How About These Legs/You Can't Play Conkers In England (Standing armlock cross hold)
Hurrah! Another Year, Surely This One Will Be Better Than The Last; The Inexorable March of Progress Will Lead Us All to Happiness (Double armbar octopus hold)
Yess thanks for compiling this! One of my favourite things about Zack is the unhinged names he has for his finishers.
I thought I'd make a list explaining each name! As you can see, they're mostly named after British pop culture deep cuts, experimental indie music, or mundane aspects of life in the UK.
Article 50 – the legal mechanism by which the UK left the EU (aka Brexit). There was a period of time where British news would not shut up about it.
Barry from EastEnders – a famous character from one of the most popular soap operas in the UK
Cremation Lily – an experimental electronic music artist
Clarky Cat/Bad Balloon – names of fake drugs from the late 90s UK satirical news show Brass Eye
Jim Breaks Armbar/Jim Breaks Special – tribute to an infamous British wrestler from the 70s
You Can't Play Conkers in England – a widely mocked clip from a documentary about the band Bros, referencing the myth that the traditional British playground game of conkers has been banned by the government for safety reasons (commonly used as a right wing talking point for some reason)
Hurrah! Another Year, Surely This One Will Be Better Than The Last; The Inexorable March of Progress Will Lead Us All To Happiness – album by the post-rock band Youthmovies/Youthmovie Soundtrack Strategies
Hypernormalisation – a 2016 documentary by Adam Curtis about the narratives of neoliberalism and how they've become decreasingly detached from reality (based on what I read anyway! I've not seen it)
Orienteering with Napalm Death – a joke by the British comedian Stewart Lee (Stewart Lee has since been made aware that Zack named a move after one of his routines and seems equal parts amused, confused and flattered by it)
Rear Naked Choke – not sure about this one. Must be some really obscure reference (jk)
Selected Technical Works vol.2 – a play on 'Selected Ambient Works Volume II', an album by Aphex Twin
South Mimms Services – motorway service station on the M25/A1(M) just north of London (I've never been but I hear it's a decent one – it's no Gloucester Services though)
Sunday Rail Engineering Works Replacement Bus Service – planned rail engineering works often happen on a Sunday in the UK and replacement bus services are usually provided for affected routes. They're notorious for being slow and unreliable and are the bane of anyone trying to get home at the weekend
Tesco Meal Deal – an iconic UK lunchtime institution for office workers and students alike: a sandwich/salad, a snack, and a drink for a fixed price (constantly increasing). There's a strong culture of judging other people's meal deal picks.
Yes! I Am a Long Way from Home – song by post-rock band Mogwai
Young Boy Killer – male trainees in Japan are known as "young boys". This hold presumably kills them
My leading theory for why his moves have such eccentric names, other than that it's very funny, is that NJPW's website always records what move a match was won with. And apart from the Zack Driver and his European Clutch, ZSJ doesn't have a distinct finisher: he's like an improv jazz artist, mixing up submission holds in free-flowing tangles of limbs until his opponent submits. So I imagine he's often in the situation where he's asked for the name of a complex hold that he either figured out the day before the match or just came up with on the fly. At which point I'm guessing he just says the first thing that comes into his head. Some of these holds were only used once as far as I know and probably will never be used again! Such is the joy of his style.
I have no idea if I'm right, but if I ever get the chance to interview him, it'll be the first question I ask.
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It's the big one. In the past, we've learned that Willow Nightingale is the most beloved AEW Wrestler, but we don't know a firm number of by how much or if she's still #1
So it's happening again, but bigger.
I have taken the list of all wrestlers on the official AEW roster page (on January 11th, 2025) and created a tournament that will put all 158 wrestlers head-to-head against the other 157.
We will still have one on one brackets and they will still be for 24 hours apiece for voting.
For my own sanity, the only real difference will be that I won't be including photos. If you don't know who someone is, you can find them here: AEW | All Elite Wrestling Roster | Official Website
Unlike other tournaments, there will be no re-dos. A tie is a tie and everyone will be ranked at the end by number of total votes in their favor.
It's taken approximately 1 week and 125 episodes of the Simpsons, but I have finally scheduled when everyone will be facing everyone else (I have taken out both Karen Jarrett and Negative One cause they're not exactly wrestlers and MVP has also not been included cause he'd never wrestled in AEW when I started). Anyway, feast your eyes on this section of the schedule
Now that I've got the starting few hundred matchups queued up, here's a few details:
There will be 155 days of voting with 78 matchups each day
For the first 117 days, every wrestler will be there exactly once
For days 118-155, there may be some days a wrestler is there twice and some they're not there at all. This was unavoidable by my mental power, but every wrestler will be in 155 matchups in total
The Bucks are matched up on Day 25
Every so often, I'll be posting a progress update to see how the rankings are going (number of votes, number of matchups won and lost, overall rank)
How often should I post a stats update?
Every week
Every 10 days
Every single day
Voting ended onJan 31, 2025
First matchups will be posted 7am EST on February 1st!
We are now past Day 118, so no longer will every wrestler appear every day and some will appear more than once a day. Everyone will still get their 155 brackets, but they've had to be unequally distributed cause any algorithm I came up with to divide them only worked until day 117 (believe me I tried I spent a week doing attempts to make it work and enlisted the two most autistic mathematical brains in my family to help and none of us got past 117)
Hey @mostbelovedwrestlertournament! I remembered seeing you talk before about trying to figure out a match running order for the MBAEWWT, and lamenting that beyond a certain point you had to abandon the nice system and brute-force it
That led me down a rabbit-hole at the time, trying to come up with nice systematic ways of scheduling big (or small) round-robin tournaments, and I got to a result I was pretty happy with! That tournament was well underway by that point so I assumed it was too late to be of any help, but now there's a new one in the works I figured I should post about it in case it's helpful!
