Pokemon Go and Individual Values

In Pokémon Go, each Pokémon has three values that determine how well it will battle: its moveset, its level, and its individual value (IV).

The moveset are the attacks that your Pokémon can use — things like mudshot and fireblast and hydropump — and can’t be changed. Every type of Pokémon has a moveset that is optimal (i.e. gives the highest possible damage per second of attacks available to you), such as Water Gun/Hydropump for the Vaporeon, and this will strongly affect how much damage you do.

The Pokémon’s level is marked by the arc in the background, which stretches from the very bottom left (Pokémon with 10 CP), to the bottom right (Pokémon that have the same level as their trainer does). When you click ‘power up’, you are increasing the Pokémon’s level, which will increase its HP and CP in accordance with its IV.

IV is the only piece of information about your Pokémon that is entirely hidden from you in the game, although it can be calculated using level, HP, CP and the information that your gym leader provides you, through external calculators. IV is broken down into three categories: Attack, Defence and Stamina, each of which take an integer value from 0 to 15, with the total IV simply being the sum of all these values (often presented as a percentage of the maximum value). So, what is a good IV for a Pokémon to have?

Thankfully, this is the same as rolling three sixteen-sided dice from 0 to 15, and we can use familiar maths to calculate both the average roll of m n-sided dice, m\cdot\left(\frac{n+1}{2}\right), and the standard deviation, \sqrt{m\cdot\left(\frac{n^2-1}{12}\right)} . This gives an average IV of 22.5 (50%) and standard deviation of 8 (18%). This means that two-thirds of all Pokémon have an IV between 14.5 and 30.5 (32% and 68%).

To illustrate this graphically, let’s consider every single possible roll of these three dice, written in code here:

for x in 0:15
  for y in 0:15
    for z in 0:15

This results in the bell curve shown in Figure 1, because there is only one way to generate 0 (that is, all dice roll zero), but there are many ways to generate a roll of 22 (192 ways, in fact).

Figure 1: Total IV plotted against the number of possible ways to achieve that IV. This shows a very strong weighting towards the centre.

While it is useful to know how rare your Pokémon is, deciding on whether to keep it should be based on how likely it is to have at least its IV; otherwise, it’s easy to see that 0 and 45 are equally rare. The probability of a random Pokémon having as good an IV or better as your current Pokémon is given by the curve shown in Figure 2.

Figure 2: The probability of finding a Pokemon with equal or greater IV than your current.

This suggests that Pokémon with 80% or 90% IV are incredibly rare, which matches up with what the Gym Leaders say: the top-tier evaluation of a Pokémon places it into this high (80%+ category). Let’s have a look at some particularly interesting IV:

  • 23 (49%) — this is the median IV, or the 50th percentile: half of all Pokémon are equal to and better than it, while half are worse than it;
  • 27 (60%) — this is the tier occupied by the top third of Pokémon;
  • 30 (66%) — the top fifth of all Pokémon have an IV of thirty or higher, meaning 80% of all Pokémon have a lower IV than 30;
  • 34 (76%) — your Pokémon is in the top 10% of all Pokémon;
  • 37 (82%) — at this point, your Pokémon is considered to be top-tier by the Gym Leaders when you select ‘Appraise’, and they are in the 94th percentile;
  • 41 (91%) — this is finally over the 90% IV mark, and represents the top 1% of all Pokémon. Anything with this IV almost has the best base stats of its kind;
  • 45 (100%) — the ultimate Pokémon. Each Pokémon you find has a 0.02% (two in ten thousand) chance of having this IV, making them incredibly rare.

To illustrate how rare these values are, let’s look at Gyarados: you need to catch a hundred Magikarp to make a Gyarados, so what is the highest Magikarp you’re quite sure you can catch (>90% chance)?

For your first Gyarados, you would be expecting an IV of at least 38 (84%). Your second Gyarados should be even higher, with an IV of 40 (88%), but after this, your probability starts falling off sharply. Your third Gyarados should have at least 41 IV (91%), but you can’t be sure of getting a 42 IV Gyarados until your fifth, or a 43 IV one until your tenth! At that point, the chance of you having a 45 IV (100%) Gyarados is 20%, so if you’re lucky you may have a truly vicious sea monster!

For some anecdotal evidence, I have caught 4327 Pokémon, meaning that I should expect to have found about one 100% Pokémon by now. And I have!

A Zubat.



