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World I'm building a sports league. The sports league has 21 teams.

This led me to a question that's an interesting intellectual puzzle I thought this forum would like:

Could the 21 teams wear different strips/kits/colours? They would have to be distinguishable at a glance.

Say you want 6 teams to have visually distinct kits, that's easy: you have a black, white, red, yellow, green, blue team. The more you have the harder it becomes.

(Obviously real teams just have an alternative kit they wear when there's a danger of confusion. I'm trying to avoid that because it makes them less strongly branded, weakens their sense of identity that little bit.)

Searching led me to this List of 20 Simple, Distinct Colors. Let me draw your attention to the 'Convenient' ordering at the top. ("I’ve arranged the “convenient” order so that if you want six colors, for example, just choose the first six. The order of the colors is inspired by their frequency of appearance on all the world’s subway maps (yes, I did count them all!)")

So you might say: "Well there you have it, 20 distinct colours, use those." But A) they're not quite distinct enough (the list includes green, lime, and mint), and B) that list was built with a constraint we don't have: we don't have to have one colour.

A team with a red strip like Arsenal is distinguishable from a team with red-and-black stripes like AC Milan, (IMO: maybe someone will argue). You don't have to use a new colour to create a new strip.

There's also shapes to think about. Imagine Team A has yellow-and-black vertical stripes, and Team B orange-and-black vertical stripes, that's a problem. But if we make one team's stripes horizontal instead of vertical, that helps a bit.

Contrasting colours might be useful here: a team in blue-and-yellow can play against either a team in blue or a team in yellow without a problem.

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    $\begingroup$ Keywords to search for livery, coat of arms, national flags, nautical communication flags. ideally 2-3 colors with a simple meaningful symbol, emphasis on simple. $\endgroup$ Sep 20, 2023 at 1:39
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    $\begingroup$ @GaultDrakkor add jockeys' silks to your list of words $\endgroup$
    – wokopa
    Sep 20, 2023 at 9:21
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    $\begingroup$ FIFA World Cup does it for 32 teams, so why not 21? Additionally, why are you concerned that alternative colors will hurt branding, when in reality it doesn't? $\endgroup$ Sep 20, 2023 at 13:11
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    $\begingroup$ @Blueriver The FIFA World Cup has alternative strips to avoid colour clashes, which the OP has said they don't want to do. $\endgroup$
    – F1Krazy
    Sep 20, 2023 at 15:05
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    $\begingroup$ @F1Krazy OP specifically stated it would hurt branding. I'm challenging that, stating that in reality it doesn't. $\endgroup$ Sep 20, 2023 at 17:38

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This problem was effectively solved at the end of the 18th century with Naval Signalling Flags. There were experiments to see which contrasts were visible and which were not. There are no green flags, for example, as the difference between green and blue was hard to spot, particularly with changing lighting at sunset.

Alphabetical flags

The 26 letters allowed you to spell words, but you were also limited by the flags in your locker and the space on your mast. The flags were supplemented by national flags, and telegraphic codes using rarely-used letters. See, for example how the famous England Expects... signal sent by Nelson was a compromise between the message, the flags they had in the signal locker, and the telegraph codes. The upshot is that each of the 26 letters had to be distinguishable in isolation (unlike letters, which can often be guessed from the surrounding ones).

Flags fulfilled much of the requirements for a sports kit. The flags had to be readable in any orientation, and under different lighting conditions.

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    $\begingroup$ Thanks for this! You got the concept very well: it's about colour-theory and visual language. $\endgroup$
    – wokopa
    Sep 20, 2023 at 9:09
  • $\begingroup$ In the same age, jockeys wore their owner's colour, so you could put your horse in a field of others. I don't know of any effort to check the colours were all distinguishable. $\endgroup$ Sep 20, 2023 at 12:37
  • $\begingroup$ The problem wasn't entirely solved until the 20th century - modern signal flags supplanted earlier ones after WWI, when it was found that word-by-word messaging via signal flags failed more often than not. The 18th century flags weren't distinct enough. $\endgroup$ Sep 20, 2023 at 12:57
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    $\begingroup$ I've added a picture to your answer; feel free to undo the edit if you want. I think it's good to note, just for completeness sake, that the distinctive alphabet flags also rely on differing shapes, and presumably the sports jerseys aren't tailored radically differently. $\endgroup$
    – KeizerHarm
    Sep 20, 2023 at 17:48
  • $\begingroup$ The 1934 flags are rather different. There have been improvements since the system was first devices. However, the point is that the original system had been tested by trying to read hoisted signals at increasing range. There is some variety of shapes, but I think you could make all the alphabetic flags square and still read them. One other difference: the letter 'S' uses green in 1934, which may be because there was a fast bright green dye. $\endgroup$ Sep 20, 2023 at 18:24
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Having played with it a bit, I'm pretty sure it is possible. I'll give my answer in visual form first, then talk through it –

