the Mechanized Menace
ARAM: Mayhem240
Augments
27
Good fits
75
Marked down
kpm.gg's letter for every ARAM: Mayhem augment on Rumble, from S (take it) to D (skip it). The list is hand-made by Team KPM and read again every patch: these are letters, not win rates.
72 augments
Best picks for Rumble
Infinite Recursion
SGain 60 ability haste, increased by 3 each time you score a champion takedown.
Eureka
SGain ability haste equal to 30% AP.
Jeweled Gauntlet
SYour abilities can now critically strike for (145% + bonus critical strike damage) damage. Additionally, gain 25% (+ 4.5% per 100 AP) critical strike chance.
100 augments
Best picks for Rumble
Recursion
SGrants 60 ability haste.
Warlock Juicebox
SGain 10% (+ 3% per 100 AP) omnivamp.
BEES!!!
SHitting an enemy champion with an ability causes you to toss a beehive at them over 1.1 seconds, which upon arrival explodes in a 425 radius to swarm enemy champions hit with bees for 2 seconds (15 to 10 (based on level) second cooldown).
68 augments
Best picks for Rumble
Escape Plan
SUpon dropping below 35% maximum health, gain a shield for 65% of your maximum health for 5.5 seconds, during which you also gain 150% bonus movement speed and have reduced size (75 second cooldown). The shield and bonus movement speed decay over the duration.
Lonely Warrior
AFor each enemy champion within 600 units of you, gain 15% bonus attack speed and 10 bonus armor and bonus magic resistance.
ADAPt
AConvert all of your bonus attack damage into ability power at a rate of 1 ability power per 0.6 bonus attack damage. Additionally, increase your ability power by 15%.

The kpm.gg desktop app puts these letters on your augment cards the moment the game offers them, for the champion you are playing.
For items and skill order, see the Rumble ARAM build: ARAM: Mayhem is played on the same map with the same items.
What each augment does: League of Legends Wiki.