So I have been thinking about how to get the total/actual threat reduced from Hand of Salvation.
Let's go back to the earlier equations:
Threat done with HoSalv:
Threat without HoSalv:
(0.98 - 0.98^11)
Threat = (0.98^10)*AT + TPS * ----------------
(1 - 0.98)
Threat = 0.817073*AT + 8.96343*TPS
To get the threat reduced, we simply subtract them:
Threat = AT + TPS*10
So the total threat reduced is 18.2927% of your initial threat plus 1.03657 times your TPS during HoS. Taking into consideration the threat generated during HoS occurs over 10 seconds, that means you basically get the two components of HoS threat reduction to be:
Threat_without_HoS - Threat_with_HoS
AT + 10*TPS - 0.817073*AT - 8.96343*TPS
0.182927*AT + 1.03657*TPS
Actual_Threat_Reduction = 18.2927%*Initial_Threat + 10.3657%*Threat_Generated_During_HoS
Take caution in this. While you do indeed reduce your initial threat by 18.2927%, the 10.3657% of your threat generated during HoS assumes a constant TPS during the 10 second period, so it is approximate.