enter image description here

We can use 7 colours simply, without needing to mix: Black, White, Green, Yellow, Red, Royal blue, Sky blue

I shied away from using orange alone: a tricky colour which is adjacent to both red and yellow. Magenta/pinks are too close to red, and there's no reason not to add a second colour to pink to help the matter.

Maroon alone could work (by 'work' I mean 'have sufficient contrast with red) – take a look –

red and maroon

– but it's better to add a contrasting colour.


Second, I started tapping the idea of contrasting colours. You can have a yellow-and-purple team because that contrasts strongly against both yellow and purple. (You couldn't have a blue-and-purple team.)

This give four extra teams: green&red, orange&blue, yellow&purple, black&white.

I made orange&blue and yellow&purple two different patterns, as they have limited contrast (orange is like yellow, blue is like purple).


We haven't utilised maroon yet. What contrasts with maroon? Blue. So put West Ham in the league.


Red&green are considered opposite colours, maximum contrast on the colour wheel. But red&yellow is also very highly contrasting. This guide to contrast for web design helped me


Looking through the list of 20 colours, I'd skipped brown, beige, olive, and grey as being too weak alone. So throw them all together! And what does that make? Camo, more or less. Add a camo team; that's very different from green.


This is getting close to 100% optimal. The problem is tractable. A colour normally only has one or two potential clashes, so you just need to make it distinct from those with some alteration.

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  • $\begingroup$ What sport is it that the ladies in the picture are playing ? $\endgroup$
    – Evargalo
    Sep 20, 2023 at 6:46
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    $\begingroup$ Looks like Gaelic football to me. Supermac's is a sponsor of Galway GAA (The Galway County Boards of the Gaelic Athletic Association) $\endgroup$ Sep 20, 2023 at 8:17
  • $\begingroup$ With (long) sleeves, you could make them the contrast colour in one pattern. But you might want to look at Jockey Silks (from horse racing) for inspiration $\endgroup$
    – Chris H
    Sep 20, 2023 at 9:55
  • $\begingroup$ The stripe patterns aren't feasible if the pattern is meant to be recognizable from a distance. Once you get far enough away, the colors will merge to form a different color. That will make your magenta-white, magenta-black, and red-blue stripe patterns look like light magenta, dark magenta, and magenta, respectively. (This is the same principle that enables things like LCD displays and halftones.) $\endgroup$
    – Abion47
    Sep 21, 2023 at 19:26
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    $\begingroup$ This has cracked it, throw in stripes in 1 of two directions, quartering, and even spots if you wanna go nuts, and the problem is gone. $\endgroup$ Sep 22, 2023 at 10:27
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With $N$ colors and $M$ different articles of clothing to color, you can create $N^M$ unique kit combinations.

If the uniform consists of shirts, pants, and shoes, you need only 3 unique colors to have 27 unique color combinations.

If the uniform consists of just shirts and pants, you need 6 colors to yield 36 unique color combinations. We can certainly get 6 unique enough colors (white, black, red, blue, yellow, green), the only question becomes is a red-blue team distinct enough from a blue-red team. If it's not, we can simply double the number of possible kits by adding stripes to all kits to make new kits.

Add in color-able embellishments like stripes and their directionality, and the number of possible kit combinations grows very quickly. 21 unique combinations is quite doable even with relatively few distinct colors and limited options for what to color - the only way it's really not feasible is if the uniform must be a single color.

