Ranking Question
$begingroup$
I'm not sure if the title properly titles my question. Here is the problem:
Imagine a game where two teams play another two teams. Each team plays 6 matches where they are partnered with one other team and face-off with a set of two other teams. Each alliance is awarded a certain amount of points based on their collective performance. Using the amount of points each alliance scores I have to rank the teams from best to worst. What do you think would be the best way to approach this?
If anything is unclear please let me know; I will update it.
combinatorics graph-theory
edited Dec 5 '18 at 22:06
amWhy
1
asked Dec 5 '18 at 21:49
Archishmaan OkonkwoArchishmaan Okonkwo
11
$endgroup$
add a comment |
$begingroup$
I'm not sure if the title properly titles my question. Here is the problem:
Imagine a game where two teams play another two teams. Each team plays 6 matches where they are partnered with one other team and face-off with a set of two other teams. Each alliance is awarded a certain amount of points based on their collective performance. Using the amount of points each alliance scores I have to rank the teams from best to worst. What do you think would be the best way to approach this?
If anything is unclear please let me know; I will update it.
combinatorics graph-theory
edited Dec 5 '18 at 22:06
amWhy
1
asked Dec 5 '18 at 21:49
Archishmaan OkonkwoArchishmaan Okonkwo
11
$endgroup$
$begingroup$
I don't think this is clear. How many teams are there in total, for example? As a general note, it's often the case that there is no unambiguous ranking in group encounters. For instance, with three teams, $A,B,C$, each of whom play each other once...if $A$ beats $B$, $B$ beats $C$, and $C$ beats $A$...which would you want to call the winner?
$endgroup$
– lulu
Dec 5 '18 at 21:53
$begingroup$
Well thats the challenge. The only data you have is the number of points. You know who plays who and thats it. The number of teams is subject to change and so is who plays who.
$endgroup$
– Archishmaan Okonkwo
Dec 5 '18 at 22:25
add a comment |
$begingroup$
I'm not sure if the title properly titles my question. Here is the problem:
Imagine a game where two teams play another two teams. Each team plays 6 matches where they are partnered with one other team and face-off with a set of two other teams. Each alliance is awarded a certain amount of points based on their collective performance. Using the amount of points each alliance scores I have to rank the teams from best to worst. What do you think would be the best way to approach this?
If anything is unclear please let me know; I will update it.
combinatorics graph-theory
edited Dec 5 '18 at 22:06
amWhy
1
asked Dec 5 '18 at 21:49
Archishmaan OkonkwoArchishmaan Okonkwo
11
$endgroup$
I'm not sure if the title properly titles my question. Here is the problem:
Imagine a game where two teams play another two teams. Each team plays 6 matches where they are partnered with one other team and face-off with a set of two other teams. Each alliance is awarded a certain amount of points based on their collective performance. Using the amount of points each alliance scores I have to rank the teams from best to worst. What do you think would be the best way to approach this?
If anything is unclear please let me know; I will update it.
combinatorics graph-theory
combinatorics graph-theory
edited Dec 5 '18 at 22:06
amWhy
1
asked Dec 5 '18 at 21:49
Archishmaan OkonkwoArchishmaan Okonkwo
11
edited Dec 5 '18 at 22:06
amWhy
1
asked Dec 5 '18 at 21:49
Archishmaan OkonkwoArchishmaan Okonkwo
11
edited Dec 5 '18 at 22:06
amWhy
1
edited Dec 5 '18 at 22:06
amWhy
1
edited Dec 5 '18 at 22:06
amWhy
1
1
asked Dec 5 '18 at 21:49
Archishmaan OkonkwoArchishmaan Okonkwo
11
asked Dec 5 '18 at 21:49
Archishmaan OkonkwoArchishmaan Okonkwo
11
asked Dec 5 '18 at 21:49
Archishmaan OkonkwoArchishmaan Okonkwo
11
11
$begingroup$
I don't think this is clear. How many teams are there in total, for example? As a general note, it's often the case that there is no unambiguous ranking in group encounters. For instance, with three teams, $A,B,C$, each of whom play each other once...if $A$ beats $B$, $B$ beats $C$, and $C$ beats $A$...which would you want to call the winner?
$endgroup$
– lulu
Dec 5 '18 at 21:53
$begingroup$
Well thats the challenge. The only data you have is the number of points. You know who plays who and thats it. The number of teams is subject to change and so is who plays who.
