Passion 9s Mutual: Which timers are optimal?

There's a shiny new passion mutual card in town, but Passion doesn't have a 7 seconds medium timer combo bonus which cute uses, nor does it have a 4s high combo bonus which cool uses, so what card do you actually want to run in that slot?

This is a new experimental content piece. It probably won't stand the test of time like the other writeups but it will at least help give some insight into the current metagame as well as the kind of research I work on on a regular basis. The content of this writeup is relatively advanced, and seeks to cater to cutting edge gamers who want to push for the top scores. But I hope it's also presented in a way that it is understandable to more people who are interested in learning more about scoring and teambuilding as well.

A lot of this data isn't exactly new, and was stuff I had computed a solid month before the card was released, but having the actual final stats of the card allows us to now collect real world simulation data which would be actually useful to more people.

Let's have a look at the data

These are the team compositions used to produce the test data.

And here are the tabulated results for all passion MASTER+ songs from lv31 to 29

6s Ensemble proves to be superior to 9s ensemble on the vast majority of songs. In fact I did some additional testing without logging data and there is only one additional song below lv29 in the entire passion M+ library that has 9s ensemble beating 6s. That song being 熱血乙女A. ミツボシ M+ has 6s ensemble beating 9s ensemble by less than 1300 points, which is the tiniest margin outside of what was recorded. Part of the reason why 6s ensemble is superior is that there currently is no passion 9s ensemble with the correct secondary stats. Yuko is visual but her second highest stat is dance which incurs another appeal penalty over the ideal composition.

7 High combo also proves to be superior to all other combo bonus timers for this composition. This can be attributed to the higher base appeal. As a matter of fact if you lock all the teams to the same appeal, which timer being optimal ends up being a much more open ended question and changes depending on song, but 7 high will still be largely dominant.

6s medium combo bonus Eve has the secondary appeal on the wrong stat (Dance) which contributes a significant appeal penalty. On the other hand 11 medium combo Kirari has the correct stats and secondary stats, but lacks the higher stat skews that the fes Yui has which contributes to the appeal difference. But the real problem with 11 seconds is that despite the better uptime, it causes mutual to miss its very first activation. This means that the first time mutual activates is at 18s and not 9s due to the first combo bonus effect only being at 11s and is a very noticeable penalty on songs with a busy intro. You can see that 11s and 7s are the closest on songs with sparse intros like Tokimeki Escalate and Sugar Heart Revolution.

But there is an additional conversation to be had here. Activation chance. 9s ensemble has a significantly higher full roll chance than the other teams. In an ideal world with an infinite amount of time to full combo the song you would eventually hit a full roll, but not everything is ideal in the real world. The exact full roll chances will vary based on song length. Citing the example posted in the earlier screenshot you can see that the change of a 6 ensemble to a 9 ensemble gives you approximately 3.2x higher chances at rolling a full activation play. This is great for people who are not aiming for number 1 score or when tackling a difficult song with very low full combo rate.

So there you have it, the ideal passion mutual composition for the vast majority of songs is going to be 9s mutual, 6s ensemble, 9s alternate, 7s concentration, 7s high combo bonus.

Data Collection Note

For the curious, the settings used when collecting the data in the table used a potential of 10/5/10 with skill 10. The window is [] and the full roll all perfect score (not optimized theomax) was used to create the table.