Keep your redshirt on: a Bayesian exploration

Author: Matthew Barsalou

The idea of red-shirted characters being frequently killed in Star Trek: The Original Series has become a pop culture cliché. But is wearing a redshirt in Star Trek as hazardous as it is thought to be? To find out, casualty figures for the Starship Enterprise were compiled using the casualty list provided by Memory Alpha.

Uniform Color

Color’s Meaning

Casualties

Comments on the Data

Blue

Science and medical

7

Gold

Command and helm

9

Includes Lee Kelso and Gary Mitchell who wore the old style chartreuse command and helm uniform. Also includes O’Neil, whose uniform was not listed, but can be observed in the episode The Galileo Seven.

Red

Operations, engineering and security

24

n/a

Unknown

n/a

15

Includes nine killed by the galactic barrier in Where no “Man has Gone Before”, three Rigelian fever victims from Requiem for Methuselah and one unknown casualty of the dikironium cloud creature in Obsession. Also includes Sam and Barnhart who were not in standard uniforms when they died.

Table 1: Enterprise NCC 1701 casualties from episodes aired between September 8, 1966 and June 03, 1969 based on casualty figures from Memory Alpha. Note: Table does not contain casualties from the Mirror Universe or anybody killed and resurrected during an episode.

Figure 1: Casualties by Uniform Color

A pie chart was created using Minitab to graphically view the data. It is obvious from the pie chart in Figure 1 that redshirts suffer most of the casualties. However, raw casualty figures are not very informative without knowing how many people were in each uniform. According to the Joseph’s Star Trek Blueprints, the only set of Enterprise blueprints endorsed by Paramount Pictures, the Enterprise’s 430 crew members consisted of 55 command and helm personnel, 136 science and medical personnel and 239 engineering, operations and security personnel. This means 16.4% of casualties were in command and helm, 5.4% were in science and medical and 10.0% were in operations, engineering and security. Of the remaining 27.3% of casualties, 12 were killed by contact with the galactic barrier or Rigelian fever, which could have affected personnel regardless of duty assignments.

Uniform Color

Casualties

Total Population

Casualties as Percent of Population

Blue

7

136

5.1

Gold

9

55

13.4

Red

24

239

10.0

Unknown

15

n/a

n/a

Total

55

430

12.8

Table 2: Enterprise NCC 1701 casualties by uniform color. Note: There were 18 security department casualties out of the total of 24 redshirt casualties. This means the security department with 90 people lost 20% of its members.

Figure 2: Chart of Casualties and Populations.

Figure 3: Chart of Casualties as a Percentage of Each department.

Based on an analysis of casualties that considers the overall total number of personnel in each color of uniform, wearing a redshirt may not be the automatic death sentence that it is popularly considered to be. On the other hand, 18 of the redshirt casualties were security personnel out of a total population of 90; 20% of the security department were casualties. Although wearing a redshirt may not of itself be particularly hazardous, personnel in a redshirt who are members of the security department should expect to pay a high premium on their life insurance.

Using what is known about Enterprise crew and casualty figures, suppose an Enterprise crew member has been killed. Discarding the 15 unknown casualties, redshirts consist of 60.0% of all fatalities where the uniform color is known; blue and gold uniforms are the remaining 40.0% of casualties. Redshirts are only 52.0% of the entire crew, but 60.0% of casualties, so what is the probability that the latest casualty was wearing a redshirt? The Enterprise often visits Starbases and takes on new crew members, so we assume sampling with replacement. Otherwise, the population size would change every time a crew member is killed.

Bayes theorem can be used to solve this. Bayes’ theorem solves for P(A|B), where P(A|B) is the probability of A given the B has happened. In this situation, that would be the probability that somebody is wearing a red shirt (A) if they are a casualty (B).

The formula is set up using what is known about the crew composition and the known casualty figures.

P(A)= Percent of redshirts in crew = 52.0%

P(~A) = Percent of crew that don’t wear a redshirt = 48.0%

P(B|~A) = Casualties not in a redshirt = 40.0%

P(B|A)= Redshirt casualties = 60.0%

The percentages are then converted into probabilities using decimal notation and plugged into the formula:

There is a 61.9% chance that any given casualty is wearing a redshirt. This really does not help the insurance premiums of operations, engineering and security personnel. Three departments wear redshirts so it may be worthwhile to take a deeper look at the data to determine if a wearing a redshirt is as hazardous as it appears to be. According to table 2, the security department suffered 18 out of the 24 red shirt deaths. What does Bayes’ theorem say about this?

Suppose a crew member finds a casualty with a redshirt. This may or may not be a member of security. Redshirts in security are 75.0% of all redshirt casualties and other redshirts are only 25%. However, security is only 37.7% of all people in a redshirt. How likely is the casualty to be a member of security?