I'll try and explain the algorithm to start with, but if it'd be more helpful I can just generate a table and send it to you in excel spreadsheet form or whatever works best for you!
For starters I'll look at a tournament with an odd number of competitors (I know that's not the case here, but it's surprisingly the easiest case, and further stuff can be developed based on it). I'll illustrate with much smaller numbers of competitors but the overall methods generalise to larger tournaments too.
Because there's an odd number of competitors, one of them has to take a bye every "night" of the tournament. I'll number them 1 to N. The solution here is very simple: just arrange them going down the left side and then back up the right, and "rotate" the list every night by pushing the left column down, the right column up, and moving the numbers that get popped off the ends to fill the gap in the opposite column:
Every competitor has one night with no match (top row of the table), and everyone appears twice in each other row, once on the left and once on the right. Nice and symmetrical!
Now we can add one additional competitor to the tournament, making it an even number. This one I'll call 0 because they're going to be a bit special (although I'll try to minimise how special they have to be!) Fitting them in in the first place is easy: just put them up against the person who had nothing to do before!
You'll notice an issue here: before, the placeholder row at the top wasn't an actual match, but now it is and it's always got the same competitor in it! Our new competitor 0 is in the first bout of every single night of the tournament. Doesn't seem very fair! We can't just rotate the 0 around as well, because if we do we'll get halfway through and start repeating matches (IIRC this is what happened halfway through the previous tournament):
Making progress from here was what nearly drove me into the arms of madness, but I finally figured something out: Number each night (counting from zero, I am a programmer after all), and on night n, swap the match between 0 and their opponent (in the first row) with the match containing the competitor whose number matches the night. So on night 0, everything stays the same. On night 1, competitor 1 is in the third row so swap the first and third rows. On night 2, competitor 2 is in the last row so I swap the top and the bottom rows. Because 2 starts on the right and 0 on the left, I also swap both of the pairs I'm moving left-right. I do the same to swap 0 and 3 on night 3, and so on:
Doing the left-right swap maintains our nice property of everyone appearing on the left and right once each, for each row across the tournament (although now everyone has one row they only appear once in, because we now have more competitors than nights). In this example, 0 and 7 only appear once on the top row, everyone else appears once on the left and once on the right. On the next row it's 2 and 5 that only appear once, then 3 and 4, then 1 and 6. 0 is still a bit special in that it generally moves up or down by two positions from night to night, whereas the other competitors move up or down by one position, but it's the most even arrangement of matches I've managed to come up with.
Unfortunately this breaks down a bit when the number of competitors is one more than a multiple of 3. This is related to the fact that in the top row of the table above, the numbers on the left go up by one each night and the ones on the right go down by 3. Look what happens if we have 10 competitors in the tournament:
All of the rows other than the top one look good still, but notice that in the top row competitors 3, 6 and 9 are very overrepresented - they're on the right-side of every opening bout!
I haven't found any ideal solution for this situation, every idea I've had involves some trade-off or another. My favourite I've come up with is to increase the number we're swapping with 0 by 2 each night, rather than by 1:
On night 1, swap 0 and 2; on night 2 swap 0 and 4, and so on. Once I get to numbers larger than 9 to swap with 0, subtract 9 from the number to "wrap around" to numbers we actually have: on night 4 I swap 0 and 8, then on night 5 I swap 0 and (10-9=1). 0 now shows up 3 times on the top row, 6 times on other rows that are multiples of 3, and not at all on nights that aren't, which is the main caveat here. It's still a reasonably even distribution throughout all the positions, so I think it'd be my choice overall. To anyone without my degree of… let's say pedantry… I imagine any of the solutions I've shown here would do the trick!
I hope this helps! (or is at least interesting!) If you'd like to use some of this but I haven't managed to explain it clearly enough, I'd be happy to put together a spreadsheet or something with a full 100-competitor schedule to follow!
So the @mostbelovedaewwrestlertournament: Round-Robin Edition recently finished a giant cycle of all 156 wrestlers facing each of the other 155. I'm a bit of a nerd for this sort of thing, and it's one of the largest datasets of its kind I'm ever likely to have access to, so (and at the encouragement of @livelaughlariat) I thought I'd have a bash at some data analysis.
Unfortunately this isn't going to look so nice, because tumblr can't handle LaTeX, or even like, HTML subscripts. If you don't want to see nasty maths in plain text, or just want to skip to fun graphs, keep scrolling.
The approach I'm going to take is as follows:
Assume any given competitor can be described by a single "quality" (or maybe "belovedness') value q_j (read as "the quality of the jth competitor" - I'll label some general unspecified person with i, j or k throughout this)
In a poll between competitor j and competitor k, seen by N potential voters, the number of votes each competitor receives (N_j) is a function of their quality q_j, their opponent's, q_k, and (obviously) N. I can express this as
defining the function v(q_j, q_k) as "the fraction of voters who vote for a competitor of quality q_j when placed against a competitor of quality q_k".
I then try and find a set of quality factors {q_i} which make the predicted results of every poll in the tournament as close as possible to the actual results.
Because I don't know what N is for any given poll (it's possible someone saw a poll but decided not to vote), I'll use as my measure the percentage margin between the two competitors, i.e. the difference between their number of votes divided by the total number of votes cast. This ensures the number N cancels out:
A simple candidate for the "vote function" is
which leads to
A disadvantage of this vote function is that it's scale-independent: doubling the quality values of everyone in the tournament would leave the result unchanged. It also doesn't allow for the possibility of someone deciding not to vote:
Because I know some people chose not to vote in polls between two people they didn't like, it would be nice if the model could account for this somehow.
