Many Worlds Theory

              I continue to be fascinated by the RGB color scheme, and extra-spectral colors in particular.  And the NFL football season starts tonight.  And so I ponder: are there any patterns/trends in the official team colors of the 32 NFL teams?  Well, I’m glad you asked.

              First of all, here are the “official” colors of the teams with their exact RGB ratings.  You will notice that there are a few teams that, perversely, have more than two team colors.

Locale	Team name	Color	R	G	B
Arizona	Cardinals	gold	255	182	18
Arizona	Cardinals	red	151	35	63
Atlanta	Falcons	red	167	25	48
Atlanta	Falcons	silver	165	172	175
Baltimore	Ravens	gold	158	124	12
Baltimore	Ravens	red	198	12	14
Baltimore	Ravens	purple	26	25	95
Buffalo	Bills	red	198	12	48
Buffalo	Bills	blue	0	51	141
Carolina	Panthers	silver	191	192	191
Carolina	Panthers	blue	0	133	202
Chicago	Bears	orange	200	56	3
Chicago	Bears	navy	11	22	42
Cincinnati	Bengals	black	0	0	0
Cincinnati	Bengals	orange	251	79	20
Cleveland	Browns	brown	49	29	0
Cleveland	Browns	orange	255	60	0
Dallas	Cowboys	navy	0	34	68
Dallas	Cowboys	blue	0	53	148
Dallas	Cowboys	silver	134	147	151
Denver	Broncos	orange	251	79	20
Denver	Broncos	navy	0	34	68
Detroit	Lions	blue	0	118	182
Detroit	Lions	silver	176	183	188
Green Bay	Packers	gold	255	184	28
Green Bay	Packers	green	24	48	40
Houston	Texans	blue	3	32	47
Houston	Texans	red	167	25	48
Indianapolis	Colts	blue	0	44	95
Indianapolis	Colts	gray	162	170	173
Jacksonville	Jaguars	gold	215	162	42
Jacksonville	Jaguars	dark gold	159	121	44
Jacksonville	Jaguars	teal	0	103	120
Kansas City	Chiefs	gold	255	184	28
Kansas City	Chiefs	red	227	24	55
Las Vegas	Raiders	black	0	0	0
Las Vegas	Raiders	silver	165	172	175
Los Angeles	Rams	yellow	255	209	0
Los Angeles	Chargers	gold	255	194	14
Los Angeles	Rams	blue	0	53	148
Los Angeles	Chargers	blue	0	128	198
Miami	Dolphins	orange	252	76	2
Miami	Dolphins	aqua	0	142	151
Minnesota	Vikings	gold	255	198	47
Minnesota	Vikings	purple	79	38	131
New England	Patriots	red	198	12	48
New England	Patriots	navy	0	34	68
New England	Patriots	silver	176	183	188
New Orleans	Saints	black	16	24	31
New Orleans	Saints	gold	211	188	141
New York	Giants	red	163	13	45
New York	Jets	green	18	87	64
New York	Giants	blue	1	35	82
New York	Giants	gray	155	161	162
New York	Jets	white	255	255	255
Philadelphia	Eagles	green	0	76	84
Philadelphia	Eagles	silver	165	172	175
Pittsburgh	Steelers	gold	255	182	18
Pittsburgh	Steelers	black	16	24	32
San Fran.	49’ers	red	170	0	0
San Fran.	49’ers	gold	173	153	93
Seattle	Seahawks	green	105	190	40
Seattle	Seahawks	navy	0	34	68
Seattle	Seahawks	silver	165	172	175
Tampa Bay	Buccaneers	orange	255	121	0
Tampa Bay	Buccaneers	red	213	10	10
Tennessee	Titans	red	200	16	46
Tennessee	Titans	navy	12	35	64
Tennessee	Titans	blue	75	146	219
Washington	Ftbl. team	burgundy	63	16	16
Washington	Ftbl. team	gold	255	182	18

I’ve already had to make a few judgement calls.  For example, most teams have three team colors: two typical colors, and then either white or black.  In most cases I’ve thrown white or black out, unless they are one of the two main colors (in my opinion).  For instance, the Cincinnati Bengals are orange and black.  I’ve only held onto three colors if I feel they are crucial to their color scheme.  The Dallas Cowboys are particularly meretricious in this regard.  They claim no less than five colors: white, blue, navy blue, royal blue, and silver.  Based on my own aesthetic color sense I have pared this down to three.

