BuzzerBeater Forums

Help - English > Good Time to Change Staff Members?

Good Time to Change Staff Members?

Set priority
Show messages by
This Post:
22
284776.9 in reply to 284776.1
Date: 3/2/2017 4:16:41 AM
Manila Bombers
PPL
Overall Posts Rated:
217217
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

This Post:
22
284776.11 in reply to 284776.10
Date: 7/31/2025 2:21:57 AM
Asingratitos BC
III.1
Overall Posts Rated:
1717
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