1: Good ability power
2: Good health
This item is essential when playing rumble.

1: Tenacity is a hugely valuable trait to any champion.
2: The magic resist helps mitigate early game magic damage.
3: The tenacity combined with rumble's Scrap shield make for an easy getaway in most situations.

1: As Rumble is a melee caster i found surviving team fights can be difficult unless you pull off at the right moment if not however and you become stuck amongst enemies Zhonya's allows for you to survive and lets your team do damage whilst the enemy team takes time to react.
2: Placing down The Equalizer and then having to use zhonya's allows for you to deal damage whilst not doing anything ( the amount of kills i have picked up doing this is astonishing )

1: There are no good ability power plus health items after Rylai's, so this is a good option to help in survival and combined with the armor and magic resist picked up in other items it can only make rumble stronger in team fights.

1: After Mercury Treads there are no great items that synergize with rumble nicely for magic resist except AByssal Sceptre.
2: Gives both ability power and magic resist both of which rumble needs.

1: Essential for any AP champion.
2: Makes rumble a huge threat, especially in team fights with his area of effect abilities.