$endgroup$
– Archishmaan Okonkwo
Dec 5 '18 at 22:25
add a comment |
$begingroup$
I don't think this is clear. How many teams are there in total, for example? As a general note, it's often the case that there is no unambiguous ranking in group encounters. For instance, with three teams, $A,B,C$, each of whom play each other once...if $A$ beats $B$, $B$ beats $C$, and $C$ beats $A$...which would you want to call the winner?
$endgroup$
– lulu
Dec 5 '18 at 21:53
$begingroup$
Well thats the challenge. The only data you have is the number of points. You know who plays who and thats it. The number of teams is subject to change and so is who plays who.
$endgroup$
– Archishmaan Okonkwo
Dec 5 '18 at 22:25
$begingroup$
I don't think this is clear. How many teams are there in total, for example? As a general note, it's often the case that there is no unambiguous ranking in group encounters. For instance, with three teams, $A,B,C$, each of whom play each other once...if $A$ beats $B$, $B$ beats $C$, and $C$ beats $A$...which would you want to call the winner?
$endgroup$
– lulu
Dec 5 '18 at 21:53
$begingroup$
I don't think this is clear. How many teams are there in total, for example? As a general note, it's often the case that there is no unambiguous ranking in group encounters. For instance, with three teams, $A,B,C$, each of whom play each other once...if $A$ beats $B$, $B$ beats $C$, and $C$ beats $A$...which would you want to call the winner?
$endgroup$
– lulu
Dec 5 '18 at 21:53
$begingroup$
Well thats the challenge. The only data you have is the number of points. You know who plays who and thats it. The number of teams is subject to change and so is who plays who.
$endgroup$
– Archishmaan Okonkwo
Dec 5 '18 at 22:25
$begingroup$
Well thats the challenge. The only data you have is the number of points. You know who plays who and thats it. The number of teams is subject to change and so is who plays who.
$endgroup$
– Archishmaan Okonkwo
Dec 5 '18 at 22:25
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The simplest is to award each team the number of points scored by its alliance in each game. Maybe you give a bonus for winning a game. You can adjust the ratio between the game score and the point score to taste. Basically you say that you are averaging over the teammates and the opponents and let it go at that.
The problem with that is the bias it introduces if the teams are uneven and not everybody teams with everybody else. Suppose one team is much better than all the rest and wins all its games by a large margin. No matter what you do, it will come in first. Those teams that partnered with the good one have an unfair advantage and those that opposed it are at a disadvantage. I can imagine saying that each team has a contribution to the overall score difference and doing a least squares fit to the results to determine the team ranking. That sounds like to much math mumbo jumbo to be acceptable in the setting.
answered Dec 5 '18 at 22:00
Ross MillikanRoss Millikan
294k23198371
$endgroup$
$begingroup$
Well to me, it doesn't matter how much math is involved. I found one solution that did the following:chiefdelphi.com/forums/showpost.php?p=484220&postcount=19 and here blog.thebluealliance.com/2017/10/05/…
$endgroup$
– Archishmaan Okonkwo
Dec 5 '18 at 22:45
$begingroup$
I don't worry about the math being too much for you, but about it being too much for your audience. It won't be easy to explain what you are doing, so it won't be "obviously fair", so a losing team may complain.
$endgroup$
– Ross Millikan
Dec 5 '18 at 22:49
$begingroup$
This is for our teams own purposes. At the end of the tournament there are alliance selections where the top teams pick from the teams at the tournament. We want an accurate way of determining who's the best. The more accurate the better. We currently use the link I posted but it seems to over estimate a good teams contributions, under estimate a bad teams contributions and people in the middle are kinda thrown around.
$endgroup$
– Archishmaan Okonkwo
Dec 5 '18 at 22:52
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3027699%2franking-question%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The simplest is to award each team the number of points scored by its alliance in each game. Maybe you give a bonus for winning a game. You can adjust the ratio between the game score and the point score to taste. Basically you say that you are averaging over the teammates and the opponents and let it go at that.
The problem with that is the bias it introduces if the teams are uneven and not everybody teams with everybody else. Suppose one team is much better than all the rest and wins all its games by a large margin. No matter what you do, it will come in first. Those teams that partnered with the good one have an unfair advantage and those that opposed it are at a disadvantage. I can imagine saying that each team has a contribution to the overall score difference and doing a least squares fit to the results to determine the team ranking. That sounds like to much math mumbo jumbo to be acceptable in the setting.
answered Dec 5 '18 at 22:00
Ross MillikanRoss Millikan
294k23198371
$endgroup$
$begingroup$
Well to me, it doesn't matter how much math is involved. I found one solution that did the following:chiefdelphi.com/forums/showpost.php?p=484220&postcount=19 and here blog.thebluealliance.com/2017/10/05/…
$endgroup$
– Archishmaan Okonkwo
Dec 5 '18 at 22:45
$begingroup$
I don't worry about the math being too much for you, but about it being too much for your audience. It won't be easy to explain what you are doing, so it won't be "obviously fair", so a losing team may complain.
