I'm a group leader so I want to share my method to you. I use google spread sheet to keep track of everyone's participation and how I do my distribution is that I try to be as fair to everybody else. I'm not biased like, only giving packs to those who participated 4 times, nope. I make sure that everyone gets a legendary pack and when someone get a legendary pack, the following they will get either hero/elite or none. Luckily my group only has a total of 24 participants in GNW so it's easier for me to distribute packs around. Here's an image of my distribution tracking:

L - Legendary, H - Hero, E - Elite, N/A - none, dash line means no participation that week, and if it's left blank it means the player hasn't joined the group those weeks.

The players with straight N/A's are my alts (Hana, Expe, Rengar, Airi). I'm the top one, Anemone. So yeah I try to be fair to everybody except for myself haha.

I hope this gives you an idea of how to distribute packs.

In my group, what i do is that the legendary pack follows a rotation system. so if u get a legend pack this week u can't get another one until all members get a legend pack. but of course it will only be rotated to those who participated in the war. For the hero and elite packs, I based it on their war participation times. If there is a tie i compare their weekly donations. What usually happens is that almost same players get the hero and elite every week. I think this is a good system since everyone will eventually get a legend pack, u just have to participate in the war. and for the hero + elite packs, giving it to members who make a difference is more important than giving it to casual players. Since those casual players have higher chance of quitting the game than those who spend many hours on the game. So basically, it is a good investment too to give it to those highly active members.