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Okay, I saw that you prefer to change 4th level staff members when they reach to 20k USD salaries.
Do you have a preference regarding 3rd and 5th level staff members?

Do this:
1) decide what's a reasonable holding time (you need this because there are fixed costs and variable costs involved). Lat's say 28 weeks (2 seasons)
2) assume you will have fired you current coach on a Sunday so you won't have to pay his salary on monday and you will only pay 2k severance to the minimal coach who will automatically replace him
3) Count like this: 2k+Signing Fee+Salary*((growth factor-1)^(28))/((growth factor-1)). The growth factor is (1.01+0.0025*([COACH LEVEL]-1)). This is what you will pay in total for the trainer over 28 weeks.

If you do this you should be able to compare different options.

Example:
Which one is better over 28 weeks? (A) Lvl 6 coach with 20k salary and 1.7 million signing fee or (B) a Lvl 6 coach with 85k salary and 1k signing fee?
(A) Total cost: 2k+1,700k+20k*((1.0225^28)/(1.0225-1))=2.47 million
(B) Total cost: 2k+1k+85k*((1.0225^28)/(1.0225-1))=3.27 million
So over 28 weeks (A) will be about 500k cheaper than (B), IF you hold both coaches for the whole period.

However if you think you can replace (B) every week, by firing the old trainer Friday-Sunday and buying an equivalent lvl 6 trainer Monday to Thursday (before training update) you will spend this:
(B') Total cost: 2k*28 (severance to minimal trainer every week)+1k*28 (hiring fee for new lvl 6 trainer every week) +85k*28 (severance fee to lvl 6 trainer every week)=2.46 million. So (B') is actually cheaper than (A).

Making sense? You can work out the actual numbers for any kind of level based on what you see people doing on the Staff market.


Last edited by Lemonshine at 2/15/2017 12:43:29 PM

Firstly, thanks for the detailed answer.

Yes your calculations make sense in terms of cost comparisons of coaches.
But the thing I was wondering was the ideal time of change for specific levels of coaches. I thought about it but I came to the solution of no maths can calculate the exact optimal time for that, so I was wondering personal experiences and points of views on that. Anyway I've already decided on some salaries to consider changing staff members.

3rd level: 16k USD
4th level: 25k USD
5th level: 42k USD

Probably they should be lower but I don't want to waste much time on staff changing.

Plus if I were the game developer, I'd remove the salary increase of staff members but anyway... :)

It depends on the type of coach.

Let's assume we're talking trainers. If you follow the logic of what I wrote you know you can spend 2k and keep rolling new staff every week (it's a pain, I know). I can guarantee you you can buy lvl4 19k salary for 1k signing fee. Therefore 2k+1k+19k=22k. If you're paying more than 22k you're probably better off rolling trainers. For Competent I think you can roll 9k trainers. For Superior you're probably looking at 45k-50k.

On this basis, for trainers I'd say:
lvl 3 = 13k
lvl 4 = 22k
lvl 5 = 48k

Trainers are more expensive than doctors or PR (lvl 5 in particular). So, as I said, I'd check what the lowest salary is that you'd be able to acquire for 1k signing fee. It surely makes no sense to pay higher than that value+3k, unless you value your time and you don't want to spend it looking for staff too frequently (in this case I think your numbers look good, for PRs I'd take 10% off and for doctors I'd use the same if they are Massage specialty and -5% to -10% otherwise)

Last edited by Lemonshine at 2/16/2017 11:32:17 AM

2) As a general question; when do you start to consider changing your staff members?

Edit: Some numbers

I suggest changing a staff when his current salary is greater than the weekly average of the total money that you will give him.

For example, suppose you got a level 5 trainer with $16,140 salary and a bid of $616,800.

After one week, his salary is $16,140 * 1.02 = $16,463. If you were to replace him after one week, the weekly average you will pay him is ($616,800 + $16,140 + $16,463) / 1 week = $649,403. You pay the current salary as severance fee. Since $16,463 < $649,403, you keep the staff.

