ADDRESS
Planar Analysis and Placement - What Kinds of Drill Do Judges Reward?
Dr. Richard Vincent Lamb
vince_lamb@yahoo.com
Preface
The following is an expanded version of my very first article in Drum Corps World, published
June, 1996. I posted it on RAMD in July 1996, so the posted version wouldn't compete with the
printed version. I've corrected the format of the tables from that in the printed version, added
three appendices, and inserted some material which was deleted from the original article
because of length and style, including more detailed statistics and notes on method.
Author's note: If you are using a web-based newsreader, such as Deja.com, choose "View
Original Usenet Format" to read tables correctly.
Introduction
Stuart Rice, the publisher of Flatland Press and a former Drum Corps World staff writer,
developed and introduced a method of analyzing marching movement called Planar Analysis.
Stuart invented this technique in order to analyze marching strictly in terms of *movement*.
Planar Analysis (1) describes all maneuvers in terms of nine basic moves (Appendix I), (2)
supplies an objective and uniform standard for judging the difficulty of any maneuver
(Appendices I and II), and (3) ignores form completely. This is in radical opposition to the usual
procedure of analyzing drill by treating a corps' marching as pretty pictures that happen to be in
motion--hence the term "Drill Design". Planar Analysis treats drill as "Choreographed
Marching". This article shows that Planar Analysis can also be applied to determine which
aspects of a corps' drill are rewarded by Visual judges and predict corps' placements at shows.
Stuart collected a wealth of data using Planar Analysis on the marching choreography of the
1995 DCI Finalists for his recent series of articles in Drum Corps World, including the moves
used, their order, their difficulty, the length of show, and the amount of time each corps marched
(Appendix III). He graciously shared his results so that this article could be written. The
correlation between a corps' ranking in each of Stuart's measures and the each corps' placement
in the General Effect Visual caption at the 1995 DCI Finals was then performed. The Analysis
was performed four different ways--with all corps, without Cadets of Bergen County (CBC),
without Crossmen, and without CBC and Crossmen.
Methods
I used Stuart's measures for Total Use, Total Difficulty, Average Difficulty per Move, Events,
Total Complexity, Total Balance, Type Sequence Balance, Type Sequence Grouping, Grammar
Sequence Balance, and Grammar Sequence Grouping (See Appendix I for an explanation of
each category)--as both raw numbers and rankings for each corps (Appendix III). I also used
three other statistics which Stuart posted on the newsgroup rec.arts.marching.drumcorps
(RAMD) in January 1996-Total Time Marching, Percent of Show Spent Marching (% Time
Marching), and General Effect Visual Rank/Placement for each corps at 1995 DCI Finals
(Appendix III). I entered the rankings for first ten statistics, the percent of show spent marching,
and the GE Visual placements into a statistical program (in this case, SPSS for Windows, but
SYSTAT for DOS, Windows, or Mac would have worked just as well). I then performed a
correlation analysis (Pearson's r, for those of you who know something about statistics) to see
how well Stuart's findings correlated with the GE Visual Rank. (Author's note: I really should
have used Spearman's r for ranked data, but using Pearson's r is not a fatal flaw in the analysis.
:-) I set a 95% confidence level for statistical significance (reasonable confidence that the
difference is real and *not* from chance alone) and waited for the results.
Results (and further notes on method :-)
None of Stuart's eleven statistics showed a significant correlation with the GE Visual Rank.
