If you are at the stage where you can beat all dungeons at max level, clear doomtower normal and stay in gold 4, then my advice is to never pull shards outside of a fusion/fragment event. The only exception to this is any guaranteed summon if you need the champion (e.g. the recent coldheart is a great example where it is more beneficial to use void shards). Every shard should be saved up and you should only use the 3 Mysteries per day for the daily quests
The reality is that the fusion/fragment events also always has a 2x event during them, so skipping a 2x outside of these costs you nothing.
The next thing you need to consider is whether the upcoming fusion/fragment event contains a champion that will help your account. Don't participate in it just for the sake of it, as getting another champion to sit in the vault won't help you at all. You'll end up spending a lot of resources on something you will never use, and if the event after that looks good then you will be screwed.
My final advice is that the champion chase and summon rush events both need to be approached differently:
Champion chase - You gain points for getting champions by any means, and not just shards. This includes drops from campaign, fusions using other champions (e.g. Broadmaw) and fragments from other sources (e.g. doom tower, Tag team arena, clan shop).
Did you finally complete all of the Drex fragments? Did you participate in the current fusion event and get all fragments for one of the champions? Don't actually summon them until the next. A legendary summon is 500 points and an epic is 250. I always keep spare champions of Broadmaw in my vault and can currently summon him up to 3 times if needed (which I haven't had to yet). I also have enough rares to summon the epics for Rhazin multiple times. Finally, I am on track to get 3 of the epics for this fragment event but I will not summon them until the next, because that is 750 points waiting.
I usually finish Champion Chase tournaments without using many shards. When I do use shards though, I never use Sacred Shards in champion chase. From a pure cost to reward ratio it doesn't make sense, and you are better off using mystery, ancient or void shards to make the difference (with the priority being in that order).
Summon Rush - From a pure economical point of view, Sacred Shards offer the biggest value in rewards for any Summon Rush. A Void shard gives 120 points but a sacred gives 500. This means that you would have to use almost 5 void shards to get the same benefit as 1 sacred, which is a complete waste of resources. As a result, I only ever use my sacred shards during a summon rush, and even then I only use the bare minimim. If you can make up any difference with Mystery Shards then they take priority over using any more sacreds.
For example, in the current event I had 11 sacreds saved up, and have opted to use 4 to get 2000 points, and then 1000 Mystery shards to get the remaining. I could use 6 sacreds but it is much easier for me to get Mystery shards than to get sacreds.