Okay, I've got a formula which I think is pretty good. It has the following properties:
1) A #1 vote counts 3x as much as a #30 vote.
2) If there's one vote for an album, the score from (1) counts fully. If two votes, the album gets the full score from the larger vote, but only a quarter the other vote. If three votes, the album gets the full biggest vote, 1/4 the second-biggest, and 1/7 the third biggest. So multiple votes boost a score, but don't easily overwhelm high-ranked single picks.
3) Votes for the artist (even if different albums) help the total score similarly, except they have about 1/15th the final weight. For example, two people ranking "Tom Waits - Rain Dogs" at position #15 would be equivalent to sixteen people each picking a different unique Tom Waits album for spot #15 -- Rain Dogs or all those fifteen other albums would have the same overall score. So votes on an artist boost a score, but again don't easily overwhelm high-ranked single picks.
The formula gives the following results on the given input data set:
A) Everyone's top 3 picks are included. (Note that with 13 people and only 64 nominees, the most we could guarantee to include would be everyone's top 4. I'll run the numbers with 128 nominees tomorrow.)
B) People who chose popular albums/artists have more of their picks filling the remaining spots. Here's the distribution. Looks like Brian has his finger on the, uh, pulse of the group. So to speak.
8 AndyW
8 AndyZ
14 Brian
10 Bruce
13 Dwight
9 Eric
10 Jane
11 Jeff
12 Karl
9 Kevin
7 Mark
7 Sarah
10 Steve
So here's the resulting 64. I didn't de-dup the list cuz I thought you might want to see whose original ranking put it there.
Score Album Artist Original Rank
1076 Spiritualized Ladies And Gent 24 Brian
1076 Spiritualized Ladies And Gent 18 Mark
1076 Spiritualized Ladies And Gent 9 Dwight
1076 Spiritualized Ladies And Gent 6 Jeff
1076 Spiritualized Ladies And Gent 5 Karl
1076 Spiritualized Ladies And Gent 3 Steve
1002 Radiohead Kid A 27 Bruce
1002 Radiohead Kid A 19 Dwight
1002 Radiohead Kid A 3 Sarah
1002 Radiohead Kid A 1 Kevin
985 Sufjan Stevens Illinoise 28 Dwight
985 Sufjan Stevens Illinoise 10 AndyZ
985 Sufjan Stevens Illinoise 3 Jeff
985 Sufjan Stevens Illinoise 3 Jane
981 Red House Paint Songs For a Blu 15 AndyZ
981 Red House Paint Songs For a Blu 14 Brian
981 Red House Paint Songs For a Blu 9 Jeff
981 Red House Paint Songs For a Blu 2 Kevin
950 Luna Penthouse 13 Mark
950 Luna Penthouse 13 Jeff
950 Luna Penthouse 8 Brian
950 Luna Penthouse 5 Steve
911 The New Pornogr Challengers 24 Kevin
911 The New Pornogr Challengers 9 Bruce
911 The New Pornogr Challengers 2 Sarah
900 Passion Pit Chunk of Change 13 Jane
900 Passion Pit Chunk of Change 13 AndyW
900 Passion Pit Chunk of Change 3 Bruce
892 The Cure Disintegration 4 Brian
892 The Cure Disintegration 1 Steve
891 Wilco Being There 22 Karl
891 Wilco Being There 10 Bruce
891 Wilco Being There 4 Kevin
877 Weezer Blue Album 23 Jeff
877 Weezer Blue Album 13 Brian
877 Weezer Blue Album 3 Dwight
867 Cat Power Moon Pix 20 Jane
867 Cat Power Moon Pix 19 Karl
867 Cat Power Moon Pix 3 Kevin
861 The Kinks The Kinks Are T 11 Eric
861 The Kinks The Kinks Are T 2 AndyW
854 Magnetic Fields 69 Love Songs 24 AndyW
854 Magnetic Fields 69 Love Songs 22 Brian
854 Magnetic Fields 69 Love Songs 2 Steve
851 The Band The Band 7 Dwight
851 The Band The Band 3 AndyZ
851 Bob Dylan Time Out of Min 20 Eric
851 Bob Dylan Time Out of Min 1 AndyW
831 Beach Boys Pet Sounds 27 Mark
831 Beach Boys Pet Sounds 18 Dwight
831 Beach Boys Pet Sounds 4 AndyW
819 Broken Social S You Forgot It I 25 Dwight
819 Broken Social S You Forgot It I 16 Jane
819 Broken Social S You Forgot It I 16 Bruce
819 Broken Social S You Forgot It I 9 AndyZ
818 Air Moon Safari 24 Steve
818 Air Moon Safari 19 Bruce
818 Air Moon Safari 5 Jeff
802 Neutral Milk Ho In The Aeroplan 18 AndyZ
802 Neutral Milk Ho In The Aeroplan 3 AndyW
795 Neko Case Middle Cyclone 9 Sarah
795 Neko Case Middle Cyclone 6 Bruce
793 Tom Waits Rain Dogs 23 Sarah
