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Lowest Possible Elo? A XKCD "what-if" Parody

9spaceking
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6/26/2014 12:28:45 PM
Posted: 2 years ago
What is the theoretical lowest possible elo? Or is there no lowest...meaning it could go all the way to infinity? Could elo potentially go into the negatives if you lose enough to bad guys, and those bad guys lose to other bad guys??
Today, I test out my theory.
My hypothesis: negative elo will be impossible.
Calculation of first loses:
To skip to the point let's suppose a 1000 elo guy lost to a 1000 elo guy, and the first guy who lost accepted the debate...
C= 100* (1000+9000)/10000
C=125 (boost by instigating/accepting the debate)
So now this guy only has 875....
And now, let's suppose some other guy with 1000 lost to another 1000 and only has 875 as well...
and they collide in another epic battle...which, this time, the other guy lost, but he accepted the debate...
C=100 * (875+7875)/8750
C=125 (again??)
and so this guy loses 125...and reaches a low, low 750. Logically, if this goes on, this guy will reach a bad zero within 5 debates if he keeps on accepting debates from pals around the same elo as him...
but now, what about zero?
Obviously the winner cannot be that guy with zero elo, since the number on top will be divided by zero. So let's say this guy with zero loses to a guy with one elo. Somehow.
C=100 * (1+0)/1000
C=100/1000
C=1/10
C=25 and 1/10. Therefore this guy who had zero elo now only has -25 and 1/10, rounded to -25 elo.
It seems that my hypothesis is disproved! People can get negative elo, after all! But now...let's get things juggled up. What if this guy with -25 elo lost to a guy with -25 elo? Yes, many, many battles would have to take place for this to happen, but just--what if?
C=100* (-25+-225)/-250
C=125
Whoa...so it looks like you always gain/lose 125 if you face a guy with the same elo as you. So now, this terrible debater only has -150.

And everything seems to be over. Easy, eh? That was nothing.

But it's not the end yet--even though we know technically a "negative infinity" is possible, we still don't know what would happen....if some good debater LOST to one of these horrid debaters.
And so...in our final hypothetical situation, the horrid guy with -150 elo faces....
MIKAL.

AND HE WINS. (Which, we know, is impossible in real life, but this is imaginary)

C= 100* (-150+81000)/-1500
C=-5390

Oh, no. That's an odd error. If this guy had accepted the debate from Mikal, he would have gained... -5415 elo???!! That's weird.
Huh, it seems the formula can turn against itself!!
AND MIKAL WOULD WIN 5415 ELO!!!! WHOA....that would be a weird feat...

But now, what if Mikal wins against this weirdo?
C=100 * (9000+-1350)/90000
C=8.5
And if he accepted the debate....well, he only has decreased elo. XD

So, the lesson is...Don't lose too much.
If you get negative elo, you'll have a darned hard time getting back up due to the elo calculation. :P
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LogicalLunatic
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6/26/2014 12:35:48 PM
Posted: 2 years ago
At 6/26/2014 12:28:45 PM, 9spaceking wrote:
What is the theoretical lowest possible elo? Or is there no lowest...meaning it could go all the way to infinity? Could elo potentially go into the negatives if you lose enough to bad guys, and those bad guys lose to other bad guys??
Today, I test out my theory.
My hypothesis: negative elo will be impossible.
Calculation of first loses:
To skip to the point let's suppose a 1000 elo guy lost to a 1000 elo guy, and the first guy who lost accepted the debate...
C= 100* (1000+9000)/10000
C=125 (boost by instigating/accepting the debate)
So now this guy only has 875....
And now, let's suppose some other guy with 1000 lost to another 1000 and only has 875 as well...
and they collide in another epic battle...which, this time, the other guy lost, but he accepted the debate...
C=100 * (875+7875)/8750
C=125 (again??)
and so this guy loses 125...and reaches a low, low 750. Logically, if this goes on, this guy will reach a bad zero within 5 debates if he keeps on accepting debates from pals around the same elo as him...
but now, what about zero?
Obviously the winner cannot be that guy with zero elo, since the number on top will be divided by zero. So let's say this guy with zero loses to a guy with one elo. Somehow.
C=100 * (1+0)/1000
C=100/1000
C=1/10
C=25 and 1/10. Therefore this guy who had zero elo now only has -25 and 1/10, rounded to -25 elo.
It seems that my hypothesis is disproved! People can get negative elo, after all! But now...let's get things juggled up. What if this guy with -25 elo lost to a guy with -25 elo? Yes, many, many battles would have to take place for this to happen, but just--what if?
C=100* (-25+-225)/-250
C=125
Whoa...so it looks like you always gain/lose 125 if you face a guy with the same elo as you. So now, this terrible debater only has -150.

