WoW Mathematics: Scavenging for Resources

Garrison missions are a great way to earn Garrison Resources, of which rewards may be further boosted by assigning followers with the Scavenger trait. Unfortunately, followers with Scavenger may not also have the required counters for the mission, and so a question arises: maximise the success chance of the mission, or boost the potential rewards up for grabs?

This commander has received the mission Out of His Element, which offers 48 Garrison Resources as a reward. He or she has the choice of assigning Auriel Brightsong, whom has a needed Group Damage counter for a 100% success chance, and Greatmother Geyah, whom has Scavenger, adding a further 200% Garrison Resources for a successful mission. Whom should he or she assign?

Treasure awaits!

Summary:

• To maximise Garrison Resources over the long term, the commander should assign Greatmother Geyah to Out of His Element.
• The commander should choose the option which maximises the expected value of the reward. Both before and after the release of patch 6.1, this usually means assigning followers with Scavenger.
• The expected value E of the rewards from a mission offering Garrison Resources is the success chance of the mission p multiplied by the total reward on success R, or E = pR .
• More generally, the commander should not take the risk for Out of His Element if the success chance is below 34% pre-6.1 or below 50% post-6.1.
• Between a rewards-boosted mission and a properly countered one, the break-even success chance p for the former is the Garrison Resources reward R* from the latter divided by that R from the former, or p = ^R*/_R . Below this, the long-term rewards are not worth the risk.

The given:

• The commander receives Out of His Element regularly and so is looking for maximum Garrison Resources over the long term.
• No followers are available who have both a Group Damage counter and Scavenger.

The detail: pre-6.1
To assign the best follower to the mission, the commander should compare expected values of the Garrison Resources rewards under Auriel Brightsong and under Greatmother Geyah. The expected value E for a p success chance of R Garrison Resources is:

E = pR

Pick me! I can counter Group Damage!

Under Auriel, the commander has a 100% chance of receiving 48 Garrison Resources, so:

E = pR
E = 1 × 48
E = 48 Garrison Resources

The commander can thus expect 48 Garrison Resources per mission over the long term.

Pick me! I am good at scavenging! Really!

Under the Greatmother, the commander has a 53% chance of receiving 144 Garrison Resources, so:

E = pR
E = 0.53 × 144
E = 76.32 Garrison Resources

The commander can thus expect 76.32 Garrison Resources per mission over the long term.

As the Greatmother offers a higher expected value, the commander should choose her.

More generally, how low can the success chance of a mission with boosted rewards go until it is mathematically not worth it to conduct? This point will be where the expected values of the two alternatives equal each other. If the Greatmother offers E = pR and Auriel offers E* = p*R*, then:

E = E*
pR = p*R*
p = p* × ^R*/_R

As p* always equals 100%:

p = ^R*/_R

For a pre-6.1 environment, the break-even probability p for Out of His Element is:

p = ^R*/_R
p = ⁴⁸/₁₄₄
p = ¹/₃ ~ 33.33%

Thus, before patch 6.1 is released, do not take the risk if the success chance is below 34%.

The detail: post-6.1
Among other changes, patch 6.1:

• Reduces the bonus Garrison Resources that Scavenger awards to 100%, from 200%.
• Increases the base Garrison Resources that some missions offer, although Out of His Element is not one of them.

Under these changes:

• Under Auriel, E = 1 × 48 = 48 Garrison Resources.
• Under the Greatmother, E = 0.53 × 96 = 50.88 Garrison Resources.

As the Greatmother still offers a higher expected value (even if only marginally), the commander should continue choosing her.

What is the break-even success chance post-6.1 then?

p = ^R*/_R
p = ⁴⁸/₉₆
p = ¹/₂ = 50%

Thus, after patch 6.1 is released, do not take the risk if the success chance is worse than a coin flip.

Bibliography

• Koebel, Adam (2015), Patch 6.1: New follower traits and reroll items, blog post, WoW Insider, viewed 22 February 2015, <http://wow.joystiq.com/2015/01/20/patch-6-1-new-follower-traits-and-reroll-items/>.