793 Tom Waits Rain Dogs 3 Karl
788 Neil Young Harvest 17 Kevin
788 Neil Young Harvest 5 Mark
787 Radiohead OK Computer 27 AndyW
787 Radiohead OK Computer 12 Karl
787 Radiohead OK Computer 10 Brian
786 Counting Crows August and Ever 18 Brian
786 Counting Crows August and Ever 4 Steve
783 Arcade Fire Funeral 15 Dwight
783 Arcade Fire Funeral 5 Sarah
769 Portishead Dummy 12 Eric
769 Portishead Dummy 7 Karl
768 Weakerthans Left and Leavin 11 Jane
768 Weakerthans Left and Leavin 8 Steve
768 Bob Dylan Blood on the Tr 30 Bruce
768 Bob Dylan Blood on the Tr 4 Sarah
764 White Stripes Elephant 18 AndyW
764 White Stripes Elephant 16 Dwight
764 White Stripes Elephant 10 Eric
758 Spiritualized Lazer Guided Me 1 Jeff
750 Rolling Stones Sticky Fingers 1 Sarah
749 U2 Joshua Tree 1 Brian
745 The Kinks Something Else 1 Eric
742 Weakerthans Reconstruction 1 Jane
738 Smashing Pumpki Siamese Dream 27 Jeff
738 Smashing Pumpki Siamese Dream 25 Steve
738 Smashing Pumpki Siamese Dream 8 Dwight
737 U2 Rattle and Hum 13 Steve
737 U2 Rattle and Hum 10 Kevin
734 Pink Floyd Wish You Were H 1 Karl
729 The Clash London Calling 1 AndyZ
727 Sufjan Stevens Seven Swans 20 Karl
727 Sufjan Stevens Seven Swans 9 Kevin
726 Yo La Tengo and then nothin 28 Kevin
726 Yo La Tengo and then nothin 6 Jane
726 Stina Nordensta And She Closed 21 Jeff
726 Stina Nordensta And She Closed 7 Steve
722 Postal Service Give Up 18 Karl
722 Postal Service Give Up 8 Jane
721 Sigur Ros Med Sud I Eyrum 2 Jane
720 Roy Harper Stormcock 1 Mark
720 Pixies Surfer Rosa 1 Dwight
720 Eluvium Copia 1 Bruce
716 Massive Attack Blue Lines 2 Eric
713 Stone Roses Stone Roses 21 Brian
713 Stone Roses Stone Roses 15 Jeff
713 Stone Roses Stone Roses 13 Eric
712 The Hold Steady Separation Sund 2 AndyZ
712 Bob Marley Legend 2 Brian
710 Afghan Whigs 1965 21 Jane
710 Afghan Whigs 1965 8 AndyZ
704 Nick Harper Light at the en 2 Mark
704 Mountains Mountains 2 Bruce
704 Laurie Anderson Big Science 2 Karl
704 Guh We Are Sunburni 2 Dwight
704 Grant Lee Buffalo Mig 2 Jeff
699 Led Zeppelin Led Zeppelin 3 Mark
692 U2 Achtung Baby 25 Brian
692 U2 Achtung Baby 10 Karl
692 Tom Waits Mule Variations 4 Dwight
692 Beatles Revolver 4 Eric
689 Wilco Yankee Hotel Fo 5 Brian
689 Low The Curtain Hit 4 Karl
688 Nirvana Nevermind 3 Brian
688 New Order Substance 3 Eric
Truly a thing of beauty. Your maths have me weak in the knees.
ReplyDeleteLet's all give Karl a round of applause.
ReplyDeleteHere's an idea concerning the 64 vs. 128: we can start with the 64 (we'll call it division 1). If things go quickly and smoothly, we can create a new bracket (division 2). Then the winner of Division 1 can compete against the winner of Division 2--champion vs. underdog (with everyone getting a vote on this final battle). I think the division 2 bracket would actually be more fun because there would be more stuff people haven't heard.
What do you think?
Okay, I am a math dummy, but can you tell me what happened to YLT I Can Hear the Heart? It's on my list, AndyW's list, and Karl's list. Is it just ranked too low?
ReplyDeleteAlso (and more importantly): Applause!
Yeah, Sarah, I was really hoping people would pick out a few that look strange so that we can double-check that the ranking formula is actually working. I think in general what you're seeing is that people's top picks are weighted heavily, but repeat-picks don't get much weight. So here's what happened to "I Can Hear the Heart": Three votes at position #17, #24, and #30 gives scores of 29, 22, and 16, respectively. The 29 counts the most, and then the 22 and 16 boost the total score up to 36.79.
ReplyDeleteI Can Hear The Heart Beating As One: 29 22 16
score 29 index 0 discount 1.00 is 29.00, albumscore now 29.00
score 22 index 1 discount 0.25 is 5.50, albumscore now 34.50
score 16 index 2 discount 0.14 is 2.29, albumscore now 36.79
Then for Yo La Tengo, it starts strong with a #6 vote (= 40 points) from someone, and the total score for the artist gets boosted up to a respectable 58.42.
