6 Steps to Understanding Relative Placement


For most new competitors in the world of dancing, relative placement is a mysterious and arcane art that requires years of study, pestering Sylvia Sykes with dumb questions, and may or may not involve the occasional goat sacrifice.

With which most Balboa dancers are already familiar anyway.

With which most Balboa dancers are already familiar anyway.

For all the seemingly complicated numbers and annotations, relative placement is a pretty straight-forward, reliable method. It answers most of the hard questions in the competition world, such as what if one judge’s score overly tips the balance, or how to deal with ties.

Unfortunately, it doesn't answer the hardest question: how do I spin like Tatiana?

Unfortunately, it doesn’t answer the hardest question: how do I spin like Tatiana?

1- It’s All About the Majority

If the organizers know what they’re doing, you’ll see an odd number of judges on a panel using relative placement – usually 5, sometimes 7 or 9. Why? Because relative placement is in the business of majority: if a majority of judges think you should win, you win. It’s as simple as that.

Take the example of Jim-Bob and Freddy-Lou.

After a fierce Chicken Hopping competition at the Boondocks Redneck Festival, the judges are simply asked to rank the competitors from first to last, that is, from the one who sucked less to the one who sucked the most. There were five judges and two contestants. One judge’s sheet might look like this:

# Name Notes

Placement

Jim Bob Mostly dirt-free, spotty Megadeth t-shirt. Good bounce.

1

Freddy Lou I don’t know what that is and it scares me a little.

2

And the tally sheet, which compiles all judges’ placements in one table, will look like this:

# Name

J1

J2

J3

J4

J5

Jim Bob

1

1

2

1

2

Bobby Joe

2

2

1

2

1

A majority is defined as more than half the judges. So here Jim-Bob would win because three judges placed him in first place.

2- The Great Art of Next Placement

But that’s just relative placement in its simplest form; competitions are rarely held with only two entries. So what if nobody has a majority of 1st? This happens a lot in competition – actually, most times. Do we resort to some other form of judging?

CAGE MATCH!

CAGE MATCH!

As entertaining as the U.S. Open would become, nope: relative placement has the answer.Let’s add Mary-Sue, Bobby-Joe and Candy-Jane to the mix. Judges have to rank them from 1st place to 5th place, and the tally sheet would look like this:

# Name

J1

J2

J3

J4

J5

Jim Bob

1

4

2

2

5

Freddy Lou

3

1

3

4

2

Mary Sue

4

3

5

3

1

Bobby Joe

2

5

1

5

3

Candy Jane

5

2

4

1

4

That looks like a great cluster. Nobody has a majority of 1, for starter. That means no majority of judges think anyone should have won.

# Name

J1

J2

J3

J4

J5

1-1

Jim Bob

1

4

2

2

5

1

Freddy Lou

3

1

3

4

2

1

Mary Sue

4

3

5

3

1

1

Bobby Joe

2

5

1

5

3

1

Candy Jane

5

2

4

1

4

1

Those columns we add on the right are used to calculate the number of placements one competitor has. In this instance, for placements from 1 to 1, everyone has 1 placement, which is not a majority. That means we cannot start placing people in order.

Then we tell ourselves, all right, is there a majority of judges who wanted to see one person in 1st OR 2nd place? That’s called “going to the next placement“, and is the cornerstone of relative placement. It’s how the system ranks competitors all the way down to last place.

Turns out yes: when we go to the next placement, Jim Bob is the only person who was placed in 1st or 2nd by a majority (3) of the judges. So we place Jim Bob in first, and the tally sheet will look like this:

# Name

J1

J2

J3

J4

J5

1-1

1-2

Place

Jim Bob

1

4

2

2

5

1

3

1

Freddy Lou

3

1

3

4

2

1

2

Mary Sue

4

3

5

3

1

1

1

Bobby Joe

2

5

1

5

3

1

2

Candy Jane

5

2

4

1

4

1

2

3- …But Sometimes You Just Need MORE Majority.

Now we go to the next placement to determine 2nd place. Is there a person who has a majority of 1st, 2nd and 3rd place?As it turns out, there is a majority of 1 through 3 for THREE competitors:

# Name

J1

J2

J3

J4

J5

1-1

1-2

1-3

Freddy Lou

3

1

3

4

2

1

2

4

Mary Sue

4

3

5

3

1

1

1

3

Bobby Joe

2

5

1

5

3

1

2

3

Second rule of relative placement: whoever has the biggest majority gets the placing.