Pokemon Go and Individual Values

Misrepresentation Pt 2 — The Senate

I didn’t analyse the Senate results in my last post, because counting had barely begun. While results still haven’t been finalised (and won’t be for a while), enough has been done now that it’s qualitatively useful to examine them. There are 76 seats in the senate, twelve for each state and two for each territory, of which 72 have been provisionally assigned and four are still in doubt. Excluding the latter, the seats are being allocated as follows:

  • Coalition: 30 Seats (45% of assigned seats)
    • 35% of popular vote
  • Labor: 27 Seats (38% of assigned seats)
    • 30% of popular vote
  • The Greens: 7 Seats (10% of assigned seats)
    • 9% of popular vote
  • One Nation: 3 Seats (4% of assigned seats)
    • 4% of popular vote
  • Nick Xenophon Team: 3 Seats (4% of assigned seats)
    • 3% of popular vote
  • Justice Party: 1 Seat (1% of assigned seats)
    • 2% of popular vote
  • Jacqui Lambie Network: 1 Seat (1% of assigned seats)
    • 0.5% popular vote

This gives a total misrepresentation of 33.8% (remembering that 0% is a senate that perfectly represents the popular vote, and 100% is equivalent to seats being assigned at random), with the usual suspects—Coalition and Labor— gaining the most benefit.

Parties gaining a benefit from this misrepresentation are Labor (7.63%), Coalition (6.3%), Greens (1.2%), NXT and JLN (0.9% each). The other parties that won seats lost on misrepresentation, with One Nation ending up 0.1% short, and the Justice Party losing 0.5%.

The biggest losers, however, were the Liberal Democrats, who gained 2.1% of the popular vote (enough for a seat and a half), but didn’t gain any seats, with the Animal Justice Party, Christian Democratic Party, Family First, and Shooters, Fishers and Farmers parties each missing out on more than 1% of the vote (from 80% of a seat for the AJP to an entire sear for SFF).

These results will gradually change over the coming months, but as a provisional analysis it does offer some qualitatively useful information:

  • The Senate is more representative than the House of Representatives (33.8% vs 46.5% misrepresentation);
  • The system disproportionately favours the two major parties (with a total of 14% misrepresentation, four tenths of all misrepresentation);
  • Minor parties with support from many states lose a significant proportion of their vote’s value: eleven parties had more votes than JLN, but since JLN supporters were almost entirely localised in Tasmania, they managed to get a seat.

As an interesting side note before the end, I decided to see the votes-to-seat ratio of each state (and territory): Tasmanians have the best representation, with only 43 thousand people per seat, while NSW has the worst, with 635 thousand people per seat (meaning a Tasmanian has about fifteen times the voting power in the Senate as a New South Welsh person).

Ultimately, the Senate was designed to serve the interests of the colonies before they became states: it was feared that the population of the large states would leave the smaller states without a voice, and no one wants to completely cede a say in their government. With that, it was decided that all states should have the same number of votes regardless of population, to enable the smaller states to stand up to the populous ones if their interests were not being served, and the Senate was seated according to state.

Of course, this is no longer the case: partisan politics now controls the country, and Senators represent their party rather than state, but this relic of federation still constitutes a significant proportion of the misrepresentation.

The misrepresentation—in both the House of Representatives and the Senate—is deliberately exploited by politicians to maintain the status quo, and since the four largest parties (Labor, Liberal, Nationals, LNP) benefit from it, and control two thirds of the vote, it will never change because it will never be in their interest to change it. Political parties don’t want better democracy, they want more power: the Coalition and Labor aren’t really fighting each other, they’re fighting the minor parties so they can maintain their duopoly in perpetuity.

Misrepresentation Pt 2 — The Senate


Misrepresentation is used in politics as a measure of how well (or badly) a political body represents its constituents.  The simplest form is the difference between the percentage of votes a candidate or party receives, and the total amount of representation they have in parliament e.g. Party A receives 20% of the vote, but only 10 out of 100 seats available in parliament, there is a misrepresentation of 10%. The sum over all candidates/parties is the total misrepresentation.

Total misrepresentation can range from 0% (the parliament exactly matches the popular vote) to 200% (the result is entirely in favour of a party who received zero votes), with 100% being the result you’d expect from assigning seats at random.