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  • $\begingroup$ The math is fine but the practical example (shirt / shorts / shoes) won't really work for sports teams. If you're playing against a team that wears the same shirt + shorts colors as your own team, the only distinguishing feature is shoe color. That's not visible enough when looking for who to pass to in most sports; your brain needs to be able to see whether there are any players from the other team in a whole area without paying individually attention at any of them. $\endgroup$ Sep 20, 2023 at 19:32
  • $\begingroup$ Shoes aren't big enough, can easily be obscured by people in the way, and aren't where you're looking in sports where you throw to people's hands, such as Ultimate (frisbee). What could work are patterns (multiple colors on the shirt), although if two have the same shape of pattern but just swap the same two colours, that's also not great for scanning a moving group of people and having your subconscious process that into a gestalt understanding of the flow, or seeing people from your team running not closely followed by anyone from the other team. $\endgroup$ Sep 20, 2023 at 19:35
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    $\begingroup$ @PeterCordes if you have e.g. stripes, where ordering is not useful, the combinatorics become NchooseM ($N!/M!(N-M)!$) rather than $N^{M}$. But even if you only have 2-color combinations of only 5 distinct colors, that's still 10 easily-distinguished stripe patterns, and then you can get another 10 from checks, another 10 from swirls, etc. If you're on the field in a red/black vs white/black match, your brain will ignore the black quickly $\endgroup$ Sep 20, 2023 at 21:01
  • $\begingroup$ @thegreatemu: Yes, that can work. As long as there's something visually different at chest to shoulder height. (I'm not sure if shorts would work well. Less bad than shoes, but not great for some sports. Maybe for a sport where long shorts are in fashion, but shorts could be hidden behind crowds more easily than shirts.) $\endgroup$ Sep 20, 2023 at 21:08
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Below I use the term livery in most places, as this is the most generic terminology for what you’re trying to talk about. It encompass not just the colors, but also the patterns, insignias, and even things like the exact style of outfit.


First, a frame challenge: Alternate livery doesn’t really hurt branding all that much.

I encourage you to look at how alternative livery is actually used in real life. In a majority of cases, a team’s primary livery is used in almost all cases, they just use different colors on their uniforms during a match, and the primary purpose is so that the two teams can be clearly distinguished while playing. While the alternative livery is often distinguished in many sports by being ‘away colors’, or an ‘away uniform’, that distinction only really exists because if a team needs to change livery for a match, it’s by convention always the team that is not hosting.

Yes, there’s some loss of visual distinctiveness when watching a broadcast of a match, and you may have to check the scoreboard or something equivalent to know for sure who is playing, but that’s about it when it comes to the alternate livery hurting branding.

Additionally, alternative livery helps with merchandising (because it gives you a wider variety of things to sell). This may be significant if the teams derive at least part of their funding from selling merchandise.


Second, an actual solution.

Pick seven distinct colors. Each team gets a unique set of three from that list of seven. Problem solved.

There are 35 possible combinations of 3 colors selected out of 7 possibilities, so this scales up to 35 teams (which helpfully lets you ‘retire’ combinations when a teams are disbanded, allowing for better consistency across such transitions). Each team will have a unique set of colors, so the entire rest of the livery, including things like patterns, can actually be identical (though it shouldn’t be identical for a couple of reasons, such as pattern recognition being important for quick identification even if the colors are distinctive).

In terms of distinctiveness, I would probably go with (using the swatches on the site you referenced) white, black, red, yellow, green, blue, and one of orange, cyan, or magenta. That gets you clear visual distinctiveness of each color, while still being reasonably distinctive even for people with color blindness.

Overall though, this requires the league to assign colors as opposed to the teams just picking their own colors, because cultural bias will tend towards specific colors being picked. You’ll notice for example that red is a very common color for sports teams in Western cultures because of it’s associations with feelings of aggression (in the sense of aggressive competitiveness more than violence, though for some sports the violence aspect fits too).

