# The Unreliable Math Behind Idol Group Sizes

A few days ago I was having a discussion with my friend about general idol stuff and I said something along the lines of “If the group had fewer members, it will be easier for the less popular members to get noticed” with reference to a certain group that had girls Wake Up! and comparing it to a trio that Sail-ed a lot.

So one thing led to another and I wanted to see how much does the size of an idol group actually affect how successful it is. So I started a quick twitter poll to see what did people feel about idol group sizes and as you can see, the reactions were mixed. I decided to get the numbers involved to see what truly is the most efficient idol group size. (The results may surprise you)

This was how I went about with doing my simulations. I was still formulating out how I would express everything so the early stages look really bare but I will explain the numbers for now.

The assumptions I took when making this were

1. The company has 100 units of “resources” for each group
2. The company has to evenly distribute out these resources to the members
3. Each girl will be given a random number from 0 to 100 to represent their “talent”
4. The value of the group will be the sum of members’ talent multiplied by the company resources invested in them.

So I ran 500 simulations on different performances of the various group sizes and this is the finalized data.

The biggest surprise is that on average, the size of the group barely had any effect on how successful the group was as a whole. However, the smaller groups had a larger deviation of results which meant that they had a chance of achieving a higher value. This also meant that they were riskier and could get very low values compared to the other group sizes.

Initial Verdict

Groups with more people were more consistent while smaller groups had a chance of getting both very high and very low scores. This meant that for companies who do not want to take such a big risk, having groups with a larger number of people usually means it’s a safer bet.

The next logical phase that caught my attention would be the inclusion of auditions. When agencies will pick the more talented people from a pool. So I redid the simulation, this time running it with the idol talent values ranging from 50 – 100. The results were very much expected as the values of the groups all shot up.

The auditions also meant that the gap between the members and the final results were also marginally smaller.

Audition Verdict

As much as it is a no-brainer, auditions do have a big part to play.

Then it came to another can of worms. Every group always seem to have members that stand out and seem to receive all the attention. Be it a Serizawa, Amamiya or Saito, you will always see a member being more popular and the agencies putting slightly more attention on them.

So this time I decided to run another simulation testing the effect of placing priority on the more “talented” members of the group and giving less attention to those with a lower “talent” value.

The random numbers were ranked, but this time the attention values were slightly changed. This was how the numbers were chosen

1. As all groups are odd-numbered, the middle ranked person will have the same attention value from before
2. The highest person will get around twice as much attention from the middle person.
3. Everyone below the middle person will get half the attention value
4. The remaining attention is then split equally among the members between the first and middle.

The simulations were run again and these were the results.

The general average value per group went up from all different group sizes, but the interesting result was that larger groups were now doing better on average than the smaller groups. As they also had a smaller deviation in their results, larger groups were performing better and more consistently with this method.

This would suggest that idol groups with more than 5 people generally would perform better, provided you placed priority over your more “talented” members.

However what this also creates is a larger disparity within the group. The disparity is calculated using the member with the highest value divided by the members with the smallest value. The values returned generally did not follow a general trend and were very random. However, you can see that by prioritizing certain members, the disparity level becomes significantly higher. This can also explain why we seem to only remember a few faces from a group that we are not familiar with.

Conclusion

Larger groups do seem to perform better provided the right tactics are held in place. This seems to hold true even if they receive the same amount of resources as groups with fewer members.

Another advantage large groups have will be a larger pool of talent to choose from and focus more on the “talented” members in order to generate the maximum amount of value possible from a group.

If you have any suggestions on how to improve this or you want to let me know where I went wrong you can just send me a tweet to @SrippiP .