To that end, I use this more complex model: of the N voters who see a given poll, only a fraction of people equal to q_j (i.e. q_j × N voters) would consider voting for candidate j. Similarly a fraction q_k would consider voting for candidate k. I'll say these fractions are independent of each other, so that (1-q_j)×(1-q_k)×N voters choose not to vote at all. Then, there are q_j (1 - q_k) N voters who would consider voting for j but not k, so they all vote for j. Similarly, q_k (1 - q_j) N voters wouldn't vote for j but are happy to vote for k, so they do. Of the remaining q_j q_k N voters who are considering voting for both candidates, the simpler model presented above applies, so an additional q_j q_k × q_j / (q_j + q_k) votes go to j and q_j q_k × q_k / (q_j + q_k) to k.
This results in a vote function
and an objective function
The fraction of potential voters who actually cast votes is
Now, I can compute the value of
for all pairs in the tournament (taking care to ignore j = k) and compare it to the prediction f(q_j, q_k) for some guess at the set of qualities {q_i}.
I use Newton's method to try and find an optimal solution - in the least-squares sense, minimising
A basic Newton solver is a bit unstable for this problem (I think because the dependence of f(q_j, q_k) on overall scaling of the qualities is still quite weak, which would be worse with the simpler model), so I remove the smallest singular values when computing the pseudo-inverse of the Jacobian matrix. It's not fast - it's a big matrix inversion per iteration! - but with that done it works quite nicely. The solution reaches an overall shape in just a few iterations, then very slowly reduces the overall magnitude of the qualities, seemingly forever. The correction term does shrink over iterations though, so I think it's converging towards something. I give it 10,000 iterations and then cut it off.
Results: Rankings
The most obvious output from this process is the { q_i } themselves. After 10k iterations of Newton's method, we have a winner. It's Willow. This shouldn't be surprising. Her overall belovedness percentage clocks in at 69% (nice)
Full rankings here:
69.23%: Willow Nightingale
61.28%: Swerve Strickland
60.81%: Toni Storm
60.14%: Adam Page
59.21%: Orange Cassidy
58.06%: Kenny Omega
52.75%: Eddie Kingston
51.36%: Kris Statlander
43.93%: Konosuke Takeshita
42.92%: Will Ospreay
42.71%: Samoa Joe
42.06%: Julia Hart
40.00%: Chuck Taylor
39.89%: Harley Cameron
38.85%: Nyla Rose
38.55%: Athena
36.08%: Wheeler Yuta
35.64%: Jon Moxley
33.72%: Jay White
33.51%: Brody King
32.04%: MJF
31.46%: Jamie Hayter
31.29%: Queen Aminata
30.08%: Mariah May
29.89%: Kyle Fletcher
29.45%: Katsuyori Shibata
28.62%: Christian Cage
28.47%: Claudio Castagnoli
27.97%: Kyle O'Reilly
27.26%: Daniel Garcia
27.10%: Kazuchika Okada
26.69%: Matthew Jackson
26.55%: Hikaru Shida
26.28%: Bryan Danielson
25.62%: Anthony Bowens
25.46%: Mark Briscoe
24.06%: Evil Uno
23.99%: PAC
23.89%: Hook
22.61%: Abadon
22.48%: Nicholas Jackson
22.16%: Powerhouse Hobbs
21.10%: Buddy Matthews
21.04%: Jack Perry
20.87%: Kota Ibushi
20.65%: Anna Jay
20.41%: Mercedes Mone
20.35%: Skye Blue
20.23%: The Beast Mortos
20.04%: Kip Sabian
19.78%: Emi Sakura
19.74%: Thunder Rosa
19.54%: Danhausen
19.21%: Bandido
18.86%: Adam Cole
18.38%: Darby Allin
17.38%: Mark Davis
17.00%: Penelope Ford
16.76%: Trent Beretta
15.96%: Marina Shafir
15.95%: Komander
15.88%: Juice Robinson
15.85%: Riho
15.78%: Yuka Sakazaki
15.41%: Killswitch
15.10%: Matt Menard
14.71%: Ruby Soho
14.67%: Hologram
14.61%: Isiah Kassidy
14.33%: Austin Gunn
14.25%: Sting
13.60%: Roderick Strong
13.05%: Bryan Keith
12.99%: Colten Gunn
12.61%: Lee Moriarty
12.55%: Nick Wayne
12.46%: John Silver
12.46%: Mr Brodie Lee
12.30%: Ricochet
12.25%: Dustin Rhodes
11.78%: Malakai Black
11.62%: Deonna Purrazzo
11.57%: Dante Martin
11.48%: Big Bill
11.42%: Red Velvet
11.20%: Taya Valkyrie
11.13%: Angelo Parker
11.09%: Shelton Benjamin
11.03%: Cope
10.96%: Keith Lee
10.72%: AR Fox
10.35%: Serpentico
10.12%: Billy Gunn
9.97%: Lance Archer
9.58%: Max Caster
9.10%: Marq Quen
8.99%: Alex Reynolds
8.85%: Angelico
8.59%: Cash Wheeler
8.57%: Bobby Lashley
8.40%: Darius Martin
8.32%: Leila Grey
7.65%: Matt Taven
7.61%: The Butcher
7.60%: Kiera Hogan
7.50%: Diamante
7.32%: Leyla Hirsch
7.03%: Brandon Cutler
7.01%: Lio Rush
6.85%: Johnny TV
6.78%: Rey Fenix
6.62%: Brian Cage
6.47%: Wardlow
6.46%: Mercedes Martinez
6.17%: Luther
6.05%: Ricky Starks
6.04%: Matt Sydal
5.89%: Dax Harwood
5.55%: Lee Johnson
5.46%: Tay Melo
5.19%: Action Andretti
5.16%: Bishop Kaun
4.48%: Scorpio Sky
4.40%: The Blade
4.22%: Mike Bennett
4.15%: Colt Cabana
4.12%: Ortiz
4.05%: Toa Liona
3.98%: Griff Garrison
3.98%: Preston Vance
3.75%: Dr Britt Baker DMD
3.71%: Michael Nakazawa
3.68%: Jay Lethal
3.63%: Peter Avalon
3.49%: Shawn Dean
3.28%: Jeff Jarrett
3.25%: Rush
3.02%: Dutch
2.96%: Josh Woods
2.92%: Dralistico
2.85%: Vincent
2.68%: Madison Rayne
2.65%: Satnam Singh
2.45%: Ariya Daivari
2.38%: Tony Nese
2.20%: Anthony Ogogo
2.14%: Aaron Solo
2.08%: Sammy Guevara
2.03%: Paul Wight
1.79%: Nick Comoroto
1.77%: Rebel
1.76%: Serena Deeb
1.73%: Miro
1.62%: Chris Jericho
1.24%: Saraya
1.09%: Kamille
Analysis: Match-by-Match Performance
Now, we don't just have a set of quality factors for all of our competitors! That optimisation I did above? It's not perfect. For every given j, k pairing, I've tried to get f_jk - f(q_j,q_k) (these are called residuals) as close to zero as possible, but they can't all be zero at the same time because there are many fewer variables to tweak (the 156 { q_i }) than residuals to minimise (of which there are over 12,000).