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    $\begingroup$ I can't be the only one who thinks Man United playing in any colour other than red doesn't feel like 'proper' Man United. Who buys posters of their sporting heroes wearing the away strip? $\endgroup$
    – wokopa
    Sep 22, 2023 at 11:30
  • $\begingroup$ @wokopa But on the flip side Man United playing in red doesn’t make them a good team, it’s not what has kept their spot in the Premier League, and it’s not what made locals in Greater Manchester fond of them. Branding is about recognition, but once they’re on the field the aspect of recognition that matters is being able to differentiate them from the other team. They could play in chartreuse and magenta paisley, and they would still be one of the best teams in the world, and would still fill the stadium when they played. $\endgroup$ Sep 22, 2023 at 16:40
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    $\begingroup$ @wokopa OTOH, not all alternate livery has to look completely different from the normal uniform like seems to be the norm for most association football clubs. See for example the NFL which keeps identical (or near identical) patterning for a team’s uniform for all variants in most cases, and just shuffles where the colors are on the uniform, or MLB, which gives most teams a white or striped home jersey and a grey away jersey, but uses consistent accent colors (socks, cap, hems, belt) for a given team. $\endgroup$ Sep 22, 2023 at 16:52
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Color combos

Every real sports league has this problem. What most of them do is to have teams pick a primary, secondary, and tertiary color. Jerseys are usually the primary (home jersey) or secondary/tertiary (away jersey). Often one of the secondary or tertiary colors is white or black and mainly used for shadow or extra contrast.

You could also try patterns, like Tartan cloth, which is a similar idea.

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Culture is a bigger obstacle than mathematics

Mathematically, this issue can be solved using the combination formula:

C(n,r) = n!/((n-r)!*r!)

Most people can consistently distinguish by name and on sight 14 colors [Black, Grey, White, Red, Dark-Red(AKA: Maroon or Burgundy), Yellow, Gold, Orange, Brown, Green, Blue-Green (AKA: Teal, Aqua, Cyan, etc.), Blue, Purple, and Pink]. Even nearly color blind people can tell the difference between black, white, red, green, blue, and gold. This gives you somewhere between 6-14 colors to work with depending on how handicap accessible you want your team kits to be. Now let's assume that kits can have anywhere from 1-3 of these colors.

For a 6 color system you get:

Cx = C(6,1) + C(6,2) +C(6,3) = 6!/(1!(6-1)!) + 6!/(1!(6-1)!) + 6!/(1!(6-1)!)

Cx = 5 + 15 + 20

Cx = 40

And for a 14 color system you get:

Cx = C(14,1) + C(14,2) +C(14,3) = 14!/(1!(14-1)!) + 14!/(1!(14-1)!) + 14!/(1!(14-1)!)

Cx = 14 + 91 + 364

Cx = 469

So, by just using colors in combination of 3 or less, you can support a league of 40-469 easily distinguished teams without any conflicts.

... So why then is this such a big problem for major sports leagues?

The reason most sports leagues have issues in not a lack of available combinations, but because some colors are just a lot more popular than others. For example: despite all of the colors to choose from, 88% of the teams in the NFL use black, blue, or red as one of their colors. 40% of the teams use 2 of these colors and 1 team uses all 3. In contrast, colors like teal, brown, and burgundy are only used by 1 team each and not a single team uses pink despite it being such a popular and recognizable color in other contexts. With this much overlap, it can get hard to tell who is who not because there is not enough colors, but because there is a strong cultural bias that causes most of the teams to gravitate towards these same 3 colors.

This is because in Western culture, black is highly associated with masculinity, red with aggression, and blue with comradery: The 3 principle virtues of the male athlete. In contrast: pink and teal are typically seen as more feminine colors and brown and burgundy are humble colors which goes against the typical virtues of an athlete.

In other words, if you want to get all of your teams to look different, it has to be through acts of regulation that force them to pick from an even distributions of colors instead of letting the teams pick their own colors. So, if you let the league assign colors instead of letting teams pick them, you could easily have 21 teams that each look uniquely deferent without needing separate home/away uniforms or other secondary features to distinguish them.

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    $\begingroup$ Your comments have merit, but you fail to consider contrast. 10 colours create 55 pairs, but some pairs are inferior to others i.e. red&orange is not very distinguishable from red, but red&blue is. $\endgroup$
    – wokopa
    Sep 20, 2023 at 19:18
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    $\begingroup$ @wokopa That is less of a concern than you think. While it can be hard to tell if a stand-alone color is red or orange without context, when you put the two next to each other, they are very distinct. So if a team were to have red and orange, it would be very clear that they are wareing 2 colors and if you have one team red and another orange, you could easily tell them apart as well. $\endgroup$
    – Nosajimiki
    Sep 20, 2023 at 20:14
  • $\begingroup$ and even if your concern is true... it does not really contradict my statement that you have 40-469 distinct color schemes depending on how much you want to cater to colorblindness. What you are describing is just one of the many patterns between the 40 ideal patterns and 469 that most people would be fine with, but a hand full of people might struggle with. $\endgroup$
    – Nosajimiki
    Sep 20, 2023 at 20:29
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It's easy. Just use whatever colour you want so long as you have 11 distinct jerseys. Some plain, some striped, it doesn't matter. Then do the rest by changing the shorts/skirt colours.

