Rationalizing Rankings

Rationalizing Rankings

It’s been a long time since the last math based opinion piece. And with a slew of rankings incoming, my goal is to make sense of why and how much ranking cutoffs end up at the end of each event.

Why Rank?

Rank and increasing rank allows the player to acquire increasing number of copies of the ranking daemon, for higher limit break and higher levels. Acquiring daemons from events is one of the most reliable and budget friendly methods of acquiring newly released daemons. The alternative to ranking higher (assuming one wanted multiple copies of the daemon), would be to spend Limit Break Orb(s) on the daemon.

The base comparison ‘currency’ for this piece would be SE cost to acquire each additional copy of a daemon through ranking or orb use.

First, the alternative to ranking: Orbs

Each 5* Orb costs 4000 Challenge Points. And how much does that cost in terms of SE?

  • If you play competitive PvP and hit opponents for 10 points a battle, 1 orb costs approximately 4000 SE.
  • If you farm with an ‘awful’ setup gaining 20 points per battle at 100% win rate, 1 orb costs 2000 SE
  • If you farm with a ‘deadly’ setup gaining 25 points per battle at 90% win rate, 1 orb costs approximately 1755 SE

 

Next, ranks:

There are a total of 7 copies of the ranking daemon that a player can acquire. Ordering them from the highest to lowest availability:

  1. Total Rank 5000 – 1 copy
  2. First, Second Half 2500 – 1 copy each half
  3. Total Rank 1000 – additional 1 copy (on top of the Total Rank 5000)
  4. First, Second Half 400 – additional 1 copy (on top of each half 2500) for each half
  5. Total Rank 300 – additional 1 copy (on top of the 2 already given for Total Rank 1000)

 

The Argument

The very first copy of the ranking daemon cannot be compared in price to a limit break orb. After all, you need at least 1 copy of the daemon in order to spend limit break orbs on it. Fortunately, the TR 5k rank is relatively uncompetitive, and corresponds approximately to points gained from spending 100% of naturally generated SE on the event, plus a small premium. For each additional copy, however, it becomes the player’s choice as to whether to spend items to rank for the next copy of the daemon, or to spend orbs instead.

Rationally, this means that players would not choose to spend items to chase each rank beyond the alternative cost to acquire an additional copy, ie, the cost of a Limit Break Orb. There are clear fallacies and pitfalls in this argument. In the heat of a ranking battle, rationality does not necessarily apply. And there is the ‘sunk cost’ argument: if players have spent a significant number of items chasing after a certain rank, they are inclined to overspend in order to achieve their goal rather than cut losses and fail to achieve their goal and ‘waste’ the items already expended in getting so far. And Orbs are limited in supply: one can only acquire 1 orb a month, so spending multiple orbs every month on the ranking daemon would clearly be impossible. There is an opportunity cost to orbing the ranking daemon: not being able to orb a daemon where multiple copies cannot be as readily acquired, like Limited Jewel Summon or Jewel Summon daemons (unless bucket loads of invokers or actual Jewels are spent).

Because orbs are so precious, even if PvP farming is used and actual SE cost of acquiring an orb is 1755 to 2000 SE, for the purposes of this calculation I will assume the SE value of each orb to be 4000 SE.

 

SE costs for each ranking can be easily converted to event points:

Tower

Every SE spent on a regular stage is converted into 60 event points.

On the final stage of each chapter, there is a bonus to the conversion rate, the highest being the final chapter of the event. In this current event (2nd Anniversary (1)) the final stage provides a 44% bonus to points. 1 SE converts to 86.4 points. This is the rate I will use for conversion.

I assume no event helpers present in this calculation. Point helpers multiply the SE:Points conversion rate further.

 

Conquest

Each point of damage to the boss HP will be converted into points, with a small bonus for each additional event daemon acquired (will neglect this bonus for simplicity).