No Tyler: we can talk about relative placement as we goddamn please.

No Tyler: we can talk about relative placement as we goddamn please.

In this case, Freddy Lou gets 2nd place, because a bigger majority of judges placed him in 1st, 2nd or 3rd place, and the final tally sheet goes like this:

# Name

J1

J2

J3

J4

J5

1-1

1-2

1-3

Place

Jim Bob

1

4

2

2

5

1

3

1

Freddy Lou

3

1

3

4

2

1

2

4

2

Mary Sue

4

3

5

3

1

1

1

3

Bobby Joe

2

5

1

5

3

1

2

3

Candy Jane

5

2

4

1

4

1

2

2

You can’t stress it enough, this is not considered a tie between the three competitors, and tie breaking rules don’t apply: he has a bigger majority than the rest.

4- First Tie Breaker: Add it Up

There are three steps to breaking a tie in relative placement, and they generally go in a very specific order.

In this Chicken Hopping competition, two competitors have the same exact majority of judges (3 each) for next place to be awarded:

# Name

J1

J2

J3

J4

J5

1-1

1-2

1-3

Mary Sue

4

3

5

3

1

1

1

3

Bobby Joe

2

5

1

5

3

1

2

3

You first try adding up the numbers that form the majority:

Mary Sue  has 3+3+1 = 7
Bobby Joe  has 2+1+3 = 6

Whoever has the littlest number (which means better overall placement from the judges forming the majority) wins. Here, Bobby Jo would take the placement (3rd) and Mary Sue would automatically get next placement (4th): Whenever a tie break occurs, you take care of that tie and place the people who were tied accordingly. No need to involve anyone else in an already messy situation.

Which is generally good life advice for most of us.

Which is generally good life advice for most of us.

So the tally sheet would end up like this:

# Name

J1

J2

J3

J4

J5

1-1

1-2

1-3

1-4

Place

Jim Bob

1

4

2

2

5

1

3

1

Freddy Lou

3

1

3

4

2

1

2

4

2

Bobby Joe

2

5

1

5

3

1

2

3(6)

3

Mary Sue

4

3

5

3

1

1

1

3(7)

4

Candy Jane

5

2

4

1

4

1

2

2

4

5

Since Candy Jane has a majority of 1s through 4s, she gets the following placement, which is unfortunately the last. Once again, think that a majority of judges thought she should have been in 5th or 4th, whereas a majority of judges thought Bobby Joe and Mary Sue should have been above her.

Relative placement prevents one or two REALLY good scores or REALLY bad scores (as is the case of Jim Bob who got two 5) to skew the results in favor of someone else.

5- Second Tie Breaker: Back to the Basics

Now what if we manipulated the scores, and the tie looked like this?

# Name

J1

J2

J3

J4

J5

1-1

1-2

1-3

Mary Sue

4

2

5

3

1

1

2

3

Bobby Joe

2

5

1

5

3

1

2

3

Marye Sue has 2+3+1 = 6.

Bobby Joe also has 2+1+3 = 6.

Well goddamn it. We’re not any more advanced than we were!

If adding up doesn’t work because it just creates another tie, we just go to the next placement to see if there is a bigger majority who wants to place some competitor over the other. That’s the second tie breaker.In this case, both have an equal majority of 1st through 3rd place, and both have the same total… But if we choose to include one more placement, we see that Mary Sue has a bigger majority of 1st through 4th place, making her the winner. In this modified version where Mary Sue got a 2nd instead of 3rd, she ends up going up one place, because more people agreed she should beat Bobby Joe.

Figuratively, guys. Jesus...

Figuratively, guys. Jesus…

That modified tally sheet would look like this:

# Name

J1

J2

J3

J4

J5

1-1

1-2

1-3

1-4

Placement

Jim Bob

1

4

2

2

5

1

3

1

Freddy Lou

3

3

3

4

2

1

1

4

2

Mary Sue

4

2

5

3

1

1

2

3==

(4)

3

Bobby Joe

2

5

1

5

3

1

2

3==

(3)

4

Candy Jane

5

1

4

1

4

2

2

2

4

5

Candy Jane still gets the short end here, because existence is an infinite void of sadness… And also because, while she has the two 1, she doesn’t have any 2 or 3 to make it up with Mary Sue or Bobby Joe. Once again, it’s all about the majority. A majority of judges did NOT think she should have placed higher.