$endgroup$
– Ross Millikan
Dec 5 '18 at 22:49
$begingroup$
This is for our teams own purposes. At the end of the tournament there are alliance selections where the top teams pick from the teams at the tournament. We want an accurate way of determining who's the best. The more accurate the better. We currently use the link I posted but it seems to over estimate a good teams contributions, under estimate a bad teams contributions and people in the middle are kinda thrown around.
$endgroup$
– Archishmaan Okonkwo
Dec 5 '18 at 22:52
add a comment |
$begingroup$
The simplest is to award each team the number of points scored by its alliance in each game. Maybe you give a bonus for winning a game. You can adjust the ratio between the game score and the point score to taste. Basically you say that you are averaging over the teammates and the opponents and let it go at that.
The problem with that is the bias it introduces if the teams are uneven and not everybody teams with everybody else. Suppose one team is much better than all the rest and wins all its games by a large margin. No matter what you do, it will come in first. Those teams that partnered with the good one have an unfair advantage and those that opposed it are at a disadvantage. I can imagine saying that each team has a contribution to the overall score difference and doing a least squares fit to the results to determine the team ranking. That sounds like to much math mumbo jumbo to be acceptable in the setting.
answered Dec 5 '18 at 22:00
Ross MillikanRoss Millikan
294k23198371
$endgroup$
$begingroup$
Well to me, it doesn't matter how much math is involved. I found one solution that did the following:chiefdelphi.com/forums/showpost.php?p=484220&postcount=19 and here blog.thebluealliance.com/2017/10/05/…
$endgroup$
– Archishmaan Okonkwo
Dec 5 '18 at 22:45
$begingroup$
I don't worry about the math being too much for you, but about it being too much for your audience. It won't be easy to explain what you are doing, so it won't be "obviously fair", so a losing team may complain.
$endgroup$
– Ross Millikan
Dec 5 '18 at 22:49
$begingroup$
This is for our teams own purposes. At the end of the tournament there are alliance selections where the top teams pick from the teams at the tournament. We want an accurate way of determining who's the best. The more accurate the better. We currently use the link I posted but it seems to over estimate a good teams contributions, under estimate a bad teams contributions and people in the middle are kinda thrown around.
$endgroup$
– Archishmaan Okonkwo
Dec 5 '18 at 22:52
add a comment |
$begingroup$
The simplest is to award each team the number of points scored by its alliance in each game. Maybe you give a bonus for winning a game. You can adjust the ratio between the game score and the point score to taste. Basically you say that you are averaging over the teammates and the opponents and let it go at that.
The problem with that is the bias it introduces if the teams are uneven and not everybody teams with everybody else. Suppose one team is much better than all the rest and wins all its games by a large margin. No matter what you do, it will come in first. Those teams that partnered with the good one have an unfair advantage and those that opposed it are at a disadvantage. I can imagine saying that each team has a contribution to the overall score difference and doing a least squares fit to the results to determine the team ranking. That sounds like to much math mumbo jumbo to be acceptable in the setting.
answered Dec 5 '18 at 22:00
Ross MillikanRoss Millikan
294k23198371
$endgroup$
The simplest is to award each team the number of points scored by its alliance in each game. Maybe you give a bonus for winning a game. You can adjust the ratio between the game score and the point score to taste. Basically you say that you are averaging over the teammates and the opponents and let it go at that.
The problem with that is the bias it introduces if the teams are uneven and not everybody teams with everybody else. Suppose one team is much better than all the rest and wins all its games by a large margin. No matter what you do, it will come in first. Those teams that partnered with the good one have an unfair advantage and those that opposed it are at a disadvantage. I can imagine saying that each team has a contribution to the overall score difference and doing a least squares fit to the results to determine the team ranking. That sounds like to much math mumbo jumbo to be acceptable in the setting.
answered Dec 5 '18 at 22:00
Ross MillikanRoss Millikan
294k23198371
edited Dec 5 '18 at 22:45
answered Dec 5 '18 at 22:00
Ross MillikanRoss Millikan
294k23198371
answered Dec 5 '18 at 22:00
Ross MillikanRoss Millikan
294k23198371
answered Dec 5 '18 at 22:00
Ross MillikanRoss Millikan
294k23198371
294k23198371
$begingroup$
Well to me, it doesn't matter how much math is involved. I found one solution that did the following:chiefdelphi.com/forums/showpost.php?p=484220&postcount=19 and here blog.thebluealliance.com/2017/10/05/…
$endgroup$
– Archishmaan Okonkwo
Dec 5 '18 at 22:45
$begingroup$
I don't worry about the math being too much for you, but about it being too much for your audience. It won't be easy to explain what you are doing, so it won't be "obviously fair", so a losing team may complain.