What this means however is that we can look at each match's residual as a measure of how surprising the result was, and in which direction. If f_{jk} - f(q_j,q_k) is positive, it means that the vote share achieved by j was higher than would be expected by just comparing their overall score and that of their opponent. By plotting these residuals per-competitor rearranged into time order, I can get an idea of whether anyone's popularity was changing over time. This is a similar analysis to what @livelaughlariat was doing previously, so I'll look at some of the same people that she did.
I've not included linear fits/correlation coefficients here like she did, for a few reasons:
I think any trends or features that show up are convincing enough on their own just from looking at the smoothed trend line, you don't need Karl Pearson to tell you what your eyes see.
Several of the features I'll try to argue are present are more localised than a global linear fit would get you.
I am a computational physicist, not a real scientist. Statistical rigour is for cowards
Max Caster shows a very pronounced growth over the course of the tournament: He starts out underperforming his expected vote shares by 0.4 (i.e. 40 percentage points!) and ends up overperforming by 20 points!
Mariah starts off vaguely growing in popularity, then starts to slide as the rumours of her leaving AEW start to gain momentum
Not much of interest for Comoroto and Deeb
Kenny pretty consistent as well
Ospreay and Toni don't move much, but Ricochet's popularity does seem to be improving a bit over the course!
Pretty big bump for Mark Davis when he briefly started appearing more, though that eventually died down when people stopped seeing him again
And a big boost for Ibushi when he finally appeared again!
Which was also replicated for Tay!
A cute one to finish - maybe somewhat tenuous? - I think that bump for Yuka Sakazaki around day 110 corresponds pretty closely with her and Takeshita announcing their marriage
Also, as I keep referring back to the simpler "everyone votes" model I mentioned above: The graphs that method's residuals produced look exactly the same as these ones. I literally couldn't see a difference. Surprising, but it's nice that the results are robust to differences in the model like that!
Stay tuned for some Social Choice Theory in the next edition!
Last time, I showed off some heavy-duty data analysis on the Most Beloved AEW Wrestler Tournament. This time I'm taking a different approach to the same thing.
Rather than trying to score everyone like I did last time, now I'm just interested in ordering them. The so-called Condorcet methods from social choice theory (voting and elections to you and me) say that one candidate beats another if they're preferred by them in a majority of voters' ballots. A lot of this terminology and theory is designed for "ranked choice" voting systems, in which each voter submits an ordered list of candidates from most to least preferred. In our case though, "preferred by a majority of voters' ballots" just means they won the poll.
A "Condorcet winner" is one who beats every other candidate in this sense. A "Condorcet cycle" occurs when you can place several candidates in a circle such that every candidate won against the person immediately clockwise of them, for example. It's impossible to pick a winner in this scenario, as every person can be considered to have "transitively beaten" (i.e. beaten someone who has beaten someone who has beaten someone who has beaten…) every other candidate in the cycle (including themself!). For example, if Eddie Kingston beat Swerve Strickland and Swerve Strickland beat Orange Cassidy, but Orange beat Eddie? That's a Condorcet cycle [spoiler: this happened]. You could also consider a draw to be one, but that's less interesting.
Now, we can draw out all 156 wrestlers standing in a circle and draw an arrow from each person (except Kamille) to everyone they beat (because she didn't). I'm not going to do that but let's imagine I did. This is a kind of graph (in the maths sense of a collection of nodes and edges, like a network) called - appropriately - a tournament.
There's an operation you can do on graphs like this called "condensation". It takes all the Condorcet cycles (in graph theory terms, "strongly connected components": every node in the component can follow arrows to reach all the others) in the graph and "condenses" them down to a single node. Here's a diagram I stole (it's CC0 so I'm allowed) from Wikipedia, created by David Eppstein
The big yellow circles and arrows are the condensation of the smaller graph. It is known that if you do this, the resulting graph (the big yellow nodes and arrows) is acyclic - which means it defines some kind of (not necessarily strict) ordering
If I apply a graph condensation (followed by transitive reduction, which removes all of the unnecessary arrows between nodes that aren't immediately adjacent) to the MBAEWWT, I get… this!
Willow wins, then there's a little Condorcet cycle containing Eddie, Swerve, Hangman, Kenny, Toni and Orange in joint 2nd place, a big Condorcet cycle of… 146 people in joint 7th place, Saraya 154th, Chris Jericho 155th and Kamille 156th.
I'll zoom in on the little cycle. It's not arranged in a nice order that shows the cyclic nature because that would be too much effort for me, but you can see that you can go Eddie -> Swerve -> Hangman -> Kenny -> Toni -> Orange -> Eddie, which prevents me from ranking any of them above any other under only the Condorcet criterion.
The same is also true of the "everyone else" cycle, but there's no point trying to show you that. What looks like a grey background there is actually around 10000 arrows.