6- Dealing With Perfect Ties

What if we go to the end of the next placements though, and we still have a tie? What if we go deeper?

Check your totems, guys and girls!

Check your totems, guys and girls!

# Name

J1

J2

J3

J4

J5

1-1

1-2

1-3

1-4

1-5

Mary Sue

3

2

5

4

1

1

2

3(6)

4(10)

5(15)

Bobby Joe

2

4

1

5

3

1

2

3(6)

4(10)

5(15)

Here, Mary Sue and Bobby Joe are pefectly tied with one of each placement. Surely, they should be awarded equal placement, right? They should both have a 3rd place plastic trophy to show their grandkids, and that should be the end of it.

Not quite.

Some events deal with perfect ties by awarding a Chief or Head Judge the power to break a tie. In this case, Judge #1 would break the tie in favor of Bobby Joe, because he placed him higher than Mary Sue.

The Chief Judge is also obligated by tradition to wear a full Judge Dredd outfit for the duration of the event.

The Chief Judge is also obligated by tradition to wear a full Judge Dredd outfit for the duration of the event.

That’s not the fairest and best way to do it though, because it does give ONE judge the final say, and nobody wants to be that person. The most logical, and coolest procedure is going into a showdown, and treating the placements as a contest between ONLY THOSE TWO competitors, checking, for each judge, who placed who in front of the other:

# Name

J1

J2

J3

J4

J5

Mary Sue

4

(2)

5

(4)

(1)

Bobby Joe

(2)

4

(1)

5

3

What is cool about it is that a showdown will practically never end up in another tie, unlike all the other tie-breakers. It’s the ultimate tie-breaker.

Here, Mary Sue wins because a majority of judges placed her in front of her tied nemesis, and the final tally sheet would look like this:

# Name

J1

J2

J3

J4

J5

1-1

1-2

1-3

1-4

1-5

Placement

Jim Bob

1

5

2

2

5

1

3

1

Freddy Lou

4

3

3

3

2

1

1

4

2

Mary Sue

3

(2)

5

(4)

(1)

1

2

3(6)

=4

=5

3

Bobby Joe

(2)

4

(1)

5

3

1

2

3(6)

=4

=5

4

Candy Jane

5

1

4

1

4

2

2

2

4

5

5

In the odd event where a showdown wouldn’t work though (for example too many people have a rearrangement of the same 1-2-3-4-5 scoring, making the showdown into another tie), you would still need the input of the Chief Judge to break the ultimate, ultimate tie.

A Nifty Recap with a Bow on it

So, to recap everything, here is a quicklist:

– Start with 1s, and check if you have a majority, or superior majority, of judges. Then, award places by going to next placement when necessary.

– If there is a tie between two contestants, isolate them and take them through the four tie breakers: adding up the majority placements; going to next placements; going to a showdown; Chief Judge score.

– Rejoice for exactly one second, then prepare for the onslaught of competitors who didn’t read this article to tear you apart.

"I'm sorry to bother you, sir, but why didn't I win if I had two 1s? ... I mean ... BRAAAAINS!"

“I’m sorry to bother you, sir, but why didn’t I win if I had two 1s? … I mean … BRAAAAINS!”

If anything is not clear, please ask.

Very special thanks to the patience, understanding and many, many explanations of my First Lady of Swing, Sylvia Sykes, without whom I would still be a blubbering, vaguely outraged idiot wondering why someone won with a solid row of 2nd places.

When not obsessing over relative placement minutia, Zack can be found at Swing ConneXion in Montreal.

Advertisements

About Zack

The Jazz Monkey View all posts by Zack

29 responses to “6 Steps to Understanding Relative Placement

  • gregbo

    On 10/29/2013, an interesting discussion about Relative Placement began on the Westie Discussion of the Day FB group. The question of how ties of three (or more, but not all couples) was raised. How is this handled in Lindy Hop competitions? For example, given the following judges’ placements, what are the final placements, and what is the justification for the method used?

    1 2 3 4 5
    2 5 4 1 3
    5 1 2 3 4
    4 4 5 2 2
    3 3 1 5 1

    • Dave Schindler

      I think the order is

      4
      3
      2
      5
      1

      The 5th row has two 1s, (more than anyone else) so they win. The first three rows tie for 1-2s, leaving the 4th row in last place.

      Now back to the 3-way tie. As Zack said, the order is: “adding up the majority placements; going to next placements; going to a showdown; Chief Judge score.”

