Topic: Time for group skill checks: problem

[Aotrs Commander]

Check my maths here, guys...

I was looking at the rules for skills in School of Hard Knocks, specifically the "time taken to use group skills" (in section 2:2).

This is listed as being the time taken for a single person to do the task, divided by

 (Max +1 -N) x N ÷ Max

where Max is the maximum number of people that COULD work on the task and N is the number of people actually working on the task.

Problem.

A task has a maximum of four people to work on it, so Max = 4. If I calculate it with all the values of N (4 through 1)...

(4+1-4) × 4 ÷ 4    => (1) × 4 ÷ 4    => 4 ÷ 4 = 1
(4+1-3) × 3 ÷ 4    => (2) × 3 ÷ 4    => 6 ÷ 4 = 1.5 (This is the example used in the rules, so this is apparently what they meant.)
(4+1-2) × 2 ÷ 4    => (3) × 2 ÷ 4    => 6 ÷ 4 = 1.5
(4+1-1) × 1 ÷ 4    => (4) × 1 ÷ 4    => 4 ÷ 4 = 1

And that, clearly, ain't right.

I suspect either there's an error in the formula... Or it's just bovine excrement.

Mathmatically more clearly, given the sequence, the formula probably ought to have been written

[(Max +1 -N) x N] ÷ Max

Or they did not mean that at all.

Maybe it should have been
(Max +1 -N) x (N ÷ Max)

(4+1-4) × (4/4)    => (1) × 1 = 1
(4+1-3) × (3/4)    => (2) × 0.75 = 1.5
(4+1-2) × (2/4)    => (3) × 0.5 = 1.5
(4+1-1) × (1/4)    => (4) × 0.25 = 1

Huh. Nope, that makes no difference (obviously, in hindsight, now I've written it out): still wrong.


Any ideas...?

[jdale]

The intent of the rule is that the maximum number of people is sort of helpful but they are also getting in each other's way. The optimal number is half that. It's more obvious if you use a higher Max, e.g. Max of 10:

(Max+1-N)	N (number of people)	Max number	Speed (higher is faster)
10	1	10	1
9	2	10	1.8
8	3	10	2.4
7	4	10	2.8
6	5	10	3
5	6	10	3
4	7	10	2.8
3	8	10	2.4
2	9	10	1.8
1	10	10	1

[OLF, i.e. Olf Le Fol]

(Max +1 -N) x N ÷ Max
...
[(Max +1 -N) x N] ÷ Max
...
(Max +1 -N) x (N ÷ Max)

These three formulae are completely and absolutely equivalent, considering the precedence of multiplication and division. What did you expect by merely adding parentheses?

[Aotrs Commander]

The intent of the rule is that the maximum number of people is sort of helpful but they are also getting in each other's way. The optimal number is half that. It's more obvious if you use a higher Max, e.g. Max of 10:

(Max+1-N)	N (number of people)	Max number	Speed (higher is faster)
10	1	10	1
9	2	10	1.8
8	3	10	2.4
7	4	10	2.8
6	5	10	3
5	6	10	3
4	7	10	2.8
3	8	10	2.4
2	9	10	1.8
1	10	10	1

Ah.

Right. Yes, that makes more sense now that I can see it's supposed to be a curve, not a straight line. (Would have helped if they'd have given a better example than they did.

Could have been better explained, I think, maybe, for those cases where you have essentially unlimited work space as for the example I was working out my head, where you'd have multiple people working at a task multiple terminals or something, where you'd essentially have to set max at 2 x number of people or something if you didn't know precisely what Max would be. (Setting Max could be a bit of an art in some cases.)

(Max +1 -N) x N ÷ Max
...
[(Max +1 -N) x N] ÷ Max
...
(Max +1 -N) x (N ÷ Max)

These three formulae are completely and absolutely equivalent, considering the precedence of multiplication and division. What did you expect by merely adding parentheses?

NJust a bit of a brain fart combined with not understanding what the formula was supposed to be doing. (Wasn't thinking with my pencil enough.)

[jdale]

It wasn't clear to me until I ran the numbers and then reread the text with them in mind. If I was writing a rule from scratch, I would probably base it on the optimal number with the assumption that at some point you just say "would you guys just get out of our way so we can work?" That would be more intuitive.

Then use a formula like N - 3*((N-1)/Optimal)
For an optimal number of 2 that yields 1 or 1.5.
For an optimal number of 5, that yields 1, 1.8, 2.6, 3.4, 4.2.
For an optimal number of 10, that yields 1.9, 2.8, 3.7, 4.6, 5.5, 6.4, 7.3, 8.2, 9.1

And if there is effectively no limit on how many people can help, then the result is essentially just N, which is fairly intuitive.