Statistics for two populations interacting with each other

Question

Lets say we have a Red team with 1000 members and a Blue team with 100 members.

After a year Red team has killed 50 Blue members and the Blue team has killed 50 Red members.

Despite both teams killing the same amount of people how truthful is the following statement

Blue members were 10 times more likely to die

Technically, it looks correct where Blue members had a 1 in 20 chance of dieing and Red members a 1 in 2 chance of dieing. Resulting in Blue member being 10 times more likely to die.

However, it feels like the statement hides the fact the populations were dieng as a direct result of their interactions with each other. The Red team was unable to take advantage of their higher population so could be seen to be weaker as a result and the opposite could be said about the Blue team who could be more dangerous by kiling the same amount with less.

Is there a more truthful way in presenting the statistics and would I be able to learn more if I had results over multiple years where the populations changed over the years?

Answer 1

If I understand correctly, your question is if being a Red member or Blue member increases your risk of dying during an interaction with the other group, if the groups were of a similar size. I think this is difficult to tell without more information about these interactions.

Consider possible scenarios that could lead to this 50 deaths/50 deaths situation. Here are some examples:

• 100 interactions between the two groups, where each interaction is a 1 vs. 1 fight between different members, and where nobody fights twice. So this is something like a 0.5 probability to die for each fighter, no matter their group. In other words, belonging to any of the two groups does not make you more apt to kill other people, the proportion of people killed in each group is just related to how many people there are in this group.

• 100.000 interactions between various individuals of the two groups, where an interaction is defined as 1 individual encountering another individual, or a group of individuals encountering another group of individuals (1 vs. 5, 2 vs. 10, 3 vs. 3 etc.). Most of these interactions are peaceful without people dying. However, 25 of these interactions lead to the death of 2 Blue members on average, and a single one interaction leads to the death of 50 Red members.

• 100.000.000 interactions over the year, mostly peaceful, where the 50 deaths on each side are the work of 2 individuals.

From this, I think this is difficult to infer anything about the groups without knowing the details of the interactions.

If you have additional data for other years that gives you the fluctuations of group sizes and deaths over time, you might be able to model how an increase of 1 person may or may not increase the ratio of people who die. But depending on the problem you want to solve, this is probably not very informative, for example if your goal is to prevent people from killing each other (you may want to explore other things, like if one of the groups has an easier access to firearms, etc.).