Notes on energy mechanics, apps to Raiden Shogun
Character bursts cost energy, usually between 40 to 90. Characters can gain energy from using their skills or by attacking and defeating enemies. Character elemental skills and enemies can generate particles/orbs. Orbs usually give more energy than particles. Particles are either elemental or 'white'. Character skills can generate usually between 1-5 elemental particles. Some weapons can generate white particles through the passive.
Each elemental particle will fill the energy gauge of all party members. If the character is off field they will usually receive less energy than on field characters. As for on field characters:
If the particle is white then the on field character can regenerate 2 energy per particle.
If the particle is of the matching element as that of the on field character, they can generate 3 energy per particle.
If the particle is of a different element from that of the on field character, they can generate 1 energy per particle.
Because of the increased energy gain from matching elements, some carries usually like to be accompanied by a battery of the same element: for example, Xiao with Sucrose, Xiangling with Bennett, Itto with Gorou, Eula with Diona, and so on.
Characters also have an attribute called ER or Energy Recharge. ER can increase the amount of energy gained by a character. For example, if a character has 200% ER they gain 2 times more energy than normal. The base ER is 100%. ER can be increased through artifacts, weapons, passives, constellations, etc.
Raiden's Q at Lv10 will regenerate 2.5 energy per hit (icd 1s) up to 5 times for a total of 12.5 energy. Raiden's passive also gives her 0.6% greater energy restoration from the Q for each 1% of ER above 100% she has. So if Raiden has 200% ER (very possible with Emblem set, Catch, and her level ascension giving ER), then the passive gives her 60% greater energy restoration from her Q resulting in \(12.5*1.6 = 20\) energy. From testing this is unaffected by a character's ER. This is a flat gain of 20 energy, and it is the same for all party members.
So Raiden's burst basically cuts the energy cost of all bursts by ~20. By comparison, Venti can refund 15 energy, and Childe can refund 20 energy for himself. The difference is that Raiden's energy generation is 'universal' and will apply to all party members without condition.
Usually, Raiden uses her E before her Q. Her E can generate on average .4 electro particles every .9s. Her Q lasts 7s so during that time her E will generate ~3.11 electro particles, which gives 9.33 energy to Raiden. If Raiden has 200% ER as before, then her E can generate ~18.67 energy during her Q. So in total Raiden can restore \( 20 + 18.67 = 38.67 \) energy during her burst. Subtracting this from 90, the effective cost of Raiden's burst is basically ~50 energy.
In general, if Raiden's ER is \(\epsilon \ge 1\), then the energy generated for herself during her Q (with her E active) is $$\begin{align} E &= 12.5(1 + .6(\epsilon - 1)) + 9.33\epsilon \\ &= 5 + 7.5\epsilon + 9.33\epsilon \\ &= 5 + 16.83 \epsilon \end{align}$$ For Raiden to recharge her burst alone (reach \(E = 90\)), she would need \(\epsilon \approx 5\) or around 500% ER, which is infeasible. Fortunately, in practice, attacking and defeating enemies will generate white particles/orbs which will further generate energy for Raiden, allowing her to spam her burst on cd more easily (with even 200% ER). But even then, Raiden's q lasts 7s and has a 18s cd, meaning 11s downtime without cd modifiers (like Chongyun field or Anemo resonance). Note that Raiden's C6 does not reduce her own cd (so it is more of a support-oriented constellation), though it can help her gain Chakra stacks faster.
The above calculation can consider the energy generated during the 18s cd of her Q. This time her E will generate around \(18(.4/.9) = 8 \) electro particles or 24 energy for Raiden. Then the energy gained during 18s is $$\begin{align} E &= 12.5(1 + .6(\epsilon - 1)) + 24\epsilon \\ &= 5 + 31.5 \epsilon \end{align}$$ So with 300% ER she can comfortably spam her burst on cd. Even with 200% ER the above will give around 70 energy, leaving only 20 more energy to fill her Q. Note the above assumes she is on field and that she makes enough hits during her Q to gain all 5 instances of energy restoration from musou isshin (unless the enemy moves all over the place, this is usually possible since she gets so much poise/interruption resistance, so she can simply tank hits and keep attacking without being staggered).
For most characters, ER is only important to the point of spamming one's burst on cooldown. Otherwise, there will be longer downtime, which will result in diminished dps. Once one has enough ER to spam bursts on cd, it is more beneficial to invest into damage (atk, crit, etc.).
However, there are some characters that have special bonuses involving ER such as Mona or the Raiden Shogun. Moreover, Version 2.1 released the Emblem set which converted ER into greater DMG bonus (similar to Mona's passive). The Emblem set became the new bis for several other characters including Beidou, Mona, Raiden, Xiangling, etc. But even for the Emblem set, once you have enough ER to spam bursts on cd, having an ATK sands usually always gives more damage than an ER sands (the 4 piece Emblem converts 25% of ER to dmg bonus, max of 75%, but based on the distribution of ATK% and ER% on artifacts, the game does not give enough ER% on the sands to outdamage an ATK% sands). For some supports such as Bennett and Yun Jin, if you only care about their support abilities rather than their damage, then opting for an ER sands may be worthwhile to spam their bursts more often.
Still the emblem domain, featuring Emblem and Shimenawa (2 piece gives ATK), became one of the most useful domains to farm (alongside the Viridescent Venerer domain) due to its importance to several key supports.
For Venti specifically, the Viridescent Venerer set is still preferred over Emblem since VV gives -40% RES, which gives a multiplicative increase in damage, buffing the team a lot more. As of 2.4, VV is one of the only artifact sets that reduce RES.
Collecting particles has different sound effects for different elements: