I was wondering how the AM Top 10 artists by songs would look like if some producers who had spread-out hits with various artists/groups were counted as just one entity. More precisely, I wanted to see how Phil Spector would fit in.

This is the formula that Henrik used to establish the rankings:


(ln(ln(10+songranking1)) + ln(ln(10+songranking2)) + ln(ln(10+songranking3)) + ln(ln(10+songranking4)) + ln(ln(10+songranking5)) + ln(ln(10+songranking6))


And, of course, the smaller the sum of the ln's of the ln's of the 6 songs is, the better.

(in the calculations below I never forgot about the offset of the +10, so don't worry)

As a sidenote, it's funny how having the distance in value between a song on an extremely good spot (for example, 10) and a song on a very very good spot (for example, 100) is larger than the distance between the song on the very very good spot mentioned before (100) and a song near the end (for example 3000).

As here's what each of those spots mean in the actual math:

10 = 1.0971887003649487029456795694485
100 = 1.5476647089811360244471376979621
3000 = 2.0806527276157964996200654959935

Compare with:

300 = 1.7468618712420882348946155451153
900 = 1.9188978071863344517042557444036

So having songs further off, or even very near the end, doesn't matter that much if you have songs very near the beginning.

For The Kinks, for example, the differences in values between their last four songs is negligible. There's more distance between "You Really Got Me" - #17 and "Waterloo Sunset" - #55 (0.23630746954581394036407202201109) than there is between "Lola" - #455 and "Sunny Afternoon" - #1866 (0.20119582569385275603049342755224).

And for the Sex Pistols, the distance from "Anarchy in the U.K." - #10 to "God Save The Queen" - #23 (0.1545759303760733119939949233784) is actually quite a bit larger than the difference from #1000 to #3000 (0.1465685722365012237852867943878 .

Anyhow.

As you know, the AM list for the songs' Top 20 is:

1. The Beatles ("Strawberry Fields Forever" - #16, "A Day In The Life" - #18, "I Want To Hold Your Hand" - #21, "Hey Jude" - #37, "She Loves You" - #99, "Yesterday" - #114)
2. The Rolling Stones ("Satisfaction" - #2, "Sympathy For The Devil" - #34, "Jumpin' Jack Flash" - #40, "Honky Tonk Women" - #122, "Gimme Shelter" - #127, "Brown Sugar" - #15
3. Elvis Presley ("Heartbreak Hotel" - #15, "Hound Dog" - #57, "Suspicious Minds" - #66, "That's All Right (Mama)" - #72, "Mystery Train" - #85, "Don't Be Cruel" - #92)
4. Marvin Gaye ("I Heard It Through The Grapevine" - #8, "What's Going On" - #20, "Sexual Healing" - #133, "Let's Get It On" - #265, "Ain't No Mountain High Enough" - #571, "Inner City Blues (Make Me Wanna Holler)" - #797)
5. The Beach Boys ("Good Vibrations" - #3, "God Only Knows" - #52, "Don't Worry Baby" - #142, "I Get Around" - #256, "Surfin' U.S.A." - #502, "California Girls" - #686)
6. Bob Dylan ("Like A Rolling Stone" - #1, "Subterranean Homesick Blues" - #137, "Tangled Up In Blue" - #272, "Blowin' In The Wind" - #286, "Positively 4th Street" - #435, "The Times They Are A-Changing" - #467)
7. Prince ("When Doves Cry" - #46, "Little Red Corvette" - #88, "Sign 'O' The Times" - #130, "Kiss" - #140, "1999" - #305, "Purple Rain" - #441)
8. David Bowie ("Heroes" - #61, "Space Oddity" - #108, "Changes" - #153, "Ziggy Stardust" - #165, "Life On Mars" - #389, "Young Americans" - #470)
9. Led Zeppelin ("Stairway To Heaven" - #9, "Whole Lotta Love" - #76, "Kashmir" - #385, "Rock and Roll" - #392, "Dazed and Confused" - #473, "Heartbreaker" - #1011)
10. Aretha Franklin ("Respect" - #5, "I Say A Little Prayer" - #205, "Chain of Fools" - #288, "I Never Loved a Man the Way I Love You" - #472, "Think" - #609, "(You Make Me Feel Like) A Natural Woman" - #669)
11. The Who ("My Generation" - #13, "Won't Get Fooled Again" - #121, "I Can't Explain" - #202, "I Can See For Miles" - #375, "Baba O'Riley" - #689, "Substitute" - #985)
12. Sex Pistols ("Anarchy in the U.K." - #10, "God Save The Queen" - #23, "Pretty Vacant" - #274, "Holidays in the Sun" - #561, "My Way" - #2188, "Blank" - #3100)
13. Jimi Hendrix ("Purple Haze" - #41, "All Along the Watchtower" - #81, "Voodoo Chile (Slight Return)" - #216, "Hey Joe" - #239, "Crosstown Traffic" - #618, "Foxy Lady" - #112
14. Chuck Berry ("Johnny B. Goode" - #6, "Maybellene" - #78, "Roll Over Beethoven" - #487, "Sweet Little Sixteen" - #854, "Rock and Roll Music" - #1008, "Memphis, Tennessee" - #1370)
15. James Brown ("Papa's Got a Brand New Bag" - #82, "Get Up (I Feel Like Being a) Sex Machine" - #141, "It's a Man's Man's Man's World" - #231, "I Got You (I Feel Good) " - #238, "Please Please Please" - #324, "Say It Loud, I'm Black and I'm Proud" - #975)
16. The Clash ("London Calling" - #35, "(White Man) In Hammersmith Palais" - #147, "Complete Control" - #395, "Rock The Casbah" - #457, "Train in Vain (Stand by Me)" - #471, "White Riot" - #555)
17. Nirvana ("Smells Like Teen Spirit" - #4, "Heart-Shaped Box" - #284, "All Apologies" - #497, "Come As You Are" - #720, "About a Girl" - #841, 1124 - "Lithium")
18. U2 ("One" - #94, "Sunday Bloody Sunday" - #223, "Pride (In The Name of Love)" - #302, "With or Without You" - #312, "I Still Haven't Found What I'm Looking For" - #396, "New Year's Day" - #46
19. The Kinks ("You Really Got Me" - #17, "Waterloo Sunset" - #55, "Lola" - #455, "All Day and All of the Night" - #876, "See My Friends" - #1740, "Sunny Afternoon" - #1866)
20. Bruce Springsteen ("Born to Run" - #25, "Thunder Road" - #174, "Born in the U.S.A." - #190, "Dancing in the Dark" - #777, "Brilliant Disguise" - #1127, "The River" - #1406)

These are the scores in order:

1. The Beatles: 8.0851630414050651935513026035555
2. The Rolling Stones: 8.4180737182811703456507274419682
3. Elvis Presley: 8.6015501628599911502741922101881
4. Marvin Gaye: 9.3651343570468697068506482670499
5. The Beach Boys: 9.4030063321355283128337598274737
6. Bob Dylan: 9.5783788134472974176590059504896
7. Prince: 9.6844698270674877211207575083268
8. David Bowie: 9.8924961564852487169644985225314
9. Led Zeppelin: 9.9101708028806205943384838076326
10. Aretha Franklin: 9.9737667477937292900838704126259
11. The Who: 10.000540996043436413369326498384
12. Sex Pistols: 10.053805860807562091859467936394
13. Jimi Hendrix: 10.087811175157719271865492972243
14. Chuck Berry: 10.169439925810908318373169238101
15. James Brown: 10.22119366729130008031134131714
16. The Clash: 10.232666520464527639475296669668
17. Nirvana: 10.282851788276097911201105759023
18. U2: 10.345362756132818039295649089181
19. The Kinks: 10.385563345783686546842941045685
20. Bruce Springsteen: 10.417556535905976917232187104153

Now, as a reminder:

Phil Spector ("Be My Baby" - #12, "River Deep Mountain High" - #22, "You've Lost That Lovin' Feelin'" - #24, "Da Doo Ron Ron" - #169, "He's A Rebel" - #308, "Spanish Harlem" - #583)

Holland-Dozier-Holland ("Reach Out I'll Be There" - #36, "Stop! In the Name of Love" - #143, "Where Did Our Love Go" - #211, "Band of Gold" - #418, "You Can't Hurry Love" - #421, "(Love Is Like a) Heat Wave" - #655)

Norman Whitfield ("I Heard It Through The Grapevine" - #8, "Papa Was a Rolling Stone" - #128, "War" - #298, "Just My Imagination (Running Away With Me)" - #338, "Ball of Confusion (That's What the World Is Today)" - #1005, "Ain't Too Proud To Beg" - #1287)

Timbaland ("Get Ur Freak On" - #59, "Work It" - #149, "My Love" - #268, "Try Again" - #615, "Promiscuous" - #620, "SexyBack" - #776)

Put them in and you get this:

1. The Beatles: 8.0851630414050651935513026035555
2. The Rolling Stones: 8.4180737182811703456507274419682
3. Elvis Presley: 8.6015501628599911502741922101881
4. Phil Spector: 8.8832050769965178514945069614674
5. Marvin Gaye: 9.3651343570468697068506482670499
6. The Beach Boys: 9.4030063321355283128337598274737
7. Bob Dylan: 9.5783788134472974176590059504896
8. Prince: 9.6844698270674877211207575083268
9. David Bowie: 9.8924961564852487169644985225314
10. Led Zeppelin: 9.9101708028806205943384838076326
11. Aretha Franklin: 9.9737667477937292900838704126259
12. The Who: 10.000540996043436413369326498384
13. Sex Pistols: 10.053805860807562091859467936394
14. Norman Whitfield: 10.073115744899609571061703602712
15. Jimi Hendrix: 10.087811175157719271865492972243
16. Holland-Dozier-Holland: 10.120127454861526363663340938984
17. Chuck Berry: 10.169439925810908318373169238101
18. James Brown: 10.22119366729130008031134131714
19. The Clash: 10.232666520464527639475296669668
20. Nirvana: 10.282851788276097911201105759023
21. U2: 10.345362756132818039295649089181
22. The Kinks: 10.385563345783686546842941045685
23. Timbaland: 10.416742978772846846813359595694
24. Bruce Springsteen: 10.417556535905976917232187104153

You could say:

"Yeah, but they're just producers. They shouldn't count that much."