P(A) = Percentage of redshirts in security = 37.7%

P(~A) = Redshirts that are not in security= 62.3%

P(B|~A) = Redshirt casualties not in security = 25.0%

P(B|A)= Redshirts casualties in security = 75.0%

The probabilities are then entered into the formula:

There is a 64.5% chance that any given casualty in a redshirt is a member of security. We can also conclude there is only a 35.5% chance that any casualty in a redshirt is not a member of security. This is in spite of security being only 37.7% of the entire population of redshirts. So what does this mean for red-shirted crew members not in security? Remember, security, operations and engineering wear redshirts. The 15 unknown crew members are not included in this calculation.

P(A) = Percentage of crew members in operations and engineering (redshirt, but not in security) = 34.7%

P(~A) = Percentage of crew members not in operations or engineering = 65.3%

P(B|~A) = Casualties not in operations and engineering = 85.0%

P(B|A)= Casualties in operation and engineering = 15.0%

The probabilities are plugged into the formula:

In spite of wearing a redshirt, there is only an 8.6% chance of a member of the operations or engineering departments becoming a casualty. These personnel should ensure that their life insurance plans are based on their departments and not their uniform color.

Although Enterprise crew members in redshirts suffer many more casualties than crew members in other uniforms, they suffer fewer casualties than crew members in gold uniforms when the entire population size is considered. Only 10% of the entire redshirt population was lost during the three year run of Star Trek. This is less than the 13.4% of goldshirts, but more than the 5.1% of blueshirts. What is truly hazardous is not wearing a redshirt, but being a member of the security department. The red-shirted members of security were only 20.9% of the entire crew, but there is a 61.9% chance that the next casualty is in a redshirt and 64.5% chance this red-shirted victim is a member of the security department. The remaining redshirts, operations and engineering make up the largest single population, but only have an 8.6% chance of being a casualty.

Red uniform shirts are safe, as long as the wearer is not in the security department.

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Comments

Azka

I have sort of been holding out hope that sehomow, some way, Joker could get this thing turned around. There is the youth, the injuries, the schedule. However, i am now, finally, convinced that a change must be made.I guess I have suspected this since about the 3rd or 4th game of his tenure, but the Mizzoo game was the final straw for me. That was a VERY bad team that beat us in Columbia. And, for all the reasons listed in the original article, Joker has, sadly and clearly, shown that he is totally lost in game situations. His decisions are not only questionable, they are unfathomable.Like so MANY others including, I suspect, Barnhart I'd love to see this work. But, what has been so clear to so many for so long is now so obvious to even a stubborn old mule such as myself. A change MUST be made. The time for discussion has long since passed.

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Claude W

In the age of steam the US Navy lost a lot engineers below decks.  Shock, Explosions, Steam burns and drowning were typical reasons. Much worse in wartime.  They use to bolt the main hatches going into engineering on the larger ships with compartments deep underwater.  You hoped that the enlisted man with the wrench would hang around after "abandon ship" was called.

In "New Generation" they seemed to loose a lot of engineers.  How did Security fare there?

v/r claude

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Spock

For the first time in my life, I was happy.

reply to this comment

Patrick Aquilone

Awesome!

But I still think I would rather be in command especially if beaming down to a planet.

reply to this comment

dholyer

So how can we get those that think the Government is the power to the solution were red shirts. Then we need to replace all hand guns with phasers. And start using Stardates for a calander.

reply to this comment

Mardi VanEgdom

Probably also true because security personnel are more likely to go off-ship and face dangers than engineering or operations.  Security people put themselves in harm's way, no matter what color uniform they are wearing.  If the security personnel were wearing gold or blue, then gold or blue uniformed personnel would be more likely to be killed.

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Carl

In the first application of Bayes theorem how do you calculate percent of redshirt crew is 52%? Should it not be 239/430x100% = 55.6%?

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meta41

The "curse of the redshirt" is not that they get killed off, but that they typically die at the onset of an episode without any character development and often without having uttered a single line.  They are fodder to demonstrate the threat that the regulars must then overcome in that episode. Still, the analysis was entertaining!

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AndStuff

I'm curious if they're counting the deaths of people who are miraculously revived. If a bridge crew member was killed, by the end of the episode, he was usually a-okay. You don't see medical personnel rushing to revive any red shirts. If they're dead, they're good and dead. Anyway, I don't think we should truly count something as a "death" if they're brought back to life later. I wonder if these statistics takes that into account. 

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Sharzade

As an Enterprise crew member, the major death factor is greatest being on an away team mission. If you are a red shirt crew member on the Enterprise then your chances of being on a given away team mission are much less than if you were a blue or gold shirt crew member (I bet Bayes' rule would show that). So the population of interest should really be “those on an away team mission” and then I think the stats would indicate you have a worse chance on being toasted in a red shirt.

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