              Also note that I have renamed the colors in most cases.  Many of the teams copy one another, using the exact same colors, but call those colors by different names.  The most egregious example is the color (0,34,68) which is used by four different teams.  Dallas calls this blue, Denver calls it Broncos navy, New England calls it nautical blue, and Seattle calls it college navy.  I just call it blue.

              Only one team has a “pure” RGB color: the San Francisco 49’ers have red (170,0,0).  You gotta give ‘em props for going all-in on red.  I guess (255,0,0) was too “bright” so they darkened it a little, but hey.

             So, is there a way to visualize this data in a graph?  The problem is displaying 3-tuples in two dimensions.  Luckily, there is a way to do this.  It’s called a chromaticity graph.  Define three new variables thus:

r = R/(R+G+B)

g = G/(R+G+B)

b = B/(R+G+B)

You can think of these variables as indicating the relative percentage of each core color, without regard to brightness.  So magenta (255,0,255) has values r = 0.5, g=0, b = 0.5, indicating that magenta is half red, half blue.  Similarly, chartreuse (128,255,0) has values r = 0.333, g=0.666, b = 0, indicating that it is 1/3 red and 2/3 green.

              Now consider plotting r vs. g.  You might think you’ve “lost” information about the value of b, but that is not the case.  Since r + g + b = 1 is necessarily true, you could always recreate the value of b if you needed it.

              Here is a plot of r vs. g, which is a chromaticity graph:

Where you have lost information is in the value of “brightness”.  For example, white (255,255,255), gray (128,128,128) and black (0,0,0) are all plotted at the exact same coordinate (r,g) = (0.333,0.333).  And blue (0,0,255) and dark blue (0,0,128) look very different, but again they map to the same point (r,g) = (0,0).

              Note that most of the “standard” colors we have names for appear on the outer edge of the triangle (since one of the three variables R,G,B is zero).  The exceptions are the grayscale colors (white, gray, black) which are at the center of mass of the triangle, and other extra-spectral colors like tan or hot pink.

              Speaking of extra-spectral colors: there are two main ways to “construct” them.  You can either:

• mix all three colors R,G,B in roughly equal measure, or
• mix R and B with very little G.

With this in mind, we see that the extra-spectrals occupy the middle portion of the triangle, as well as the bottom edge:

              OK, so back to my original goal…visualizing the NFL team colors.  Here is a chromaticity plot of all the team colors in the above table:

What trends do you notice?

• There are plenty of reds, of all varieties.
• All the blues have a major element of green as well.  That is, there is a cluster of colors around azure and cyan, but no true blues.  The blue with the least green is Buffalo Bills blue, at g = 27%.
• There are no true greens.  In fact, there are few greens at all.  The maximum green is g = 57% for the Seattle Seahawks.
• There are no pinks: nothing anywhere close to magenta.
• There is almost a “main sequence” like in an H-R diagram, running from cyan to gray to yellow.  Why do so many NFL colors have g ≈ 33%?
• There is a huge cluster of colors around “gold”.

I’m sure you can find other patterns.  Here is a map of the “under utilized” colors for NFL teams:

The pink/magenta thing makes sense.  For some reason, people think these are not masculine colors.  (This was not always the case.  Pink used to be associated with boys.)  But what about the lack of green?  And the lack of true blue without green?  I have no idea.  Maybe someone can enlighten me.

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