What now remains is to break some arrows to let us pull this out into something vaguely linear. I'll use the Schulze method, which is preferred by nerds all over the place.
The resulting graph gets rid of the cycles, but is now very very wide. For ease of viewing on modern screens I've plotted it with Willow at the top and Kamille at the bottom.
Which is to say…
Do you love the colour of the Most Beloved AEW Wrestler Tournament?
Right, I think that's all the analysis I have in me! Thanks to @mostbelovedaewwrestlertournament for running the thing, and all the voters for providing so much data to churn through!
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So the @mostbelovedaewwrestlertournament: Round-Robin Edition recently finished a giant cycle of all 156 wrestlers facing each of the other 155. I'm a bit of a nerd for this sort of thing, and it's one of the largest datasets of its kind I'm ever likely to have access to, so (and at the encouragement of @livelaughlariat) I thought I'd have a bash at some data analysis.
Unfortunately this isn't going to look so nice, because tumblr can't handle LaTeX, or even like, HTML subscripts. If you don't want to see nasty maths in plain text, or just want to skip to fun graphs, keep scrolling.
The approach I'm going to take is as follows:
Assume any given competitor can be described by a single "quality" (or maybe "belovedness') value q_j (read as "the quality of the jth competitor" - I'll label some general unspecified person with i, j or k throughout this)
In a poll between competitor j and competitor k, seen by N potential voters, the number of votes each competitor receives (N_j) is a function of their quality q_j, their opponent's, q_k, and (obviously) N. I can express this as
defining the function v(q_j, q_k) as "the fraction of voters who vote for a competitor of quality q_j when placed against a competitor of quality q_k".
I then try and find a set of quality factors {q_i} which make the predicted results of every poll in the tournament as close as possible to the actual results.
Because I don't know what N is for any given poll (it's possible someone saw a poll but decided not to vote), I'll use as my measure the percentage margin between the two competitors, i.e. the difference between their number of votes divided by the total number of votes cast. This ensures the number N cancels out:
A simple candidate for the "vote function" is
which leads to
A disadvantage of this vote function is that it's scale-independent: doubling the quality values of everyone in the tournament would leave the result unchanged. It also doesn't allow for the possibility of someone deciding not to vote:
Because I know some people chose not to vote in polls between two people they didn't like, it would be nice if the model could account for this somehow.
To that end, I use this more complex model: of the N voters who see a given poll, only a fraction of people equal to q_j (i.e. q_j × N voters) would consider voting for candidate j. Similarly a fraction q_k would consider voting for candidate k. I'll say these fractions are independent of each other, so that (1-q_j)×(1-q_k)×N voters choose not to vote at all. Then, there are q_j (1 - q_k) N voters who would consider voting for j but not k, so they all vote for j. Similarly, q_k (1 - q_j) N voters wouldn't vote for j but are happy to vote for k, so they do. Of the remaining q_j q_k N voters who are considering voting for both candidates, the simpler model presented above applies, so an additional q_j q_k × q_j / (q_j + q_k) votes go to j and q_j q_k × q_k / (q_j + q_k) to k.
This results in a vote function
and an objective function
The fraction of potential voters who actually cast votes is
Now, I can compute the value of
for all pairs in the tournament (taking care to ignore j = k) and compare it to the prediction f(q_j, q_k) for some guess at the set of qualities {q_i}.
I use Newton's method to try and find an optimal solution - in the least-squares sense, minimising
A basic Newton solver is a bit unstable for this problem (I think because the dependence of f(q_j, q_k) on overall scaling of the qualities is still quite weak, which would be worse with the simpler model), so I remove the smallest singular values when computing the pseudo-inverse of the Jacobian matrix. It's not fast - it's a big matrix inversion per iteration! - but with that done it works quite nicely. The solution reaches an overall shape in just a few iterations, then very slowly reduces the overall magnitude of the qualities, seemingly forever. The correction term does shrink over iterations though, so I think it's converging towards something. I give it 10,000 iterations and then cut it off.
Results: Rankings
The most obvious output from this process is the { q_i } themselves. After 10k iterations of Newton's method, we have a winner. It's Willow. This shouldn't be surprising. Her overall belovedness percentage clocks in at 69% (nice)
Full rankings here:
69.23%: Willow Nightingale
61.28%: Swerve Strickland
60.81%: Toni Storm
60.14%: Adam Page
59.21%: Orange Cassidy
58.06%: Kenny Omega
52.75%: Eddie Kingston
51.36%: Kris Statlander
43.93%: Konosuke Takeshita
42.92%: Will Ospreay
42.71%: Samoa Joe
42.06%: Julia Hart
40.00%: Chuck Taylor
39.89%: Harley Cameron
38.85%: Nyla Rose
38.55%: Athena
36.08%: Wheeler Yuta
35.64%: Jon Moxley
33.72%: Jay White
33.51%: Brody King
32.04%: MJF
31.46%: Jamie Hayter
31.29%: Queen Aminata
30.08%: Mariah May
29.89%: Kyle Fletcher
29.45%: Katsuyori Shibata