Seven statistics, all except Balance, Sequence Grouping, and Grammar Balance Grouping, have
positive but non-significant correlations with GE Visual Rank; high ranks in these statistics
generally meant that a corps scored higher in GE Visual, but the relationship was not stong
enough to be accepted as real. Balance has *no* correlation at all with GE Visual
Rank--balanced use of all types is completely irrelevant to the score. Sequence Grouping and
Grammar Balance have negative but non-significant correlations with GE Visual Rank--the
higher a corps score in these areas, the lower its placement in the GE Visual caption. I expected
weak correlations because I had performed a correlation analysis just between GE Visual Rank
and % Time Marching in January 1996, when Stuart had posted these on RAMD. When all corps
where analyzed, % Time Marching was only 66% likely to be related directly to GE Visual
Rank. Stuart himself pointed out the most probable reason was that most corps marched between
70% and 85% of their shows, but Cadets of Bergen County (CBC) marched only about half of
their show, and this threw off the correlation. I then re-ran the analyis without CBC. Lo and
behold! Without CBC, there was a 95.3% probability that % Time Marching contributed to the
GE Visual Rank--a significant relationship! I decided to repeat the analysis for the rest of the
statistics, but this time deleting CBC from the data. The result was that two other statistics, Total
Use and Total Difficulty, showed statistically significant correlations with GE Visual Rank, with
confidences of 98.4% and 97.9%, respectively.
While these findings told me which aspects of the other corps' drills contributed significantly to
their GE Visual Scores, it did not help me in accounting for CBC, which earned second place in
GE Visual at DCI Finals last year. I decided to normalize Total Use and Total Difficulty for the
time each corps spent marching, resulting in Use per Second Marching and Difficulty per
Second Marching. The idea was to determine whether CBC's high GE Visual Ranking could be
accounted for by having high degrees of use and/or difficulty during the time they were
marching, even if the short time they actually marched prevented them from racking up high
values of Total Use and Total Difficulty. I also calculated Events per Second Marching and
Difficulty per Event to see if these were significant, either with or without CBC being
considered.
To my pleasant and gratified surprise, the correlations between GE Visual Rank and Use per
Second Marching and Difficulty per Second Marching were both highly significant when all
corps (including CBC) were examined, with confidences of 99.8% and 99.3% respectively. They
were also strongly correlated with GE Visual Rank when CBC was left out of the analysis, with
confidences of 99.6% and 98.2% respectively. Neither Events per Second Marching nor
Difficulty per Event showed a significant correlation, although Difficulty per Event came close,
with a confidence of 94.2% when CBC was left out of the analysis. Table 1 lists the complete
results.
TABLE 1. Statistical significance of Planar Analysis statistics versus GE visual scores (rank vs.
rank). Starred (*) statistics have confidences of at least 95%. Crossed (+) statistics are
time-normalized ones added by me.
Statistic Rank Correlation (r) Confidence (1-p)
w/CBC no/CBC w/CBC no/CBC w/CBC no/CBC
Use/sec. *1 1 0.8290 0.8105 99.8%* 99.6%*
Diff/sec. *2 3 0.7370 0.7249 99.3%* 98.2%*
Gram.Group. 3 9 0.4857 0.3921 87.0% 73.8%
Seq. Bal. 4 7 0.4773 0.4427 86.2% 80.0%
Diff/event 5 6 0.4271 0.6164 81.0% 94.2%
Total.Diff. 6 4 0.3768 0.7125 74.7% 97.9%*
Use 7 2 0.3727 0.7339 74.1% 98.4%*
Events 8 10 0.3434 0.3358 69.9% 65.7%
Events/sec 9 11 0.3433 0.2587 69.9% 53.0%
Complexity 10 6 0.3266 0.5023 67.3% 86.1%
%T March. 11 5 0.3182 0.6932 66.0% 95.3%*
Diff/move 12 12 0.2931 0.1257 61.8% 27.1%
Balance 13 13 0.0000 0.0420 0.0% 8.8%
Seq.group 14 14 -0.3098 -0.1842 64.6% 38.9%
Gram.Bal. 15 15 -0.5862 -0.5109 94.2% 86.9%
I ran analyses that excluded the Crossmen to see what effect they had on the confidence of the
statistics. With Crossmen excluded but CBC included, there was no change; the same two
statistics, Use per Second Marching and Difficulty per Second Marching, were significant.
