. Scizor will pretty much always be in the top there (Until gen. 5, debatably, but that's a whole 'nother bucket of worms there).

And if these stats would continue, I'd read them and take note. Just know that this has got my support, and find it an interesting take on pokemon usage. I also like the graph shown in the link, as it gives a good visual representation on how the Pokemon make an impact on diversity in tiers.
 
April -------- March
0.982237088 0.982308722
Ew. OU had like, 0 change. I know its been stale for a while, but never THAT stale, hopefully having Kou and Froslass BL will change that up.
 

eric the espeon

maybe I just misunderstood
is a Forum Moderator Alumnusis a Researcher Alumnusis a Top CAP Contributor Alumnusis a Tiering Contributor Alumnusis a Top Contributor Alumnus
How would any UU<->BL changes do anything whatsoever to OU? In either of those tiers they are still entirely legal in OU.
 

jc104

Humblest person ever
is a Top Contributor Alumnus
Actually, the UU/BL/OU status probably does have an impact on how much a pokemon is used in OU. Certainly to a complete newcomer or to someone who has not used one of the pokemon before, having OU/BL status makes it look better. People also have attachments to certain pokemon making them want to use them even after they have been made OU/BL, instead of using them in UU as they would have previously.

Its certainly not going to be a big impact, but you never know - better check the stats.

Edit - cresselia went down in OU upon its banning from UU, but Porygon-Z and Honchcrow both went up.

Also, the hype that surrounds the suspect test may encourage OU usage
 

eric the espeon

maybe I just misunderstood
is a Forum Moderator Alumnusis a Researcher Alumnusis a Top CAP Contributor Alumnusis a Tiering Contributor Alumnusis a Top Contributor Alumnus
It may have a small, unpredictable, effect on specific already rarely used Pokemon, but I really doubt this has any measurable impact on OU's diversity. Though, I should have been more clear I was reffering to diversity of OU.
 
Hmm... so by my understanding, the diversity would be affected most by changes of the most used pokemon, aka scizor. If scizor's usage went down, it would cause diversity to go up, and vice versa. Similarly, someone spamming magikarp would have to use quite a few of them to affect diversity stats, as the usage percentage gets squared, weighting the most used pokes more.
 

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