28.62%: Christian Cage
28.47%: Claudio Castagnoli
27.97%: Kyle O'Reilly
27.26%: Daniel Garcia
27.10%: Kazuchika Okada
26.69%: Matthew Jackson
26.55%: Hikaru Shida
26.28%: Bryan Danielson
25.62%: Anthony Bowens
25.46%: Mark Briscoe
24.06%: Evil Uno
23.99%: PAC
23.89%: Hook
22.61%: Abadon
22.48%: Nicholas Jackson
22.16%: Powerhouse Hobbs
21.10%: Buddy Matthews
21.04%: Jack Perry
20.87%: Kota Ibushi
20.65%: Anna Jay
20.41%: Mercedes Mone
20.35%: Skye Blue
20.23%: The Beast Mortos
20.04%: Kip Sabian
19.78%: Emi Sakura
19.74%: Thunder Rosa
19.54%: Danhausen
19.21%: Bandido
18.86%: Adam Cole
18.38%: Darby Allin
17.38%: Mark Davis
17.00%: Penelope Ford
16.76%: Trent Beretta
15.96%: Marina Shafir
15.95%: Komander
15.88%: Juice Robinson
15.85%: Riho
15.78%: Yuka Sakazaki
15.41%: Killswitch
15.10%: Matt Menard
14.71%: Ruby Soho
14.67%: Hologram
14.61%: Isiah Kassidy
14.33%: Austin Gunn
14.25%: Sting
13.60%: Roderick Strong
13.05%: Bryan Keith
12.99%: Colten Gunn
12.61%: Lee Moriarty
12.55%: Nick Wayne
12.46%: John Silver
12.46%: Mr Brodie Lee
12.30%: Ricochet
12.25%: Dustin Rhodes
11.78%: Malakai Black
11.62%: Deonna Purrazzo
11.57%: Dante Martin
11.48%: Big Bill
11.42%: Red Velvet
11.20%: Taya Valkyrie
11.13%: Angelo Parker
11.09%: Shelton Benjamin
11.03%: Cope
10.96%: Keith Lee
10.72%: AR Fox
10.35%: Serpentico
10.12%: Billy Gunn
9.97%: Lance Archer
9.58%: Max Caster
9.10%: Marq Quen
8.99%: Alex Reynolds
8.85%: Angelico
8.59%: Cash Wheeler
8.57%: Bobby Lashley
8.40%: Darius Martin
8.32%: Leila Grey
7.65%: Matt Taven
7.61%: The Butcher
7.60%: Kiera Hogan
7.50%: Diamante
7.32%: Leyla Hirsch
7.03%: Brandon Cutler
7.01%: Lio Rush
6.85%: Johnny TV
6.78%: Rey Fenix
6.62%: Brian Cage
6.47%: Wardlow
6.46%: Mercedes Martinez
6.17%: Luther
6.05%: Ricky Starks
6.04%: Matt Sydal
5.89%: Dax Harwood
5.55%: Lee Johnson
5.46%: Tay Melo
5.19%: Action Andretti
5.16%: Bishop Kaun
4.48%: Scorpio Sky
4.40%: The Blade
4.22%: Mike Bennett
4.15%: Colt Cabana
4.12%: Ortiz
4.05%: Toa Liona
3.98%: Griff Garrison
3.98%: Preston Vance
3.75%: Dr Britt Baker DMD
3.71%: Michael Nakazawa
3.68%: Jay Lethal
3.63%: Peter Avalon
3.49%: Shawn Dean
3.28%: Jeff Jarrett
3.25%: Rush
3.02%: Dutch
2.96%: Josh Woods
2.92%: Dralistico
2.85%: Vincent
2.68%: Madison Rayne
2.65%: Satnam Singh
2.45%: Ariya Daivari
2.38%: Tony Nese
2.20%: Anthony Ogogo
2.14%: Aaron Solo
2.08%: Sammy Guevara
2.03%: Paul Wight
1.79%: Nick Comoroto
1.77%: Rebel
1.76%: Serena Deeb
1.73%: Miro
1.62%: Chris Jericho
1.24%: Saraya
1.09%: Kamille
Analysis: Match-by-Match Performance
Now, we don't just have a set of quality factors for all of our competitors! That optimisation I did above? It's not perfect. For every given j, k pairing, I've tried to get f_jk - f(q_j,q_k) (these are called residuals) as close to zero as possible, but they can't all be zero at the same time because there are many fewer variables to tweak (the 156 { q_i }) than residuals to minimise (of which there are over 12,000).
What this means however is that we can look at each match's residual as a measure of how surprising the result was, and in which direction. If f_{jk} - f(q_j,q_k) is positive, it means that the vote share achieved by j was higher than would be expected by just comparing their overall score and that of their opponent. By plotting these residuals per-competitor rearranged into time order, I can get an idea of whether anyone's popularity was changing over time. This is a similar analysis to what @livelaughlariat was doing previously, so I'll look at some of the same people that she did.
I've not included linear fits/correlation coefficients here like she did, for a few reasons:
I think any trends or features that show up are convincing enough on their own just from looking at the smoothed trend line, you don't need Karl Pearson to tell you what your eyes see.
Several of the features I'll try to argue are present are more localised than a global linear fit would get you.
I am a computational physicist, not a real scientist. Statistical rigour is for cowards
Max Caster shows a very pronounced growth over the course of the tournament: He starts out underperforming his expected vote shares by 0.4 (i.e. 40 percentage points!) and ends up overperforming by 20 points!
Mariah starts off vaguely growing in popularity, then starts to slide as the rumours of her leaving AEW start to gain momentum
Not much of interest for Comoroto and Deeb
Kenny pretty consistent as well
Ospreay and Toni don't move much, but Ricochet's popularity does seem to be improving a bit over the course!
Pretty big bump for Mark Davis when he briefly started appearing more, though that eventually died down when people stopped seeing him again
And a big boost for Ibushi when he finally appeared again!
Which was also replicated for Tay!
A cute one to finish - maybe somewhat tenuous? - I think that bump for Yuka Sakazaki around day 110 corresponds pretty closely with her and Takeshita announcing their marriage
Also, as I keep referring back to the simpler "everyone votes" model I mentioned above: The graphs that method's residuals produced look exactly the same as these ones. I literally couldn't see a difference. Surprising, but it's nice that the results are robust to differences in the model like that!
Stay tuned for some Social Choice Theory in the next edition!
The usual suspects (@thewaythroughthewoods, @thepenultimaterolo, @yoshihashismattebum) tagged me to talk about music again, so here goes! On Repeat playlist on spotify, it goes like this!
