I've been wondering whether it's worth upgrading my 6-star crafting managers to 7-star or not. Here's some maths around that, along with some maths around purchasing new slots vs new managers. I break it down like this because I see two scenarios: you're either deciding to upgrade a manager, or you're choosing between a new manager slot/manager or a better manager.

When should I upgrade a manager?

Scenario:
You already at least 4 managers, and you're trying to decide if you're better off upgrading one or keeping all 4.

How to do it:

A good purchase has a cost less than the performance, where these are:
Performance = [manager improvement for n-star]
cost = 3*[manager improvement for (n-1)-star]
a "good purchase" has:
[manager improvement for n-star] > 3* [manager improvement for (n-1)-star]

Base improvement of each manager:

Global multipliers (e.g. due to station/room upgrades) can be factored out, so we only need to look at the base improvement for each manager. Note that total manager improvement is 1 + x, where x is the value in table below.

Manager Type	3-star	4-star	5-star	6-star	7-star
Crafting & Smelting	0.05	0.1	0.2	0.4	0.7
Mining	0.05	0.1	0.2	0.3	0.5
Cargo & Speed	0.1	0.2	0.4	0.6	1

Example calculation

• Is it better to upgrade my 6-star crafting managers to a 7-star manager?
  • Using the table, cost = 3*0.4 = 1.2
  • performance = 0.7
  • Cost > Performance, so my ability to craft will be reduced

Comments

• Using "junk managers" for upgrades
  • The example calculation I used was for turning 4 managers of one type into a new manager. In this case, upgrades after 5-star are always a loss is crafting/mining/cargo ability. If you have a manager with primary and secondary cargo, this is "junk" when you need a smelting manager. To account for this, you can adjust the "cost".
    • e.g. in the example calc, the cost becomes 2*0.4 if you have 1 junk manager, 1*0.4 if you have 2 junk managers, and 0 if you have 3 junk managers
• Leaders
  • Leaders improve your manager by a factor of 2,3,or 4
  • If you can "easily" unlock the leader perk and the upgraded manager is the leader, then performance is always greater than cost. i.e. 2* (manager improvement for n-star) >= 3* (manager improvement for (n-1)-star) for all managers. In this case, it is always better to upgrade your manager
• Manager Slots
  • if you have fewer managers than slots, you may be better off having the mining boost from multiple "primary manager bonus" than a single primary manager bonus.

When should I buy a manager slot?

Scenario:

Your manager slots are full and you're deciding whether to purchase a new manager slot and manager, or whether you should purchase more managers to upgrade your existing managers.

Assumptions:

• Brilliant Academy recruits are the best value, so I'll assume you're only purchasing those.
• For simple maths, I'll assume that this only gives 4-star managers and that at a minimum you have 4-star managers
• if you have less than 4-star managers, you should probs be buying brilliant academy managers more than anything

How to compare:

We need to use "return on investment" as a metric this time.
Cost = credits used
improvement = [new manager multiplier] - [old manager multiplier]
Return on investment = ROI = improvement /Cost

• option 1: purchase a slot and a manager
  • Cost = Slot cost + 500 credits
  • Improvement = 4-star manager improvement - 0
  • ROI = improvement/cost
• Option 2: purchase more managers
  • cost = 500*3^NumberOfLevels
    • e.g. promoting a 4-star to a 5-star has Number of levels = 1, cost = 500*3^1= 1500
    • e.g. promoting a 4-star to a 6-star has NumberOfLevels = 2, cost = 500*3^2 = 4500
    • e.g. promoting a 4-start to a 7-star has NumberOfLevels = 3, cost = 500*3^3 = 13'500
  • improvement
    • Use the table, I don't see an obvious formula.
    • e.g. 4-star crafting to 5-star crafting has an improvement of 0.2 - 0.1 = 0.1
  • ROI = improvement/cost
• Choose the option with the largest ROI

Example calc

Do I unlock the 17th manager slot and a new manager, or do I upgrade an existing 4-star crafting manager?

• Option 1: purchase a slot and a manager
  • Cost = 800 + 500 = 1300 credits
  • Improvement = 0.1 (I'm assuming it doesn't matter what manager you get)
  • ROI = 0.1/1300
• Option 2: upgrade manager
  • cost = 500*3^NumberOfLevels = 500*3^1 = 1500 credits
  • improvement = 0.2 - 0.1 = 0.1
  • ROI = 0.1/1500

If you don't care what type of new manager you get, you're better off getting the 17th slot

Comments:

• Slot price increases.
  • If you don't care what manager you get, this stops being the cheapest method at around slot 21.
• The "slot method" relies on luck
  • If you want to improve your crafting speed, there's no guarantee that you'll purchase a crafting manager. Hence, the cost for a desired manager is higher.
  • Assuming each manager type (there are 5) is equally likely, the expected cost for a given manager type is 5*500 = 2500 credits. So, if you have a desired manager type, the worst-case cost is: cost = 5*500*3^NumberOfLevels