With both Crossmen and CBC excluded, the effect was minor, but interesting. Use per Second
Marching, Difficulty per Second Marching, Total Use, and Total Difficulty were still significant,
but Difficulty per Event became significant (confidence of 95.2%) while % Time Marching no
longer was (confidence of 90.9%). Apparently, Crossmen were insufficiently rewarded for their
difficulty per event (6th) but their relatively low percent of time marching (8th) was noticed
enough to affect their score!
Discussion
The two measurements most closely and widely associated with a corps' GE Visual placement
were Use per Second and Difficulty per Second. These were significantly correlated with GE
Visual rank in all analyses. The first describes how many different moves a corps used in a set
time. The second represents the difficulty of a corps' marching per unit of time. They were
determined by dividing the number of moves used during a show (Total Use) and the combined
difficulty ratings of all moves used (Total Difficulty), respectively, by the number of seconds a
corps spent marching. Total Use and Total Difficulty were significantly correlated with GE
Visual placement in the two analyses without CBC. The reason for this pattern is that most corps
marched between 70% and 85% of their shows, but CBC marched only slightly more than 50%
of their show. This made their Total Use and Total Difficulty the lowest of all corps at finals.
Once these categories were adjusted for the short time the corps marched, CBC had the third
highest scores in Use per Second and Difficulty per Second among all the corps (Table 2).
TABLE 2. Planar Analysis statistics found to be significantly correlated with each corps' GE
Visual Placement.
All Corps Minus CBC Minus X-men Minus CBC and X-men
Use/second Use/second Use/second Use/second
Difficulty/sec Difficulty/sec Difficulty/sec
Difficulty/second
Total Use Total Use
Total Diff. Total Diff.
% T Marching
Diff/Event
Use per Second and Difficulty per Second were selected as the two best measurements and then
checked for how well they predicted a corps' GE Visual placement. Each corps' ranks in Use per
Second and Difficulty per Second were added together, the corps arranged by score from low to
high, and the rank from its Planar Analysis rank compared it to its GE Visual standing. Table 3
shows the resulting placings.
TABLE 3. Comparison of corps rankings from Planar Analysis with ranking from GE Visual
score.
CORPS RANK FROM PLANAR ANALYSIS GE VISUAL RANK DIFFERENCE
Cavaliers 1 1 0
Cadets of Bergen County 2T 2 0
Blue Devils 2T 3 1
Madison Scouts 2T 4 2
Phantom Regiment 6T 5 1
Santa Clara Vanguard 5 7 2
Bluecoats 8 6 2
Glassmen 9T 8 1
Colts 9T 9 0
Crossmen 6T 11 5
Carolina Crown 11 12 1
Magic of Orlando -- 10 --
Planar Analysis clearly called the winner--Cavaliers. It did not distinguish among the second
through fourth place corps. This is consistent with the how competitive these corps were with
each other, as the Madison Scouts beat CBC early and Blue Devils were ahead of both the
Scouts and CBC until the last week of the season. For all the remaining corps except Crossmen,
the placements predicted are at most two off their actual GE Visual ranks, but are at most only
one off their overall placements.
Crossmen present a special problem. Their predicted placement is five off their actual ranking.
Stuart resolves this in his column by noting that Crossmen had design problems--their forms
were compressed, cluttered, and hard to read. Consequently, the difficulty of their drill was not
rewarded. Although Planar Analysis ignores form--it does not matter whether an arc or a line is
being rotated about its end, the motion is still scored the same--the Crossmen demonstrate that
form does matter. In a perverse way, the Crossmen also demonstrate that how much of the show
is marched matters as well. Percent Time Marching is determined by the number of seconds a
corps marched during its show divided by the show length. It is significantly linked to GE Visual
placement only with Crossmen present and CBC absent.