You might have a grey and white striped jersey thats similar to a blue and white one. But the red shorts, versus the green tell you which is which at a glance.

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Main colors are red, orange, yellow, green, blue, purple. Black and white are not considered technically colors but they are distinct.

So that makes about 8 main and distinct colors.

So some teams might have both shirts and pants the same color. That makes eight teams.

Other teams might use different colors for shirts and pants. Eight times eight is sixty four. If a team with red shirts and purple pants and a team with purple shirts and red pants are counted as having different color combination then there are one hundred twenty eight two color combinations in addition to the eight color combinations.

In heraldry white and yellow are counted as the metals silver and gold, and red, blue, green, purple, and black are counted as the colors. Two colors or two metals can be placed side by side in a pattern, but a color can not be placed upon a color, nor a metal upon a metal, to ensure sufficient contrast.

Thus using heraldic colors there would be ten color combinations, or twenty if a black shirt and gold pants are considered different from a gold shirt and black pants. And that is with the shirts and pants being the same color all over instead of having patterns or having images in a different color on them.

In medieval warfare being able to recognize the heraldic designs on shields, surcoats, and banners at a distance to tell friend from foe could be a matter of life and death, so if the members of team wear their coat of arms or their heraldic badge in a large size on their clothing it should be easy enough to tell who is who.

If the sports players and fans know the rules of whatever heraldry like system your society uses, Someone could described the heraldry of a team in a sentence or two and the people who hear that description will be able to recognize it at first sight from the description.

There is a figurative expression "draped in the flag" for someone who claims to be so patriotic that you can picture them wearing the flag wrapped around them. (Which can be literally true if someone has a coat of arms and banner of that coat of arms and wears clothing with the coat of arms on the clothing, the same pattern as on their banner.) And of course it is entirely possible for sports teams in our world to have their flags. Thus fictional sports teams might have their flags, and the uniforms of players might have their flags printed on them.

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  • $\begingroup$ your math is a bit off $\endgroup$
    – njzk2
    Sep 21, 2023 at 20:33
  • $\begingroup$ not sufficient contrast to use black with red? or blue? or green? $\endgroup$
    – njzk2
    Sep 21, 2023 at 20:35
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    $\begingroup$ "Black and white are not considered technically colors" - According to whom? Adobe has some thoughts on this. It's not part of the rainbow, but that's hardly the only way to decide what is and isn't a color. The very first definition for "black" when I looked up just now was "Being of the color black". $\endgroup$
    – William
    Sep 22, 2023 at 16:48
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Solved in real world

When a sporting event includes multiple teams simultaneously, their attires have to all be different:

Formula One cars in multiple liveries (Morio, CC BY-SA 3.0 http://creativecommons.org/licenses/by-sa/3.0/, via Wikimedia Commons)

The use of patterns, sponsor names and logos distinguishes the teams well enough for a profitable sport.

There are 10 teams in Formula 1 and 17 in NASCAR, close to your parameters.

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    $\begingroup$ As a long-time F1 fan, I'd argue that while F1 cars are always different, they're not always distinct, which is what OP is after. Compare the 2006 Toyota with the 2006 Super Aguri, for example. $\endgroup$
    – F1Krazy
    Sep 20, 2023 at 14:15
  • $\begingroup$ @F1Krazy: While it is true that there are confusable liveries in some years, it's also the case that in many years every car is easily distinguishable. Accordingly, I think this answer is correct. $\endgroup$ Sep 20, 2023 at 17:11
  • $\begingroup$ At a glance, I count five cars in that image that use a red/black or red/yellow/black color; I couldn't tell you which was which. especially if you left off the words, and I definitely couldn't tell you which was which if they were quickly zipping past. Granted, cars can have some intricate detail, because they have immobile surfaces; clothes flap around and can cover up details. $\endgroup$
    – ArmanX
    Sep 20, 2023 at 19:23

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