There's only 1 cylinder affected so I wouldn't think the TPS would be likely. Given the super rich condition I would suspect a bit of detritus in the one injector, not allowing it to fully close. Also see the cam pulley issue as less likely due to the engine running well once the throttle is opened somewhat.

After a look at any info you could glean from Protune, you could disconnect the battery to reset the adaptive fuel maps and see how that changes things. If no change then its not likely a software fault, but rather hardware related. The injectors are easy enough to remove and inspect/test.

Last edited by Bitsobrits; 20/05/21 12:11 AM.

Steve
Late 2012 M3W