The ZxH/ZxR rates actually seem to be based not on BAR but on PEBAR rates, which are not always the same. (I think PE stands for Price Engine.)

For example, consider a “wonderful” room at W Dallas, from 1/29 until 2/1. The available rates are

• DAILY21: $179 (nonrefundable)
• DAILY0: $179 (nonrefundable)
• DAILYW: $219 (nonrefundable, includes parking)
• BAR8: $249 (refundable until 6PM on 1/28, the day before checkin)

but if you use the Z3H promotion, your (nonrefundable) rate for the first two days is a PEBAR8 rate of $219; this works out to an average rate of $146 over the three nights.

Or consider a “spectacular” king room at W Fort Lauderdale on the same dates. The non-promotional rates are

• DAILY21: $398.10 (nonrefundable)
• DAILY0: $442.33 (nonrefundable)
• BAR4: $469.00 (refundable until 6PM on 1/26, 3 days before checkin)

but the (nonrefundable) Z3R promotional rate is based on a PEBAR4 rate of $489.00 for the first two days (which works out to $326 on average).