After two weeks, his salary is $16,463 * 1.02 = $16,792. If you were to replace him after two weeks, the weekly average you will pay him is ($616,800 + $16,140 + $16,463 + $16,792) / 2 weeks = $333,097. Similarly, $16,792 < $333,097 so you keep the staff

Continuing this, we achieve the optimal holding time after 47 weeks. Here, his current salary will be $16,140 * (1.02)^47 = $40,936.58 while the average amount you will pay him is ($616,800 + $16,140 + $16,140*(1.02) + $16,140*(1.02)^2 + ... + $16,140*(1.02)^47)/ 47 weeks = $40,373.74. Now, his current salary $40,936.58 is greater than the average amount, so you may find another staff.

The idea for this rule is while the current salary is lower than the average, the average goes down per week which makes your staff more worth it. On the other hand, if the current salary is higher, then the average amount you pay him continuously goes up so the staff is not worth it anymore.

A better strategy is to allow changing your staff before the optimal holding time if you find another whose weekly average at the optimal holding time is less than the weekly average of your staff currently. But you need a lot of time constantly looking at the staff market so this may not be feasible.



Last edited by Greedy at 3/3/2017 11:11:20 AM

Resurfacing an old related post.

The calculation of the unique correct pair (how_much_should_I_bid_to_hire_this_guy, how_long_should_I_keep_him_after_hiring) can be found numerically for any desired amortized (i.e. average over time) weekly cost.

Essentially, if you decide how much you want to spend weekly on average and the level of the staff member, which is a natural starting point when looking to hire staff ("I want to be paying $10k/week on average"), there is a unique value of the bidding fee that you should pay and an associated optimal retention period after buying (independent of speciality, of staff type).

There are two pieces if anyone wants to implement this:

(1) Use the amortized cost formula mentioned above, i.e.

$$A(S,T,L) = \frac{h}{T} + \frac{S}{T} \cdot \frac{(1+g(L))^{T+1}-1}{g(L)}$$

where:

- $S$ = Starting salary
- $T$ = Duration (weeks)
- $L$ = staff level (1-7)
- $g(L)$ = Weekly Fractional Growth: 0.01 + (L-1) \times 0.0025
- $h$ = Hiring cost

We are trying to find optimal values for (T, h).

Note that the optimal retention time T_opt can be inferred for a given (S, L, h) by simply checking numerically what is the integer value of T between [1, 100] that minimizes A(S, T, L, h). Let's denote the associated optimal amortized cost A_opt(S, L, h). The remaining task is to invert this relation and solve for h.

(2) Choose the level L of staff that you want to buy. Choose an array of reasonable starting salaries S for that level e.g. for level 4 it might be [$7000, $7100, ..., $10900, $11000]. Now use bisection search to find the hiring fee that leads to the desired A_opt.

Some preliminary results below (sorry, I don't know how to format tables here - you can load it in a CSV ->Spreadsheet). First column has the starting salary.

How to read these tables: If you want to be spend on average no more than $11000/week on a level 4 staff, and you see an available level 4 in the market with starting salary $8000, do not bid more than $20000 (rounding from the table value of $19506). If you pay $20000, then you should keep him for 18 weeks. (If you end up paying less, you should keep him a little less.)

Level 4 Bidding price:
Salary,$9000/week,$10000/week,$11000/week,$12000/week,$13000/week,$14000/week
7000,7097,24170,47035,75145,108071,145387
7500,,12981,31853,55968,84900,118253
8000,,4354,19506,39901,65084,94778
8500,,,9628,26548,48255,74413
9000,,,1976,15573,33987,56852
9500,,,,6762,22036,41792
10000,,,,,12189,28987
10500,,,,,4201,18195
11000,,,,,,9201

Level 4 Retention Duration (Weeks):
Salary,$9000/week,$10000/week,$11000/week,$12000/week,$13000/week,$14000/week
7000,14,20,26,31,35,39
7500,,16,22,27,31,35
8000,,12,18,23,27,32
8500,,,14,19,24,28
9000,,,11,16,21,25
9500,,,,13,18,22
10000,,,,,15,19
10500,,,,,12,16
11000,,,,,,13




Last edited by Maatsaas at 7/31/2025 2:22:23 AM