$endgroup$
– Ross Millikan
Dec 5 '18 at 22:49
$begingroup$
This is for our teams own purposes. At the end of the tournament there are alliance selections where the top teams pick from the teams at the tournament. We want an accurate way of determining who's the best. The more accurate the better. We currently use the link I posted but it seems to over estimate a good teams contributions, under estimate a bad teams contributions and people in the middle are kinda thrown around.
$endgroup$
– Archishmaan Okonkwo
Dec 5 '18 at 22:52
add a comment |
$begingroup$
Well to me, it doesn't matter how much math is involved. I found one solution that did the following:chiefdelphi.com/forums/showpost.php?p=484220&postcount=19 and here blog.thebluealliance.com/2017/10/05/…
$endgroup$
– Archishmaan Okonkwo
Dec 5 '18 at 22:45
$begingroup$
I don't worry about the math being too much for you, but about it being too much for your audience. It won't be easy to explain what you are doing, so it won't be "obviously fair", so a losing team may complain.
$endgroup$
– Ross Millikan
Dec 5 '18 at 22:49
$begingroup$
This is for our teams own purposes. At the end of the tournament there are alliance selections where the top teams pick from the teams at the tournament. We want an accurate way of determining who's the best. The more accurate the better. We currently use the link I posted but it seems to over estimate a good teams contributions, under estimate a bad teams contributions and people in the middle are kinda thrown around.
$endgroup$
– Archishmaan Okonkwo
Dec 5 '18 at 22:52
$begingroup$
Well to me, it doesn't matter how much math is involved. I found one solution that did the following:chiefdelphi.com/forums/showpost.php?p=484220&postcount=19 and here blog.thebluealliance.com/2017/10/05/…
$endgroup$
– Archishmaan Okonkwo
Dec 5 '18 at 22:45
$begingroup$
Well to me, it doesn't matter how much math is involved. I found one solution that did the following:chiefdelphi.com/forums/showpost.php?p=484220&postcount=19 and here blog.thebluealliance.com/2017/10/05/…
$endgroup$
– Archishmaan Okonkwo
Dec 5 '18 at 22:45
$begingroup$
I don't worry about the math being too much for you, but about it being too much for your audience. It won't be easy to explain what you are doing, so it won't be "obviously fair", so a losing team may complain.
$endgroup$
– Ross Millikan
Dec 5 '18 at 22:49
$begingroup$
I don't worry about the math being too much for you, but about it being too much for your audience. It won't be easy to explain what you are doing, so it won't be "obviously fair", so a losing team may complain.
$endgroup$
– Ross Millikan
Dec 5 '18 at 22:49
$begingroup$
This is for our teams own purposes. At the end of the tournament there are alliance selections where the top teams pick from the teams at the tournament. We want an accurate way of determining who's the best. The more accurate the better. We currently use the link I posted but it seems to over estimate a good teams contributions, under estimate a bad teams contributions and people in the middle are kinda thrown around.
$endgroup$
– Archishmaan Okonkwo
Dec 5 '18 at 22:52
$begingroup$
This is for our teams own purposes. At the end of the tournament there are alliance selections where the top teams pick from the teams at the tournament. We want an accurate way of determining who's the best. The more accurate the better. We currently use the link I posted but it seems to over estimate a good teams contributions, under estimate a bad teams contributions and people in the middle are kinda thrown around.
$endgroup$
– Archishmaan Okonkwo
Dec 5 '18 at 22:52
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3027699%2franking-question%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
I don't think this is clear. How many teams are there in total, for example? As a general note, it's often the case that there is no unambiguous ranking in group encounters. For instance, with three teams, $A,B,C$, each of whom play each other once...if $A$ beats $B$, $B$ beats $C$, and $C$ beats $A$...which would you want to call the winner?
$endgroup$
– lulu
Dec 5 '18 at 21:53
$begingroup$
Well thats the challenge. The only data you have is the number of points. You know who plays who and thats it. The number of teams is subject to change and so is who plays who.
$endgroup$
– Archishmaan Okonkwo
Dec 5 '18 at 22:25