In the recent election in Australia, the total misrepresentation for the House of Representatives (which forms the government) was 46.5%; that is to say the total disparity between seats won in parliament and the popular vote is extremely significant. The largest misrepresentation comes from the Coalition (Australia’s conservative party), who won 15.2% more seats than they would have if the votes were proportional. The only other significant winner from this system was the Labor party (ostensibly left, but is doing its best to pursue the Coalition rightwards), with a misrepresentation of 11% in their favour.

Nothing more clearly demonstrates how rigged this system is in favour of the duopoly than the only other party with a large misrepresentation: The Greens. With 9.2% misrepresentation against them, instead of receiving 9.2% of seats (14), they received 0.7% (1).

A misrepresentation of 46.5% indicates that our electoral system is deeply flawed, even if we accept its populist nature. Deep changes need to be made, but there’s no political will to make them, as the winners of this system have no interest of losing their control of the political apparatus, and no one funding them wants to risk competition from grassroots movements.


30 Days of Pride — Week 4

My final post of thirty days of pride! A bit belated, because I got distracted by the Australian election, but here nonetheless.

23: Share a picture of your family or friends.
My Family.
24: Share your greatest achievement.

My greatest achievement would probably be getting into the Ph.D. programme at the University of Queensland. I think I’ll elaborate on this when (if!) I graduate!

25: Take a selfie! You’re beautiful.
2016-06-18 12.18.51.jpg
Photo of me in bad lighting!
26: Who in the queer community (past or present) inspires you?

Julia Serano: her manifesto Whipping Girl had a huge impact on me when I was first exploring queer literature.

Florence Nightingale: a lesbian superhero who saved a huge number of lives; what is there not to love?

27: Treat yourself today, and share a picture of it.

I was actually flying back from a conference in the USA this day, so here’s my delayed treat!

2016-07-05 08.23.35
Muesli, absolutely loaded with fruit and Manuka honey.
28: How are YOU going to change the world?

I’m a scientist who is currently studying quantum mechanical effects in biological systems. I’m hoping to use my research to help create more efficient organic solar cells, organic LEDs, and higher-yield crops.

The future is in renewable energy and I want to help us towards that future.

29: What do you love most about yourself?

To be honest, this one took the longest time to think of an answer to, but I think I would have to say kindness. I love that other people see me as kind, and I love being able to help them.

30: Why are you proud to be queer?

Because I’m part of a community of people who want to make the world better; that want to help the poor and disenfranchised; that respects consent in a way that just doesn’t exist in the monocishet community.

I’m proud because I can be myself, a poly lesbian who’s an active intersectional feminist, and have that identity be respected and even encouraged.

My queerness is tied with my sense of community, with my relationships, and my people: they are something to be proud of.


30 Days of Pride: Week 1 | Week 2 | Week 3 | Week 4

30 Days of Pride — Week 4

Australian Election 2016

For those unaware, the Australian Federal election is on this coming Saturday (02/07), and there’s a real risk that the Liberal-National Coalition (our conservative parties) will regain government for another three years. This would be terrible for numerous reasons, as I contended in a post on Facebook:

If you intend to vote for the Coalition this election, you are saying that you care more about perpetuating the myth that conservative governments are better at economics than the welfare of me, my friends, and my people.

You are saying that the rich and the powerful matter more than the poor and dispossessed.

You are saying that the messages of demagogues, xenophobes, and homophobes are more enthralling to you than egality, equality, and equity.

You are saying that your beliefs are lacking empathy and completely antithetical to my conception of morality.

You are saying that you personally do not care if I am hurt or harmed.

You are, in short, saying that you are not my friend, and I would appreciate you make this manifest by removing yourself from my friend’s list, rather than continue this charade with false-face and false-heart.

The Coalition wants to give businesses a $50 billion tax cut, while cutting welfare. They say that this would end up being profitable in their models … but their models assume that government spending doesn’t impact people’s well-being, which is clearly a ludicrous assumption.

Meanwhile, they want to hold a plebiscite to allow same-sex marriage. If this sounds good, it’s not: the other major parties (Labor and Greens) promise to legalise it through an act of parliament, in the exact same way the Coalition banned it in the first place. The plebiscite will cost over $100 million, and they intend to ignore the result: if the plebiscite shows that the Australian population are willing to endow queer people one of their rights, then the Coalition will allow a conscience vote, rather than a binding one. It’s a farce.