1. Holes - Teenage Halloween
I cannot for the life of me remember why I know this song. I'm sure I got it from a shared spotify blend playlist (with @thepenultimaterolo and @yoshihashismattebum) at some point, but I think I mentioned it at some point and neither of them recognised it… I guess maybe it was a case of something coming up on spotify radio for someone and then spotify deciding to put it on a personalised playlist because they'd listened to it once. Anyway, it bangs so I'm glad spotify decided to Mandela-effect me into listening to it
I'm aggregating songs that are all on here because I've been listening to this album all the way through lately. I've been through this before on here, so I'll keep it short: PUP are great! I'm enjoying their new album and the first time I saw them live was maybe my favourite gig experience ever.
3. Rattlesnake - King Gizzard and the Lizard Wizard (+ Melting)
KG+LW are another repeat from my previous music post: I've been going through their back catalog a bit since first getting into them with PetroDragonic Apocalypse; or, Dawn of Eternal Night: An Annihilation of Planet Earth and the Beginning of Merciless Damnation and I've enjoyed Flying Microtonal Banana a lot lately. Very different vibe, as is to be expected between (or often within) their albums
4. Von Dutch - Charli XCX
Spotify has correctly figured out that this was my favourite song off of brat
5. so american - Olivia Rodrigo
So many love songs make love sound kinda dreary and sombre, so I appreciate that Olivia makes it sound so fun and exciting here. I just think she's neat!
6. Chocolate Cake - Crowded House
This album is one I remember fondly as one of my parents' CDs from my childhood, and for some reason I got the urge to listen to it again recently. I think this song in particular is here because it's the first on the album, I might have gone with Weather with You or It's Only Natural if I were choosing a favourite
7. Big Yellow Taxi - Joni Mitchell
This came up in a pub quiz a few weeks ago and it's just a really good song. I think the fact that the intro sounds quite similar to (fellow good song) Take Your Mama by Scissor Sisters helped it stick in my head somehow. Listening to the two back-to-back to compare probably helped it end up on this list too.
8. Deadstick - KGLW
A single from King Gizz's upcoming album, which I'd been listening to a bit because it had just come out!
9. man at the garden - Kendrick Lamar
Not sure why Spotify's chosen this song from GNX in particular to put on this list, I probably would have gone with wacced out murals, squabble up or tv off as favourites. I'd never really managed to get into Kendrick before, but I enjoyed this album quite a lot!
10. Secret Smile - Semisonic
A slightly rogue story here: I really liked this song when I was about 5 years old, forgot it ever existed, then heard it in
^this episode of One Hit Wonderland, thought "oh wow, never knew that was by the same band as Closing Time" and listened to both songs a bunch in a short space of time. Turns out this is the one that made the cut!
Okay the Spotify banner things should work on mobile now, had to change to a *third* way of embedding tracks from Spotify because
a) copying the embed directly from Spotify into the post editor produced something entirely nonfunctional
b) copying the same thing into the html editor produced something that seemed to work until I looked at it on mobile and was then about 30% functional
c) turns out just pasting a raw link to Spotify straight into the post editor generates something that actually works, thanks to @thepenultimaterolo for telling me about this solution that should have been obvious to me but was for some reason not
I can tell I'm going to enjoy being an active user of Tumblr, the Nothing App™
The usual suspects (@thewaythroughthewoods, @thepenultimaterolo, @yoshihashismattebum) tagged me to talk about music again, so here goes! On Repeat playlist on spotify, it goes like this!
1. Holes - Teenage Halloween
I cannot for the life of me remember why I know this song. I'm sure I got it from a shared spotify blend playlist (with @thepenultimaterolo and @yoshihashismattebum) at some point, but I think I mentioned it at some point and neither of them recognised it… I guess maybe it was a case of something coming up on spotify radio for someone and then spotify deciding to put it on a personalised playlist because they'd listened to it once. Anyway, it bangs so I'm glad spotify decided to Mandela-effect me into listening to it
I'm aggregating songs that are all on here because I've been listening to this album all the way through lately. I've been through this before on here, so I'll keep it short: PUP are great! I'm enjoying their new album and the first time I saw them live was maybe my favourite gig experience ever.
3. Rattlesnake - King Gizzard and the Lizard Wizard (+ Melting)
KG+LW are another repeat from my previous music post: I've been going through their back catalog a bit since first getting into them with PetroDragonic Apocalypse; or, Dawn of Eternal Night: An Annihilation of Planet Earth and the Beginning of Merciless Damnation and I've enjoyed Flying Microtonal Banana a lot lately. Very different vibe, as is to be expected between (or often within) their albums
4. Von Dutch - Charli XCX
Spotify has correctly figured out that this was my favourite song off of brat
5. so american - Olivia Rodrigo
So many love songs make love sound kinda dreary and sombre, so I appreciate that Olivia makes it sound so fun and exciting here. I just think she's neat!
6. Chocolate Cake - Crowded House
This album is one I remember fondly as one of my parents' CDs from my childhood, and for some reason I got the urge to listen to it again recently. I think this song in particular is here because it's the first on the album, I might have gone with Weather with You or It's Only Natural if I were choosing a favourite
7. Big Yellow Taxi - Joni Mitchell
This came up in a pub quiz a few weeks ago and it's just a really good song. I think the fact that the intro sounds quite similar to (fellow good song) Take Your Mama by Scissor Sisters helped it stick in my head somehow. Listening to the two back-to-back to compare probably helped it end up on this list too.
8. Deadstick - KGLW
A single from King Gizz's upcoming album, which I'd been listening to a bit because it had just come out!
9. man at the garden - Kendrick Lamar
Not sure why Spotify's chosen this song from GNX in particular to put on this list, I probably would have gone with wacced out murals, squabble up or tv off as favourites. I'd never really managed to get into Kendrick before, but I enjoyed this album quite a lot!