I will assume a SE to Points conversion rate where players are looping level 200, with 7 million HP, and do 1.5million damage each 18SE, thus spending 18+19+19+19+19=94 SE to acquire 7 million points. The rate is 1 SE : 74,468 points

Of course with more efficient teams, or with more copies of event helpers, much higher SE:points rates are achievable. Also to note that in conquest HP grows over 200 levels, the lower levels are much less efficient. But I shall keep things simple here without factoring in those calculations.

 

Putting all this together:

Rank SE expenditure Score (Tower) Score (Conquest)
TR 5k 14 days, 24 hours, 12SE per hour

14*24*12=4032

4032*86.4 = 348,365 4032*74,468 = 300 mil
FH/SH 2.5k Halve the TR 5k expenditure, add the SE cost of 1 orb

4032/2 + 4000 = 6016

519,782 448 mil
TR 1k Add FH and SH 2.5k expenditure, add the SE cost of 1 orb

6016*2 + 4000 = 16032

1,358,165 1,193 mil
FH/SH 400 Halve the TR1k expenditure, add the SE cost of 1 orb

16032/2 + 4000 = 12016

1,038,182 894 mil
TR 300 Add FH and SH 400 expenditure, add the SE cost of 1 orb

12016*2 + 4000 = 28032

2,421,965 2,087 mil

 

If you have been paying attention to rank cut offs, clearly this table is a good deal off on numerous aspects. There have been a lot of flaws in the comparison, and a lot of assumptions made:

 

  1. That the players value the ranking daemon as dearly as they would a limit break orb in terms of SE cost. There are players to whom the idea of spending orbs on event daemons is rejected in its entirety, in which case ranking becomes a simple matter of supply and demand.
  2. Players might disagree strongly with me about the SE value of each orb. To some players the orb is sacred, beyond any SE price. To others, they would literally value it at 1755 or 2000 SE, or however many SE it cost  to acquire it in the first place. Some might even value the orb at 25 mochi, which is what it sells for. [25 mochi can be approximated to 375 SE (1 mochi:15SE)].
  3. I assume that the event daemon is worth ranking for. Unvalued daemons generally are not worth spending additional items or orbs on. Non competitive events generally produce cut offs lower than these. However, even with objective (we try) reviews on event daemons, players do not necessarily base their judgement entirely based on strength or utility of the daemon. Players may value daemons for the occasion (like Anniversary), or art / artist / voice actor, or simple personal preference. Sometimes even non game related factors, like exam season, or a business trip make certain players skip certain events.
  4. At the very top end of the competition, the 6th and 7th copies of each ranking daemon is probably worth less than the 4th or 5th copy (where abilities are frequently locked as). Rationally, players would not spend 6 orbs on limit breaking a single daemon – at most 4, to get to MLB, beyond which no further benefit is achieved, other than for selling daemons for mochi, which is either a terrible idea (selling back to system for 25 mochi only) or a very long term investment (selling on auction house in 1+ year’s time. Certain copies of the ranking daemon might be worth much more than other copies as well, especially if powerful abilities are locked behind that copy, example Cindrella’s LB3 copy unlocking her skill damage boost caused the TR1k rank to explode.
  5. The value of each additional copy of the ranking daemon is not necessarily fixed. Players might value the orb more than the second or third copy of the daemon, but value the orb less than the 4th or higher copies of the daemon – hence decide to settle for LB2 and spend 2 orbs to MLB the daemon.
  6. The value of each additional orb to be spent might not be fixed. Players might value the first orb they spend on a ranking daemon at a certain cost, but subsequent orbs at greater cost, to reflect rising opportunity costs of spending multiple orbs on one daemon.
  7. The efficiency of conquest is much lower at the lower levels and free SE alone generally would not get the average player up to looping 200 even if they were fully SE efficient. I have also ignored the SE cost of searching and encountering each level of the conquest boss, this would otherwise be taken out of the SE normally generated. Teams may also be much much much more efficient than assumed. It is not unheard of that top players can kill the 200 in 2 or 3 hits rather than 5, without helpers.
  8. I have ignored the possible presence of helpers. Some helper daemons are traded not simply for their helper ability but for general use. Amanojaku [Valentine’s Day], Amor, Saigyo are examples of helper daemons that are popular, because they are of use in the teams. For those events a bulk of players traded or drew for them so the resulting ranking scores would be inflated further.
  9. I have assumed that ranking first and second halves are equally weighted. This is clearly not true, because helpers are tradeable on the second half of events, and total ranks also close simultaneously with the second half ranks so players would watch both ranks on that same cutoff. Second half ranks are generally higher than First Half ranks.
  10. The limit break attributed to an orb on a daemon cannot be sealed. In other words, the orbed copy cannot be sold other than to the system for a fixed 25 mochi. This may have effect on players’ desire or reluctance to spend orbs on event daemons.