Conclusion
So, what does Planar Analysis have to say about how a corps' marching choreography
contributes to its corps' GE Visual Placement? First, difficulty matters. Given the same level of
execution, the corps with the more difficult drill (as measured by Planar Analysis) will be better
rewarded. Second, how difficulty is achieved also matters. Given the same level of execution
and difficulty, the corps that uses more moves (even many simple ones in combination) will
score higher than one that concentrates on fewer, but more difficult moves. As Stuart has noted,
this was the secret to the Cavaliers' success. They employed polymovement (many simple
moves used in combination) to great effect. This allowed them to edge out CBC, who, when they
did march, used the most difficult moves of all the finalists, but used on average one less move
per event than Cavaliers.
Third, time matters. It matters because judges (in this case, C. Williams, the GE Visual Judge
for DCI Finals last year) appear to be judging difficulty and use per unit of time--say during ten
second samples of a corps' show during the time the corps marches. This is what allowed CBC to
place as high as they did. They do not appear to be keeping track of the overall difficulty and use
over an entire show. Time also matters because corps are generally, but not always, rewarded for
marching a higher percentage of their shows. Finally, as the Crossmen demonstrated to their
misfortune, form *does* matter. If a corps' forms are not easily read, either because of design or
execution problems, then its choreography, no matter how difficult or complex it is, will not be
rewarded.
Planar Analysis is more than an academic exercise in examining how drum corps march. It is
also a practical tool for evaluating drum corps marching. It determined which aspects of a corps'
drill were rewarded by judges and predicted corps' placements. The technique does so because it
supplies an objective and uniform standard for judging the difficulty of any maneuver. Because
of its success, Planar Analysis promises to be a major innovation in describing marching
choreography.
APPENDIX I--Explanation of Terms for Planar Analysis
by Stuart E. Rice and Richard "Vince" Lamb
The Three Categories of Movement.
1. Periodic - Movements which change a formation's orientation.
2. Translatory - Movements which change a formation's location.
3. Contrapuntal - Movements which change a formation's contour.
The Nine Movement Types (in order of difficulty ranking).
1. Circuitous - "Follow-the-leader" movements in lines with no beginning and no end.
2. Canonic - "Follow-the-leader" movements in a line with a single leader.
3. Rectilinear - Movements which send a formation in a single direction.
4. Polar - Movements which disintegrate a formation.
5. Antilinear - Movements which change a formation's direction.
6. Rotational - Movements which turn a formation on a pivot-point located inside the formation.
7. Revolving - Movements which turn a formation around a pivot-point located outside the
formation.
8. Formal - Movements which change a formation's size.
9. Structural - Movements which change a formation's shape.
Categories of Planar Analysis.
Technical
1. Total Use - How many movements were used in a show.
2. Total Difficulty - Combined difficulty level of a show's movements.
3. Average Difficulty per Move - Difficulty level of a show's average move.
4. Total Events - Number of important moves in a show (based on size and placement of
formations).
5. Total Complexity - How many different kinds of movement are used simultaneously during
the average Event.
6. Average Difficulty per Event - Difficulty level of a show's average Event.
7. Use per Second - The number of moves used during a show (Total Use) divided by the
number of seconds a corps spent marching.
8. Difficulty per Second - The combined difficulty ratings of all moves used (Total Difficulty)
divided by the number of seconds a corps spent marching.
9. Percent Time Marching - The number of seconds a corps marched during its show divided by
the show length in seconds.
Creative
10. Total Balance - How close a show comes to using all nine types of movement equally
11. Variety - How close a show's Events come to using all nine types of movement equally.
12. Variety Grouping - How often a show's Events repeat the same type of movement.
13. Grammar - How close a show's Events come to using all three categories of movement
equally.
14. Grammar Grouping - How often a show's Events repeat the same category of movement.
APPENDIX II--You Be The Judge!
By Richard "Vince" Lamb
Try Planar Analysis for yourself. Use it to play one of the favorite audience games at
shows--You Be The Judge!