10. Secret Smile - Semisonic
A slightly rogue story here: I really liked this song when I was about 5 years old, forgot it ever existed, then heard it in
^this episode of One Hit Wonderland, thought "oh wow, never knew that was by the same band as Closing Time" and listened to both songs a bunch in a short space of time. Turns out this is the one that made the cut!
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So it looks like @yoshihashismattebum, @thepenultimaterolo, and @thewaythroughthewoods have stood in front of a mirror and said my URL three times, compelling me to break my vow of silence and produce one (1) "post" on this "blog". My task is to spell out my URL with song titles
TL:DR - here's a playlist
Side A (don't worry about it)
Unacceptable - Bad Religion
Never Fight a Man With a Perm - IDLES
Paralytic States - Against Me!
Aneurysm - Nirvana (1)
I checked your cellphone - Otoboke Beaver (2)
Rollercoaster - Lauran Hibberd
Extraordinary Girl/Letterbomb - Green Day (3)
Dragon - King Gizzard and the Lizard Wizard (4)
ballad of a homeschooled girl - Olivia Rodrigo (5)
Red Wine Supernova - Chappell Roan (6)
Art of Dying, The - Gojira (7)
Crying in Amsterdam - Sløtface
Knights of Cydonia - Muse (8)
Edmonton - PUP (9)
These Spectacles Reveal the Nostalgics - The Hives
Liner Notes
There seem to be two studio versions and lots of live versions of this; the one I'm thinking of is the studio version that was the B-side to Smells Like Teen Spirit, but the live versions I've heard are also good. Not so keen on the Incesticide version though
Or in Japanese, 携帯みてしまいました by おとぼけビ～バ～
Extraordinary Girl is, imo, one of the weaker tracks on American Idiot, but Letterbomb is probably my favourite (sub-9-minute) song on that album so I figured I'd take advantage of the weird way the track listing is arranged to sneak an L in here
King Gizz are bonkers good but a lot of their music isn't really my jam, genre-wise. This is one occasion where they made an album in a genre I like, and the results are excellent. 16th note double kick drumming at 145bpm for 40+ bars straight? Nice. Vocals in four different octaves? Of course. Two verses of chanting in Latin? Why not?
I'm not the only person I know who's mistaken the intro to this for a PUP intro. I don't think there's any other pop star I can say that of.
Yeah this is a repeat from the lists of two of the people who nominated me for this. Well-deserved.
If I said 3 songs back that King Gizzard's drumming was impressive, Mario Duplantier's is inhuman. I've seen a 10-minute video essay about what polyrhythm he's even drumming in the intro, and the kick drumming on the chorus is like 40% faster than on Dragon. Wild stuff.
I feel like Muse work best in the "horseshoe theory" region of a scale from sublime to ridiculous, and this song is a good example
This is from one of the two EPs that soundtracked a locked-down 2021 for me - very cathartic, and much-needed at the time
Side B (A.K.A you should have worried about it)
Ur Mum - Wet Leg
New Born - Muse
Passport - Sløtface
Alone at Home - Jonathan Coulton
Ignoreland - REM
Reject - Green Day
Everlong - Foo Fighters
D-7 - Nirvana (1)
Bulls on Parade - Rage Against the Machine/Denzel Curry (2)
Red Light - The Regrettes
A.K.A. I-D-I-O-T - The Hives
Coast, The - PUP (3)
Kyoto Now! - Bad Religion (4)
EAT - Poppy (5)
Toxicity - System of a Down (6)
Liner Notes
It's a cover of a song by The Wipers (you didn't think I was going to choose a normal Nirvana song, did you?) As far as I can tell Nirvana never released a studio recording, so I'm treating the version recorded live at the BBC as my canonical version
Couldn't choose between the original version and Denzel Curry's cover here. I'd highly recommend seeking out Denzel's version if you've not heard it before, so that's the version I've put on the playlist. The youtube video is still worth watching as well though.
The vibes of this song are brilliantly creepy. Final few lines give me chills every time. Apparently it's based on an old Inuit story the singer's parents terrified him with as a child, which is cool!
This is a brilliant climate protest song. Actually, the Bad Religion song on Side A is also an environmental protest song, released 12 years earlier. Nothing changes, does it?
This is the title track from the other EP that soundtracked my 2021. I think it's the first time I remember hearing Poppy going fully into metalcore screaming and I love it
This is maybe a bit of a basic pick for a SOaD song? I nearly went for Tentative instead because Mezmerize/Hypnotize were my first of their albums as a teenager; but decided that I do actually think Toxicity is the better song
I've been lucky enough to see some of the artists on my list perform live - those artists are bolded in the listings. Sløtface are a special case - I had tickets to a show in March 2020, which didn't happen because they couldn't leave Norway and I couldn't leave my house. I've got tickets to see them later this year though, which is exciting!
As you can no doubt tell, I had a hard time fitting in everything I wanted to include - I ended up with a list of about 20 artists I wanted songs by, and only 15 letters in my URL.
I ended up with shortlists of 5+ songs starting with different relevant letters for some artists, so it took quite some shuffling to arrange everything in a way I was happy with. I even asked my combinatorialist friend if he could identify what sort of combinatorial optimisation problem I had on my hands (either a knapsack problem variant with a weird objective function, or maybe some kind of covering problem), but that didn't go anywhere so I ended up brute-forcing it.
Artist's impression of me brute-forcing it.
In the end I had two songs for some letters that I was unwilling to cut, so double list was the only thing for it. Struggled in the other direction with some of the repeated letters, but managed to get there in the end. Managed no artist repeats within a list and the only one repeated album across the whole thing. I'd consider all of these recommendations to also be album recommendations (apart from the few that aren't from an album)
My actual workings
You may notice if you are weird and look closely that a couple of songs here differ from what I've finished up with - there was flux going on right up until I actually wrote up this post!
Uhhhh everyone I know on here tagged me in the first place so... if you wanna do another one go for it I guess?
