There are 2 types of biases. First is the "trigger-bias" which come aroud the thereshold when one called for the specific type of trigger . The other is the "anti-bias" you get calling off the specific type of trigger. In run 13 large amount of statistics are belongs to BHT1 and BHT3 triggers. At the same time both triggers has considerable amount of events which overlap with JP2 trigger.  So even if one specifically doesnot call for the paticular tigger "trigger-biases" will be always there.
In the case of BHT1 trigger efect of "trigger bias" is much worse than "effect of "anti-bias". 

As a example I called only for JP2->Fire()  (left ) and   JP2->Fire() && !BHTi->Fire() (right) ,  below shows the E/P in momentum slices.

Eventhogh NOT including HT triggers gives stable E/P we doesnot necessarialy want to use sample with no HT triggers. One reason it will reduce our statistics. What we can do is minimize the effect of trigger bias. As you can see since the BHT1 has considerably low thereshold than BHT3 if including BHT1 causes for trigger bias even at low momentum. So it is good to opt out low triggers and keep BHT3.  

Best kind of option is  the following. We could call this as a "minimum-bias" sample.

(!BHT2 && !BHT1 && !BHT0)

E/P mean-fit for (!BHT2 && !BHT1 && !BHT0) , (click here)

if we doesnot call for BHT3 our sample consist with events which fired JP2 trigger  plus JP2 overlap with BHT3 events. But once we calls for BHT3 trigger such as (BHT3 && !BHT2 && !BHT1 && !BHT0) the "trigger-bias" from BHT3 will be more visible than before because there are more BHT3 only triggered events than BHT3 overlap with JP2 events.  Nevertheless both option can use with a momentum cut just below the thershold value.

Here's the comaprison between  E/P vs momentum slices for  2 trigger options,

Same distribution in ring-by ring shows need of an low momentum cur for very forward eta. (outtermost 2 eta)

one could suggest that momentum cut = 3.0 will be a good thereshold. (if you go further you will loose statistics also). Looking in to ring-ID 1, 2,39 E/P start to be stable above 3.0 . 

E/P Vs P in momentum slices for ring by ring , (click here)

1) "biased" trigger options 

2) "minimum-biased" trigger option

3) "unbiased"- trigger option