Below is a judging sample judging form. Here is how to use it. For each event (each time a
corps or band changes movement types being used, roughly equivalent to time between drill sets
or to a musical phrase), check off all the movement types being used, then list how many
marching errors (out of form, out of step, falls, or other) you see.
After the corps' or bands' performance is over, total the number of different moves used during
each event. Then total the difficulty of the moves used for each event. The difficulty is given by
the number of the kind of move at the top of the sheet. Enter the total number of moves used and
total amount of difficulty of the moves at the box in the bottom. Then total all the errors you see.
Add the total difficulty and the total use. Subtract the total errors. The result is the corps' Raw
Planar Analysis score. Since most corps or bands march about the same amount of time, this
should work. If you want to be really precise, take a stopwatch to the show and time how long
the corps or band marches. Then divide the Raw P. A. Score by the number of seconds to get the
Adjusted Score. Compare your results to the judges' placements. Have fun!
Vince Lamb
CLIP HERE
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CORPS/BAND:
SHOW:
DATE:
LENGTH OF SHOW:
TIME SPENT MARCHING:
TABLE OF MOVES
1. a Circuitous (follow-the-leader closed formation)
2. abc Canonic (follow-the-leader open formation)
3. c Rectilinear (single direction)
4. dg Polar (multiple direction/scatter)
5. bc Antilinear (variable direction)
6. e Rotational (internal focal point)
7. ce Revolving (external focal point)
8. f Formal (expand/contract)
9. g Structural ("reshape")
The formation:
a - Changes order
b - Changes direction
c - Changes location
d - Changes interval consistency
e - Changes orientation
f - Changes size
g - Changes shape
MOVES USEDTOTAL TOTAL EVENT 1 2 3 4 5 6 7 8 9 USE DIFFICULTY ERRORS
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TOTALS | + -
=
PLANAR ANALYSIS SCORE:
CLIP HERE
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If you want to participate in a study, send your sheets to me this fall at:
Vince Lamb
c/o Drum Corps World
P. O. Box 8052
Madison, WI, 53708-8052
If you have e-mail, send the Corps Name, Show Location and Date, Number of Events, Total
Use, Total Difficulty, Total Errors, Time Spent Marching, and % Time Marching as well as the
Raw and Adjusted Planar Analysis Scores to dcwpoll@yahoo.com. I'll update you on the results
at the end of the season.
Thanks and good luck! Hope to see lots of your responses!
APPENDIX III--Planar Analysis of DCI 1995 for GE Vis Rankings 1-9, 11-12
Corps (in order of GE Vis Ranking):
CVLRSCBC BD SCTS PR BLCTSSCV GLSMNColtsMagicCRMSNCC
1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th
Total Use:
1 11 3 2 8 5 4 5 9 - 5 10
Total Difficulty:
1 11 3 2 8 5 6 7 9 - 4 10
Average Difficulty per Move:
10 1 2 6 5 4 8 7 11 - 3 9
Total Events:
2 5 4 1 8 11 5 10 9 - 7 3
Total Complexity (types per event):
1 9 2 8 5 10 6 3 7 - 4 11
Total Balance (average deviance from average use per type):
5 7 10 11 1 2 4 6 3 - 9 8
Variety:
8 4 1 5 6 3 9 7 2 - 11 10
Variety Grouping:
6 10 11 8 2 7 3 1 4 - 5 9
Grammar:
7 10 8 6 5 3 11 9 4 - 1 2
Grammar Grouping:
6 2 4 5 8 9 1 3 10 - 7 11
Table of Use:
Corps: CVLRSBD SCTS PR CRMSNSCV GLSMNBLCTSColtsCBC CC
Cir 13 4 4 3 - 1 4 - - 1 4
Can 22 13 22 9 12 10 16 16 11 9 6
Rec 30 10 10 9 3 7 9 9 9 8 6
Pol 39 24 21 19 25 24 7 14 20 12 21
Ant 10 9 8 10 10 9 7 6 7 7 6
Rot 14 15 19 9 14 17 17 14 12 15 15
Rev 5 2 2 1 1 1 4 2 3 - 2
For 11 6 8 5 4 8 4 11 5 7 4
Str 41 27 28 20 18 12 19 15 13 14 13
1. Total Use
179 122 109 89 87 87 87 85 80 77 73
2. Total Difficulty (# of uses x difficulty ranking - 1-9):
1st CVLRS 927
4th SCTS 646
3rd BD 586
11th CRSMN 468
6th BLCTS 466
7th SCV 465
8th GLSMN 459
5th PR 455
9th Colts 408
12th CC 401
2nd CBC 398
3. Average Difficulty per movement use (Total Diff./Total Use):
2nd CBC 5.45
3rd BD 5.38
11th CRSMN 5.37
6th BLCTS 5.356
5th PR 5.352
4th SCTS 5.29
8th GLSMN 5.27
7th SCV 5.22
12th CC 5.20
1st CVLRS 5.17
9th Colts 5.10
4. Total Events:
4th SCTS 55
1st CVLRS 54
12th CC 38
3rd BD 35
2nd CBC 33
7th SCV 33
11th CRSMN 32
5th PR 31
9th Colts 31
8th GLSMN 30
6th BLCTS 29
5. Complexity (av. number of movement types used per event):
1st CVLRS 3.31
3rd BD 3.11
8th GLSMN 2.90
11th CRSMN 2.75
5th PR 2.74
7th SCV 2.69
9th Colts 2.58
4th SCTS 2.218
2nd CBC 2.212
6th BLCTS 2.10
12th CC 2.02
6. Balance - av. use of type overall (av. deviance from av. use):
5th PR 9.44(+/- 3.49 - 37%)
6th BLCTS 9.66(+/- 4.81 - 50%)
9th Colts 8.88(+/- 4.56 - 51%)
7th SCV 9.88(+/- 5.20 - 53%)
1st CVLRS 19.88(+/-11.18 - 56%)
8th GLSMN 9.66(+/- 5.61 - 58%)
2nd CBC 8.11(+/- 4.79 - 59%)
12th CC 8.55(+/- 5.18 - 61%)
11th CRSMN 9.66(+/- 6.81 - 71%)
3rd BD 12.11(+/- 9.47 - 78%)
4th SCTS 13.55(+/-11.39 - 84%)
7. Type Sequence Balance (% of possible):
3rd BD 64.5
9th Colts 63.3
6th BLCTS 63.1
2nd CBC 62.0
4th SCTS 61.2
5th PR 57.6
8th GLSMN 56.8
1st CVLRS 55.7
7th SCV 54.7
12th CC 54.2
11th CRSMN 53.1
8. Type Sequence Grouping (% of possible):
8th GLSMN 17.9
5th PR 17.7
7th SCV 16.48
9th Colts 16.46
11th CRSMN 15.8
1st CVLRS 15.7
6th BLCTS 15.5
4th SCTS 15.2
12th CC 15.0
2nd CBC 14.9
3rd BD 14.3
9. Grammar Sequence Ballance (% of possible):
11th CRSMN 76.6
12th CC 76.5
10th Colts 74.4
6th BLCTS 75.0
5th PR 73.3
4th SCTS 70.9
1st CVLRS 70.4
3rd BD 69.6
8th GLSMN 67.8
2nd CBC 66.6
7th SCV 64.5
10. Grammar Sequence Grouping (% of possible):
7th SCV 69.7
2nd CBC 68.7
8th GLSMN 66.6
3rd BD 64.7
4th SCTS 63.58
1st CVLRS 63.52
11th CRSMN 61.2
5th PR 61.1
6th BLCTS 59.5
9th Colts 57.7
12th CC 57.6
Copyright Richard V. Lamb. Posted by permission of the author.