And everything seems to be over. Easy, eh? That was nothing.

But it's not the end yet--even though we know technically a "negative infinity" is possible, we still don't know what would happen....if some good debater LOST to one of these horrid debaters.
And so...in our final hypothetical situation, the horrid guy with -150 elo faces....
MIKAL.

AND HE WINS. (Which, we know, is impossible in real life, but this is imaginary)

C= 100* (-150+81000)/-1500
C=-5390

Oh, no. That's an odd error. If this guy had accepted the debate from Mikal, he would have gained... -5415 elo???!! That's weird.
Huh, it seems the formula can turn against itself!!
AND MIKAL WOULD WIN 5415 ELO!!!! WHOA....that would be a weird feat...

But now, what if Mikal wins against this weirdo?
C=100 * (9000+-1350)/90000
C=8.5
And if he accepted the debate....well, he only has decreased elo. XD

So, the lesson is...Don't lose too much.
If you get negative elo, you'll have a darned hard time getting back up due to the elo calculation. :P

Actually, if you lose too much then you can fix it by creating a new account.
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9spaceking
Posts: 4,213
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6/26/2014 12:41:30 PM
Posted: 2 years ago
yes. That's another solution. I should have added that...
"When your elo is going into the negatives, don't even try. Just make a new account." :P
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xXCryptoXx
Posts: 5,000
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6/26/2014 1:02:56 PM
Posted: 2 years ago
At 6/26/2014 12:28:45 PM, 9spaceking wrote:
So, the lesson is...Don't lose too much.
If you get negative elo, you'll have a darned hard time getting back up due to the elo calculation. :P

I thought if you had negative ELO you could gain ELO by losing.
Nolite Timere
phantom
Posts: 6,774
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6/26/2014 3:25:21 PM
Posted: 2 years ago
1,000 Elo is the minimum. You can't go lower than that.
"Music is a zen-like ecstatic state where you become the new man of the future, the Nietzschean merger of Apollo and Dionysus." Ray Manzarek (The Doors)
9spaceking
Posts: 4,213
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6/26/2014 3:38:18 PM
Posted: 2 years ago
At 6/26/2014 3:25:21 PM, phantom wrote:
1,000 Elo is the minimum. You can't go lower than that.

why? Does the elo equation not work for those with 1,000 elo??
Equestrian election
http://www.debate.org...

This House would impose democracy
http://www.debate.org...

Reign of Terror is unjustified
http://www.debate.org...

Raise min. wage to $10.10
http://www.debate.org...
phantom
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6/26/2014 3:43:13 PM
Posted: 2 years ago
At 6/26/2014 3:38:18 PM, 9spaceking wrote:
At 6/26/2014 3:25:21 PM, phantom wrote:
1,000 Elo is the minimum. You can't go lower than that.

why? Does the elo equation not work for those with 1,000 elo??

It's simply the base Elo. Those with a 1,000 Elo can't lose points. I assume Juggle/OreEle made it that way partially to prevent problems such as those that you mentioned.
"Music is a zen-like ecstatic state where you become the new man of the future, the Nietzschean merger of Apollo and Dionysus." Ray Manzarek (The Doors)
9spaceking
Posts: 4,213
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6/26/2014 5:04:37 PM
Posted: 2 years ago
At 6/26/2014 3:43:13 PM, phantom wrote:
At 6/26/2014 3:38:18 PM, 9spaceking wrote:
At 6/26/2014 3:25:21 PM, phantom wrote:
1,000 Elo is the minimum. You can't go lower than that.

why? Does the elo equation not work for those with 1,000 elo??

It's simply the base Elo. Those with a 1,000 Elo can't lose points. I assume Juggle/OreEle made it that way partially to prevent problems such as those that you mentioned.

interesting.
Equestrian election
http://www.debate.org...

This House would impose democracy
http://www.debate.org...

Reign of Terror is unjustified
http://www.debate.org...

Raise min. wage to $10.10
http://www.debate.org...