As a proud queer woman, and as an intersectional feminist, I can’t stand the thought of allowing these racist, xenophobic, queerphobic people to run our country and throw their full might against the poor and minorities of all stripes. If you choose to vote for them, you are favouring demagoguery and trickle-down economics, and I have absolutely no idea why you read this blog.

Australian Election 2016

30 Days of Pride — Week 3

This is my third week of the ‘30 Days of Pride‘ challenge, celebrating pride month; links to the previous weeks are available at the bottom of the page!

Day 15: Name a company that is positive force of change for the queer community.

To me, positive force of change for the queer community implies improving the lot in life for all queer peoples in a truly intersectional manner. This is making it very difficult for me to think of a company: my experience of companies, especially corporations, is that they focus almost exclusively on cis, white, able-bodied, and young LG people, completely ignoring the rest of the gender and sexuality alphabet, and amplifying already-existing social privileges.

Disabled people are often completely ignored. Bi people are erased. The most persecuted group amongst us, trans women of colour, see their existence wiped from our history. The poor don’t gain any of the benefits of the gradual assimilation of queer people into the broader community, but suffer the most from the losses.

Ultimately, I don’t think you can be a positive force for the queer community in its entirety as an organisation that generates profits from the labour of others: those profits are stolen wages, and contribute to the perpetuation of economic inequalities that hurt the queer community so strongly.

Day 16: Name one of your best qualities.

I find it really hard to think of good things about myself (thanks depression!), but the quality I hold closest to my heart is kindness. I want to help my community, I want to help people, I want to make everyone happy. Kindness is one of my principal values, and I hope that it’s something that can be recognised in my behaviour.

Day 17: Share something you’d like to improve about yourself.

My mental illness, or coping strategies for it. I have disorders of anxiety, depression and dysphoria, and it very much impacts my life: the past fortnight, for example, I was panicking so much that I couldn’t get to work. I’m working hard to improve that, and hopefully I’ll have a strong enough grip on it soon that I can cope, at least to external observation, as well as a neurotypical person can.

Day 18: Name someone you know who inspires you. Why?

I’ve been thinking on this one for a while. Previously, I have listed scientists I know, such as Mahananda Dasgupta, Tamara Davis, and Ivan Kassal, but I’m not entirely sure that’s true anymore. Now I’m inspired by the fellow members of my queer community here in Queensland, my partner, and my other friends.

Perhaps the friend who inspires me most is Kaitlin Cook (those of you on Twitter may know her as @StarsTooFondly). She’s a final year PhD student, and has done amazing sci-comm work, all while managing to be an amazing and supportive person. There are too many things to say here, some personal and others that should be shouted to the world, but I’ll leave it at this: love you Kaitlin, and hope the future treats you well ❤

Day 19: Share your favourite memory.

I tend to have really, really bad memory recollection, so I can’t think of any big moments in my life, but at the moment my favourite would have to be going to the art gallery with my partner, and sleeping on the grass in front of it with her.

Day 20: Share something you love about one of your significant others.

Okay, I edited the name of this one to be poly-inclusive; even though I only have one partner at the present, I am poly myself. To pick out a single thing I love about Thisby is hard: she’s intelligent, witty, kind, supportive, creative, and loving.

To pick one thing, though, she’s fun. She’ll talk my ear off with conversation, and listen intently when I respond. She’ll take me out for breakfast, just so that we can sit and hold hands while reading. She’ll take me to art galleries, comic book stores and other live events because she thinks that I’ll like them. Most of all, she’ll entertain my childishness and happily reciprocate.

Day 21: How did you meet this significant other?

Pure luck. I was part of the queer collective (QC) at my university, and was fairly active on the group’s Facebook page. One of the people on the page friended me, thought I was interesting enough, and told his flatmate Thisby that she should friend me.

And it might have ended there, because I don’t accept random friend requests, but Thisby had a horribly/artistically distorted display picture, so I mistook her for a member of the QC and accepted her friend request. And from there we started talking, bonding over a mutual love of penguins being tickled, but she was still just a friend’s flatmate to me, albeit an interesting and friendly one.

That changed, however, when we were both invited independently to a mutual friend’s birthday: we met in real life for the first time, found out we only love a few hundred metres from each other, and have seen each other almost daily since.

Day 22: Share a picture of you and your best friend.
Thisby, my partner and best friend, and myself at our first Queer Ball together. Her face is still hidden, because I’m fond of mystery!


