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Completing the ToB Collection Log
To complete the ToB collection log in an efficient matter is a lot more straight forward. There are 4 sets of items to consider.
Pet: Flat Rate based on kill count (1/650 or 1/500 from reg/hmt & drops significantly beyond 2 deaths.
Purples: Based on team size & mvp
HMT Kits: Based on hardmode ToB kill count, scales based on deaths
Capes: Flat Kill count.
The goal would be to complete ToB with the 2k cape and having all purples, pet & kits prior.
Simulation for trio regular ToBs till 7/7 purples completion
mean kill count in terms of X/7 Completion Rate
As such: Expected 7/7 purple completion is: 28.5 purples
Efficient Path to Completion
The most efficient path to complete Theatre of blood would be as follows:
1- duo or trio regular tob until 7/7 Purples
2- Hardmode ToB completion as soon as you possibly have the skill set (344 avg hmt completion)
Note: HMT should only be done in 4-5 mans for faster completions
3- 4-5 man regular ToB till 2k cape
-Note: Pet should be 0-time via completions, no need to factor it in
If you are only missing pet, 5man hmt is the best way to receive one
Note: Make sure you have mastered the raid prior to touching HardMode ToB, its the hardest raid in the game, so ensure you have mastered all high level strategies prior to touching it. There is a good guide on Youtube by "Help Me RNG" that explains hmt in detail.
This table shows why it's important to focus on 2-3 mans for purples due to the slim chance you go dry.
S/O Ranger Fain for going 2893 (300 hmt) kc for Scythe & then going 800 HMT for Sanguine Kit
Driest Ironman for Scythe that I know
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Proof
Expected GP per Purple at ToB
HMT has a reduced chance for an avernic, but higher chance for other purple type. However, given the expensive price of avernic, it doesn't increase the gp per purple rate by much.
Likewise, one thing to note about hmt: the purple rate is better, but its significantly affected by deaths,
As such, it's safe to assume, for a vast majority of players:
GP per Raid Calculation based on team size & Raid Type
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GP per Hour for each Raid Type & Scale
In this table, you can see the GP/H on the right in (millions). As expected the gp/h drops significantly on team size due to the chance of seeing the purple remaining the same but having to be split between more players.
This is assumed based on the total raid time which includes downtime. This assumption is somewhat reasonable for an average good team, however it can definitely be pushed faster by gamer teams.
You may ask why this is relevent? We can use this data to compare the GP earned from each scale going for 2k ToB cape.
Profit per Timee Spent at ToB
If we do the same exercise as ToA, We can assume 5man ToB as the fastest way to get completion, but compare the time saved from doing 5mans to other scales in terms of potential additional GP profit per hour saved.
For instance, if you did 4man regular ToB instead of 5 mans. You would only lose around 33.3 hours of time, but gain a total of 938M additional GP on average. This results in an effective gp/h of 28.2M gp/h.
As such, if you value your time beyond 28.2m gp/h, you should avoid 5man tobs.
This exercise was only performed for 5 man. You could compare 4man to trios & so on for yourself and/or adjust the raid completion times according to your own personal skill/comfort.
Please Remember, in no way should this data be taken seriously. Do what you prefer/enjoy
In my case when I did 2K ToB grind, i did a lot of 5 man HMT beyond completion because i found them much more enjoyble then regular ToB.