Yo La Tengo: 40 29 22 18 16
score 40 index 0 discount 1.00 is 40.00, artistscore now 40.00
score 29 index 1 discount 0.33 is 9.67, artistscore now 49.67
score 22 index 2 discount 0.20 is 4.40, artistscore now 54.07
score 18 index 3 discount 0.14 is 2.57, artistscore now 56.64
score 16 index 4 discount 0.11 is 1.78, artistscore now 58.42
But the album score counts much more than the artist score -- 15 times as much. The resulting score of 610 isn't enough. If the album score had been higher, it would have made a big difference.
I Can Hear The Heart Beating As One (Yo La Tengo)
total 36.7857142857 * 15 + 58.4158730159 * 1 = 610.201587302
I just realized it would much easier to read all this if I normalized the final scores by dividing by 16. I'll do that in the future...
Looking at extended results, I think "I Can Hear.." is the best example of a three-vote that got shafted. M.I.A. "Kala" is an interesting example, because tho it doesn't make the 64 list, it actually does much better than YLT "I Can Hear". It got two votes at #12 and #13, and those slightly higher starting votes put the album score at 42.25. The score for M.I.A. as an artist is around 50, lower than YLT, but the album score makes all the difference.
ReplyDeleteAt the risk of being repetitive, "I Can Hear..." is a good reason to have a Division 2 tournament. C'mon folks, who's with me?
ReplyDeleteJust for fun, here's the list from number 65 on down to "I Can Hear...". This will look different from the Top 128 list because I'll change the formula to be less aggressive about including people's top picks.
ReplyDelete43.0 Low The Curtain Hit 4 Karl
43.0 John Coltrane Blue Train 4 AndyZ
42.9 Belle and Sebas If You're Feeli 23 Steve
42.9 Belle and Sebas If You're Feeli 9 Jane
42.8 M.I.A. Kala 13 Sarah
42.8 M.I.A. Kala 12 Bruce
42.3 Beatles Abbey Road 5 Dwight
42.0 Polyphonic Spre Together We're 4 Jeff
42.0 Poison Flesh And Blood 4 Mark
42.0 Christopher Wil Surf Boundaries 4 Bruce
42.0 Anathallo Canopy Glow 4 Jane
41.9 His Name Is Ali Stars on ESP 17 Jane
41.9 His Name Is Ali Stars on ESP 12 AndyZ
41.8 Bruce Springste The Wild, the I 5 AndyZ
41.5 Do Make Say Thi Winter Hymn Cou 5 Bruce
41.2 Will Oldham Lost Blues And 6 Karl
41.2 Rolling Stones Between the But 7 Eric
41.2 Low Trust 6 Steve
41.0 The Velvet Unde The Velvet Unde 5 AndyW
41.0 The Stooges Fun House 5 Eric
41.0 Karen Dalton In my own time 5 Kevin
41.0 Iron and Wine Our Endless Num 5 Jane
40.6 Pearl Jam Versus 6 Kevin
40.6 Lambchop Is a Woman 6 AndyZ
40.6 Cat Power You Are Free 7 Sarah
40.6 Beck Midnite Vulture 21 Kevin
40.6 Beck Midnite Vulture 13 Dwight
40.5 Bob Dylan Bringing It All 8 AndyW
40.4 Beck Odelay 7 Brian
40.1 REM Automatic for t 26 Steve
40.1 REM Automatic for t 11 Brian
40.0 Ween The Mollusk 6 Dwight
40.0 Paul Simon Graceland 6 Brian
40.0 Johnny Cash Unchained 7 AndyW
40.0 James Brown 20 All Time Gre 6 Eric
40.0 Dread Zeppelin Unledded 6 Mark
40.0 Bright Eyes I'm Wide Awake, 6 Sarah
40.0 Bob Dylan And T The Basement Ta 6 AndyW
39.6 Bjork Homogenic 15 Sarah
39.6 Bjork Homogenic 15 Karl
39.4 Will Oldham Lie Down in the 8 Sarah
39.4 Rolling Stones Let It Bleed 9 Brian
39.4 Cut Copy Bright Like Neo 7 Bruce
39.1 Wilco Summerteeth 19 AndyW
39.1 Wilco Summerteeth 16 Sarah
39.1 Joni Mitchell Blue 26 Kevin
39.1 Joni Mitchell Blue 12 Jane
39.1 Johnny Cash American IV: Th 18 Jeff
39.1 Johnny Cash American IV: Th 15 Kevin
39.0 Tindersticks Tindersticks [1 7 Jeff
39.0 The Killers Hot Fuss 7 Mark
39.0 The Elected Sun, Sun, Sun 7 AndyZ
39.0 Patty Griffin Living with Gho 7 Kevin
39.0 Mineral The Power of Fa 7 Jane
39.0 Bruce Springste Ghost of Tom Jo 8 Kevin
38.7 Neil Young Everybody Knows 9 Eric
38.3 Luna Tigerlilly 10 Steve
38.1 Yo La Tengo I Can Hear The 30 AndyW
38.1 Yo La Tengo I Can Hear The 24 Sarah
38.1 Yo La Tengo I Can Hear The 17 Karl
I mostly get it now. Thanks for explaining, K.
ReplyDelete