30 Days of Pride: Week 1 | Week 2 | Week 3 | Week 4

30 Days of Pride — Week 3

30 Days of Pride — Week 2

This is my second week of the ‘30 Days of Pride‘ challenge, celebrating pride month; if you missed the first week, click here. I’m beginning to think being demiro is playing on easy mode …

Day 8: Who is your greatest supporter?

My greatest supporter would have to be my partner, Thisby. A brightly-coloured fiery woman, she’s fantastic to have around, and always seems to know when I need supportive cuddles and when I need cheering up.

2016-03-12 17.27.22
Thisby, blushing bashfully as I try to take a photo
Day 9: Do you identify with a certain ‘tribe’? Which one?

I definitely identify with the women-loving-women community. I love our shared sense of culture, how much we’ve grown away from patriarchal norms (although I still recognised there’s a long way to go), and our attitude towards ageing. It’s nice to enter a room full of supportive — and in my circle, fiercely feminist and intersectional — women, and know that you’re both safe, and if you say something harmful that you’ll be called out on it in a manner that supports your education.

I would much rather the momentary embarrassment of being told my behaviour is harmful than continue harming people obliviously.

Day 10: What’s the most influential LGBTQ event you’ve attended?

I’ve attended a few rallies, especially concerning Safe Schools, and went to my first Pride march last year, but on the whole I wouldn’t describe any of them as particularly influential. Since I have an anxiety disorder, getting to the really loud rallies that are impactful is a great difficulty, often to the point of impossible.

Day 11: When was the first time you fell in love? Who was it with?

My first boyfriend, E. (house rules: not putting in full names without explicit consent). He was kind and caring, and we played a lot of ERP together online as our relationship was long distance. Unfortunately, because of different life goals and the distance, our relationship broke apart (amicably), but he was still my first.

Since then, I’ve not fallen in love with another guy, although there have been women and genderfluid/nonbinary individuals!

Day 12: Name your favourite fictional LGBTQ character.

Oooh, here’s some fun! Let’s try a bunch of different approaches:

Headcanon: Hermione Granger. I know that canonically she ended up with Ron and lived happily ever after, but in my mind she ends up with Ginny post-graduation. Rowling picked the wrong Weasley!

Playable Characters: Commander Shepard (F) from Mass Effect. I loved getting close to each of the different characters, and exploring their interactions, and I just love gradually turning Ashley Williams from a gruff human-supremacist into a caring person.

Books/Comics: Rain, from the webcomic Rain. A young trans woman moves to a new school, presenting female full-time for the first time. Unfortunately, it’s not a very accepting religious school, and there’s someone from her past there … will it haunt her?

Honestly, it’s a beautifully written comic that will make you laugh and cry, will let you see the impact of both dysphoria and acceptance, and make you fall in love with this wonderful young woman.

Film/Television: I would say Susan Ivanova from Babylon 5, who was supposed to get together with Talia Winters, but then things ended badly and we never got to see it on screen. So that moves Willow Rosenberg from Buffy up to first place!

Day 13: Are you religious? Why or why not?

No. I was raised in a Roman Catholic family, but my family weren’t especially religious, and encouraged my interest in science and learning from a young age. As I learned more and more about the universe, I noted increasing discrepancies with what I was being told by my Catholic school, and gradually drifted from the faith.

Now I don’t believe in God for the same reason anyone who doesn’t believe in a thing doesn’t believe in it: I’ve not been given sufficient evidence to allay my doubts. As it stands, I’ve seen nothing that indicates any supernatural being at all, much less the specific one in whom I was taught to believe by my religion.

Day 14: Tag your insta-crush.

Well, being demi got me out of this one! Sorry for the unsatisfying answer, but this is an example of the internalisation of alloromantic norms in queer spaces.

But as a bonus, I will say the first video game character that I ever had a crush on: Aerie, from Baldur’s Gate II. An Avariel (winged-elf) who has had her wings removed and was sold to a circus, all she wants to do is help people, and even though she’s terrified of the world she’s willing to be brave in order to offer that help.

Unfortunately, she’s not romanceable as a female character (you’re stuck with only Anomen as your choice, and he’s both horrible and boring), but she is really fun to get to know, and she is so easy to feel protective towards. It really helps that she’s voiced by Kath Soucie, better known for her roles as Phil & Lil from Rugrats, or the mother from Dexter’s Laboratory. 


30 Days of Pride: Week 1 | Week 2 | Week 3 | Week 4

30 Days of Pride — Week 2