 

Conclusion

While there are many flaws to looking at ranks and item expenditure like this, I think it rationalizes the alternative to spending heavily on events.  Past a certain item expenditure on ranking it might be a more rational decision to use a limit break orb instead.

 

How much do you value your Limit Break Orbs? How rational or otherwise do you think the player base is with regards to strategic and rational ranking?

 

 

 

Appendix:

Similar table, but with orb valued at 2000 SE instead

 

Rank SE expenditure Score (Tower) Score (Conquest)
TR 5k 14 days, 24 hours, 12SE per hour

14*24*12=4032

4032*86.4 = 348,365 4032*74,468 = 300 mil
FH/SH 2.5k Halve the TR 5k expenditure, add the SE cost of 1 orb

4032/2 + 2000 = 4016

346,982 299 mil
TR 1k Add FH and SH 2.5k expenditure, add the SE cost of 1 orb

4016*2 + 2000 = 10032

866,764 747 mil
FH/SH 400 Halve the TR1k expenditure, add the SE cost of 1 orb

10032/2 + 2000 = 7016

606,182 522 mil
TR 300 Add FH and SH 400 expenditure, add the SE cost of 1 orb

7016*2 + 2000 = 16032

1,385,185 1,193 mil

 

 

Last, but not least, DB wishes Mitama, Otogi and all the players a happy 2nd Anniversary.



8 thoughts on “Rationalizing Rankings”

  • I can safely say that only 5000 ppl will be happy at the end of the ranking. Granted some might rank in FH and not in SH or vice versa but that’s just splitting hairs….. 😉

  • Gotta say, the values seem quite close. However, would like to point out that in addition to the “sunk cost”, you might want to note there are some last min event point rushers. Personally, during the Anniversary (I), I almost missed Hibiki (Sunspear). I was sitting happily at ~1200rank, cause I just wanted a copy… And about 30 min before FH, I returned to find myself around rank 4000. Burnt 3 tonics (or is it 5) just to make it back to rank 2000. And finally, end FH, was at rank 2400+. Almost didn’t make it, For players who want to make use of this ranking suggestion, I’d suggest going a little bit further, aim for FH 400 if you want FH 2500, or you might find yourself just falling outside of the ranking needed. Cause other than “sunk cost”, its worst when you choose not to give up, but come back only to have failed.

    Still, Happy Anniversary everyone!

  • I think another aspect to participating in the rank events moreover would also to increase one’s level and it’s a quicker way to obtain multiple copies of a daemon, the tower events are also another great way to obtain a large number of magatama. While you could go for a limit break orb, you’re limited to only getting 1 a month and you gain no EXP when participating in PvP and you receive no magatama.

  • I promised to rank someone in this event that I appreciate so I will go with everything, although it will be very bloody, thanks for the post Aki, and happy anniversary to all.

  • Haopy anniversary~

    Hopefully this article benefits some ppl. Meanwhile i belong to the group Orb are too precious group.

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