      Since you have 5 judges (odd number), and they tie in placements all the way to 5th place, you can settle this with showdowns.

      Showdown 1:
      (1) 2 3 4 5
      2 5 4 (1) (3)
      5 (1) (2) 3 4

      So, competitor 1 is last of this group (4th overall) because they have the fewest wins in the first showdown.

      Showdown 2:
      (2) 5 4 (1) (3)
      5 (1) (2) 3 4

      Competitor 3 wins this one, taking 2nd overall.

      No need to take a 3-way tie to the Chief Judge. You only need that if you get a 5-way tie with 5 judges, as you (gregbo) pointed out below.

      • Zack

        “The 5th row has two 1s, (more than anyone else) so they win.”

        That’s not how relative placement works. You need a MAJORITY of whatever section of numbers you got at (1-1, 1-2, etc…)

      • Dave Schindler

        In the 1-1 phase, competitor 5 has two 1s, while everyone else has one. Isn’t that a majority? What am I missing?

      • Dave Schindler

        Ah, I see what you meant. I was using majority of ranks instead of majority of judges, which is more of a score-weighted ranking (1s having more weight than 2s). So, the end result is still the same, but for the wrong reason. The 4th and 5th competitors get ranked 5th and 1st respectively due to the majority in phase 1-3.

        So, is my ranking still correct?
        4
        3
        2
        5
        1

      • Dave Schindler

        Man, I have fat fingers! I was trying to type out an answer too fast and got the order wrong. I even copied and pasted the wrong order again. Anyway, what I meant to type is this:

        4
        2
        3
        5
        1

        So, the scoring sheet should look like this after the first showdown (hopefully my ASCII art works after posting):

        # J1 J2 J3 J4 J5 1-1 1-2 1-3 1-4 1-5 rank
        ______________ ___________________ _____
        1|(1) 2 3 4 5 | | 1 2 3(6) 4(10) 5(15) | | 4 |
        2| 2 5 4 (1) (3)| | 1 2 3(6) 4(10) 5(15) | | ? |
        3| 5 (1)(2) 3 4 | | 1 2 3(6) 4(10) 5(15) | | ? |
        4| 4 4 5 2 2 | | 0 2 2 4 – | | 5 |
        5| 3 3 1 5 1 | | 2 2 4 – – | | 1 |

        And the 2nd showdown (between 2 and 3) would result in #2 beating #3.

        By the way, I’ve written an app that can calculate relative placement, including the showdown tie-breakers. The only case that stumps it is the circulant matrix type ties where the same number of competitors as there are judges, tie with 1 showdown win each. In that case, it declares a tie and tells you to defer to the head judge.

        If there’s any interest, I’ll share it. It can run in Android. And I could get it to run on iOS without too much difficulty, but again, I’d only bother if there’s interest.

      • Zack

        Wow sorry, for some reason WordPress doesn’t email me anymore when I have new comments.

        It’s kinda hard to decipher the ASCII, not gonna lie… But it does pose an interesting subtlety.

        The mistake you made, from my point of view, was determining the “loser” of the three-way tie first, and then went into a second showdown. That’s not how relative placement works (in my interpretation – I’d be interested to hear about others, but this one seems the most logical). I go from top to bottom, that is from 1st to last. Because you chose the “loser” first, it changed the actual results.

        In this extremely rare case where three people have the exact same numbers (and given I’ve correctly interpreted your placements) I would do a three-way showdown like this (substituted letters to identify the couples, because I’m fly like dat):

        A – 1 2 3 4 5
        B – 2 5 4 1 3
        C – 5 1 2 3 4

        Becomes:

        A – 1 2 2 3 3
        B – 2 3 3 1 1
        C – 3 1 1 2 2

        Which would mean that couple C is second place since they have a “bigger majority” of 1-2. Then, third place goes to couple B because the votes that count are 1-2-2 for A and 1-1-2 for B.

        In the end though, I think a good majority of events go for the “head judge” method” (not that I agree). Thanks for the mental exercise though!

        App sounds cool, I’m sure a lot of events would be interested in having that, providing all the correct rules are in place of course.

      • gregbo

        Dave, I would like to see your app. Is the source code available anywhere such as github?

      • Dave Schindler

        I don’t have it on github. Give me a bit of time, and I can get it on a website. I’ve set it aside for now, as I have a lot of work to do automating registrations and competitions for a mid-sized swing event this weekend.

