Skill pile-up in GURPS

Abstract (if you don't like long blog posts)

In this post, I explore the resolution of tasks when performed by more than one character. I focus on a searching task that must be completed within a given time frame, and seeking an object that is assumed to be there. I wrote this to help me prepare for an upcoming challenge that may happen in the Palantir quest. It is also usable in the more general case where multiple testing overestimates the odds of success when too many people are trying to do the same thing

• Observation: More people added to an already crowded kitchen doesn't result in a better meal.  
• Cause: There is a cognitive and communication-based overhead to the division of a task.
• Leadership: A leader overcomes this cognitive/communication overhead
• Conclusion : A successful leadership manages the division of a task to overcome this overhead.
• Conclusion : Leading all but one worker into a set of complementary supporting tasks brings the highest possible payoff, but is also the most sensitive to incompetence of the lousiest team members (and leaders).  

Scenario

The orcs have broken through the outter defenses. There is not a lot of time to spare! The scriptorium contains one key document that must not fall in the hands of the enemy. Unfortunately, the scriptorium was vandalized by fleeing dwarves in the past week: the whole place is a mess. Six dwarves with Research-12 are tasked to find this document within the hour. This task is considered to be hard (-4), because of the disorder caused by vandalism.  All six dwarves head for a set of shelves, however, the mess on the floor is such that something could easily be missed. One of the dwarf takes charge: Dwarf Bob will be scanning the most promising scroll cases that the other four will pre-screen from the shelves. 

"GM, what is this task's difficulty? Come on, we're six working together... cakewalk right? Why don't we just all roll and see if one of us gets a success?" 

Two dwarves walk into a scriptorium...

The simplest team is a team of two. Let's look at how to resolve this scenario for a pair of dwarves.

Case 1 : Independent attempts

The most simple case is where two dwarves enter the room and start searching independently. This may not be an optimal strategy, but we need to discuss it anyway here. Both dwarves will have a target number of 8. This means that each has 25% chance of success, and the chance of having at least one dwarf succeed is 43% .

That one fails doesn't influence the odds for the other dwarf. This is not as self-evident had Dwarf A had Research-20 and Dwarf B, Research-12. It would be tempting to say that if the really good one failed already, the odds should be worst for the second dwarf. However, unless the first dwarf makes an even worst mess (or tidy thing up) while searching, the difficulty level should be unchanged.

One last note, I don't think that a second check by one character should be allowed in the event of a failure. The margin of failure may be used to determine at which difficulty level the check would succeed, and how much time must be added to the search before it matched this difficulty level. After all, given infinite time, something that is there will be found.

Case 2 : Complementary attempts

Let's consider an alternative where the scriptorium is large and the search task can be trivially shared. The task difficulty needs to be adjusted for each dwarf to reflect that less volume needs to be searched in the same amount of time. A hard (-4) task may be downgraded to very unfavorable (-3). Individual odds are now based on a target score of 9. This means an individual probability of 37% and an overall probability of success 67%.

There is a snag in this model. It doesn't really makes sense if both dwarves succeed since there is only one thing to find. The check with the highest margin may be selected as the truly successful one, and the other simply assumed to have positively determined that the object is not there.

Had the dwarves decided to take the same amount of time to cross-check each other's work, the complementary attempts process would repeat itself, unchanged if the scriptorium remains unchanged. The odds of finding the target object jumps to about 90%. This higher probability really comes down to the fact that the total time searching in this room is multiplied by 2.

Case 3 : Supporting attempts

A compelling case is that where one of the dwarf does the research, and the other dwarf acts as a support. This has the advantage that the support dwarf may be using another skill than research if it makes sense. The GM must make the call to determine whether a supporting dwarf automatically alters the difficulty level of a check. An example where no check is needed is when Dwarf B simply fetches and put back piles of scrolls for Dwarf A to examine (making the task very unfavourable -3 or -2). Alternatively, Dwarf B may be using his research skills to identify the most promising sections for Dwarf A to search. The alternative option may alter the target score for Dwarf A based on the check's margin, and capped at +/- 5. The potential effect should be higher, but coming with a risk that the supporting dwarf makes life harder for Dwarf A.  The cap, if used at all, should be such that a supported skill check potentially benefit the most from this strategy.  

The cases where n dwarves walk into a scriptorium

I'm a computer scientist. My favorite question starts with: "What if an infinite number of...". So...

What if an infinite number of dwarves walk into the scriptorium. Let's say, more practiacally, as many dwarves as there are scrolls in the room. If each dwarf checks one distinct scroll, then the target scroll is sure to be found. The problem is no longer a matter of whether each dwarf are good at research, but whether whoever lead the operation can competently coordinates all of the dwarves to do this silly task. 

Case 1 : Independent attempts (no leader)

Here n dwarves are essentially competing for space and resources. This is an uninteresting possibility: the task difficulty should reflect the clutter and chaos of having n people stepping on each other's toes. GM's call. GMs of the world, go to town with a stiff penalty, this is not a search party, it's a n-dimensional posse.

Case 2 : Complementary attempts (with leader)

This case is interesting and crops up a lot in adventuring parties. Figuring out how to split a task in n parts becomes increasingly a matter of leadership than researching skills. First, assuming a perfect leadership, we first need to determine the difficulty level of the task is divided into n parts. 

In absence of an explicit leader, two people can work together without penalty. Three to five at -2 (very unfavourable), 5-10 at -4 (Hard), 10-20 at -6 (very hard), 20+ at -10 (impossible). This should be task-independent and based on the limitations of people's ability to coordinate. For example, 6 dwarves trying to split the search spontaneously would make an unfavorable task (-1) into a Hard one (-5): the odds of missing something altogether gets large when each dwarf thinks that someone else has already looked there. 

A leader can lead a lot of people, and this number is task-dependent. The limit on the number of truly complementary "moving parts" is, however, task-independent. This is why squads were of size 8, and contemporary sections are made of three fire teams of two soldiers. The margin of a leadership check should be used to offset the penalty incurred by the division of a task into complementary ones. A GM should decide on a bonus cap that makes sense. To pick up on the previous example, if one of the dwarf decides to act as a leader, he will be able to apply his margin against the -5 (hard penalty of having 5 people trying to complement each other). A failure makes things worst as some parts of the scriptorium will be overlooked while other are checked more than once. It makes sense that a leader should first succeed a check in the skill required to analyse the task, at average difficulty (+0), in order to be able to use his/her leadership. It makes no sense to have someone coordinating a task that he/she cannot understand.  

Case 3 : Supporting attempts

Here, we are entering a dangerous territory. One researcher and n-1 support dwarves. What can possibly go wrong? The leader here can be the researcher, or a third party. The challenge is to coordinate a set of n-1 complementary supporting tasks. There is both a potential for benefit and for disaster. In order to keep things simple, it make sense to treat the sum of all margins of the supports checks, minus the penalty for the number of complementary tasks, plus the leadership's margin. This has the consequence of yielding the largest boost to the ultimate research check if the supporting staff is competent, and under a good leadership. I can see that such benefit should be capped by the margin of the leadership roll. For example, if the Leadership check succeeds by +4, the most benefit from collaboration will be +4. If the leadership check fails by 2, the check has no mininum but cannot be any larger than -2.

Conclusion

I plan to playtest this approach whenever the occasion arises. It took a while to think about it, but not really to use around the table. I like methods that leaves most of the decision as hand waving to the GM. I love the use of the narrative terms average, unfavorable, hard, very hard, impossible to make quick calls. I hope that if you made it this far into the post, that it helped you think about this fairly common problems in RPGs. Maybe even to come up with better, more elegant solutions.