Yes, however, Elvis was a mere singer. He didn't write his songs, or play on them, or do much creatively - he sang. If he's got a right to be there, surely the list above is not that wrong for Timbaland and co. After all, without their unique production flavors, the songs would be mere ditties.

Question is: will he dethrone the masters?

That's it. I've just about had enough. Time to disable smilies forever!

Starting with the next one, anyway...
Also.

As a sidenote, it's funny how having the distance

I mean "it's funny how the distance".

As a sidenote, it's funny how having the distance in value between a song on an extremely good spot (for example, 10) and a song on a very very good spot (for example, 100) is larger than the distance between the song on the very very good spot mentioned before (100) and a song near the end (for example 3000).


I mean Tends To Be Larger, in general. 3000 is just one example, and as such is a bad example, because in that case it's not larger, obviously - but it does show the disparity well.

But yeah, it's true that:

"Like A Rolling Stone" (#1) to "Nothing Compares 2 U" (#100) = 0.67307332605744710622011969296061

Whereas:

"Nothing Compares 2 U" (#100) to "My Girl" (#3000) = 0.5325724620579830153115857610178 (!!!)

As you see, there's a shorter road between #100 and #3000 than between #1 and #100.

So, if you happen to be an artist without a song somewhere in the Top 100, or preferrably on a ridiculously good position, you can shed away your hopes of doing well in the AM Artists by Songs ranking.

Yes, that's my main problem with the artist calculation method. Highly ranked songs/albums just have too much influence. I don't know how to improve this though, so I suppose I shouldn't complain.

Stephan, let's test a tamer version of Henrik's formula.

(ln(ln(100+songranking1)) + ln(ln(100+songranking2)) + ln(ln(100+songranking3)) + ln(ln(100+songranking4)) + ln(ln(100+songranking5)) + ln(ln(100+songranking6))

The offset is now 100, so the Top 100 problem goes away from the very start.

This has interesting consequences that make sense (to me anyway):

1. 116 + 118 + 121 + 137 + 199 + 214: 9.628954264683365760695587560512 (The Beatles)

2. 115 + 157 + 166 + 172 + 185 + 192: 9.7600201291809682382093285402615 (Elvis Presley)

3. 102 + 134 + 140 + 222 + 227 + 258: 9.810196865992598204254313643032 (The Rolling Stones)

Interesting, but it seems that when I use +10 the resulting artist ranking better fits my taste than when I use +100. Or +50. Or even +25. Strange!

Well. The larger the offset is, the more that consistency is valued over peaks.

It feels less crazy than the 10 offset where 13 positions have more value than 2000 positions, in the case of the Sex Pistols.

With offset 100:

#10 to #23: 0.023486399987704138501743110009405
#1000 to #3000: 0.13797629963985694623367981493921

I guess I'll wait until Henrik has a say about this. But it rather makes more sense to me for Elvis to be above The Rolling Stones - after all, his 6 songs are all in the Top 100, whereas The Stones rely on the boosts of their first three.

Then again, it is true that, as humans, our perception relies more on peaks than on consistency.

What to do, what to do?

For example, have you noticed that, when you stumble on a song you like by someone you can't stand, your apreciation of them on the whole immediately increases?

So, if you happen to be an artist without a song somewhere in the Top 100, or preferrably on a ridiculously good position, you can shed away your hopes of doing well in the AM Artists by Songs ranking.

You can do well, but you can not be in the top. And rightfully so, I think. An artist without a top song just isn't a top song artist.


It feels less crazy than the 10 offset where 13 positions have more value than 2000 positions, in the case of the Sex Pistols.

With offset 100:

#10 to #23: 0.023486399987704138501743110009405
#1000 to #3000: 0.13797629963985694623367981493921

This is harder to explain, and I'm a bit surprised too about these figures. But it fits with the number of critics lists you need to be included in to climb the AM list. A few entries and whoops, you go from nowhere into the top 1000. The same few entries probably wouldn't be enough to climb from #23 to #10.

What about songwriters? Bacharach and Goffin/King would be right up there I bet. It would also boost Kris Kristofferson and Lennon/McCartney if we'd give non-Beatles hits to both of them. Also, when you look at producers, I would bet Quincy Jones is up there too. Plus, it's not really fair but George Martin would be #1 of all-time considering he has almost all of the Beatles stuff, plus Jeff Beck, Gerry and the Pacemakers, America and some Kenny Rogers. But, I suppose with the formula it would be a tie.

Well, only the first 6 songs count, so none of those would make the Top 20.

(Because they don't have Top 100 songs.)

That means that The Beatles, with a whooping 54 songs that make the Top 3000, only get their first 6 songs counted when the rankings are made.

Although, between you and me, their songs feed on each other. Liking one song a lot makes you like others more, and so on.

So they end up with 54 somehow, instead of 15 or so.