  • gregbo

    If the judges ranked each of the couples in the following way, the chief judge would have to break the tie.

    J1 J2 J3 J4 J5
    Jim Bob 1 2 3 4 5
    Freddy Lou 2 3 4 5 1
    Mary Sue 3 4 5 1 2
    Bobby Joe 4 5 1 2 3
    Candy Jane 5 1 2 3 4

    If you go to condorcet.ericgorr.net, there is more documentation, plus a calculator that you can use to see interim and final calculations for a variety of voting (ranking) methods.

    • Zack

      Yes, in the odd case where every contestant would get the same exact scoring, you would need a chief judge – whose score would incidentally be the only one that actually matters. I’ll change the article to reflect that!

  • Richard Michel

    human’s biased ? yes ,all about perception(professional ..personal) or/and too close to the subject, which implies all of the above…..Food for thought..still luv u son i’m biased..cause i luv u

    • Zack

      There is no bias in this, it’s a scientific method of compiling (admittedly biased sometimes) judges’ scores… Not sure what the point is, but love you too!

  • Burnie

    Cool; Thanks for putting this out here simply for folks. Tired of training folks from an older more confusing posting out there. I remember my training with Sylvia, and I’m sure she’ll correct me if I’m wrong, but, I remember being told that most competitions don’t use the 1st tie breaker you listed of adding up scores. Most competitions use the 2nd tie breaker of using the judges to break the tie. Either way if more people know how to use relative placement and to use an odd number of judge then I’m glad they do it either way…

    • Zack

      Well if they don’t, they should. It just makes sense, not mentionning that Sylvia, as far as she told me, is generally using this exact method (minus the last showdown tie-breaker, sometimes she does use the head judge prerogative).

  • Terry Rippa

    We’ve been using Relative Placement since 1985. There is also an addendum on “judging the judges”. From the Dallas DANCE website:
    http://dallasdance.com/rpframes.htm

    • Zack

      I understand where it’s coming from, but I wholly disagree with the removal of a judge’s scoring thing – first of all, mathematically, it will lower the number of judges to an even number, augmenting the chances of ties… It also strikes me as very bizarre, as in, if you know in advance this judge is no good, why hire them in the first place?

      I’m curious to see in which case it would be warranted.

  • Sara

    Just on 4 . . . I think column 2 should be a 1? But now I’m afraid to say anything. Thanks Zack!

    Doh.

  • Sara

    Okay, I obviously didn’t read 5 before my comment above. You can ignore that part. Sorry!!!

  • Sara

    Hi, don’t know if you saw this already or not, but under 5- Tie Breaker, Mary Sue’s second column should be a 1, not a 2, I think. (Wasn’t looking for errors, just couldn’t figure out the math on that one.) Thanks! Super informative!!

  • Anna

    But why does Candy Jane have a 2 in her 1-1 column in the second score sheet of section 4?

  • Anna

    Found my error!!! Please ignore my previous comment!

  • Anna

    Great article! Love the pics, humor and the way your broke it down.

    Two things: Check the first tie-breaker. According to the scores, I’m not sure it would be necessary. (MS 1st-3rd-3rd versus BJ 1st-2nd-3rd)

    Also, I think Candy Jane’s scores morphed unintentionally. Not sure how she wound up in 5th at the end with 2-1st placements. Early on (Section 4) she had a 1st, 2nd, 4th but wouldn’t that still put her ahead of Mary Sue’s 1st, 3rd, 3rd in the same sheet?

    • Zack

      Thank you!

      I think the scoring is good. I reviewed it pretty obsessively.

      Everytime two persons have the same number of judges as majority (in this case both MS and BJ have three judges placing them from 1st to 3rd), we consider this a tie-breaker. You have to go through the tie-breaking process and place these guys accordingly…

      Which is also why, incidentally, CJ got last – as I state in the article, she may have a 1st and 2nd, but no majority of judges (at least three judges in this case) placed her high enough to make a difference. 1-3-3-5-5 in relativement placement would even beat 2-1-4-4-4… or even 4-1-1-4-4.

      I did, however, manipulate scores along the article to help illustrate certain points (for example I had to take placements from other competitors to illustrate the last perfect tie).

      Still sucks for Candy Jane… She just needs to practice more.

  • Annie

    I mean yeah I am biased but this is a great article, well written and funny, but most of all pertinent, clear and greatly useful for those of us who have to run those comps! Bravo Zack et merci!

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: