I'll put a list of rewards and the number of times i got that reward, so another player copy and add rewards and so on. That way we can see the real reward "randomness". Don't add items that you got outside the raid.
EDIT: Sorry for not saying before, but it's not a theory about how you get better stuff, it's just to see if raid rewards really are random or some items has a bigger chance to drop.
example:
me- (6) ascendant shards
player 2- (6+3 = 9) ascendant shards
player 3- (9+6 = 15) ascendant shards
LIST
[b]Primary Weapons[/b]
(0) Fatebringer, Legendary Hand Cannon
(1) Vex Mythoclast, Primary Exotic Fusion Rifle
(1) Atheon's Epilogue, Legendary Auto Rifle
(2) Vision of Confluence, Legendary Scout Rifle
(0) Praedyth's Timepiece , Legendary Pulse Rifle
(0) The Last Word, Exotic Hand Cannon
(0) Hawkmoon, Exotic Hand Cannon
(0) Suros Regime, Exotic Auto Rifle
(0) Hard Light, Exotic Auto Rifle
(0) Monte Carlo, Exotic Auto Rifle
(1) Red Death, Exotic Pulse Rifle
(0) MIDA Multi-Tool, Exotic Scout Rifle
(0) Universal Remote, Primary Exotic Shotgun
[b]Special Weapons[/b]
(1) Praetorian Foil, Legendary Fusion Rifle
(2) Praedyth's Revenge, Legendary Sniper Rifle
(4) Found Verdict, Legendary Shotgun
(0) Patience and Time, Exotic Sniper Rifle
(0) Ice Breaker, Exotic Sniper Rifle
(0) Plan C, Exotic Fusion Rifle
[b]Heavy Weapons[/b]
(1) Corrective Measure, Legendary Machine Gun
(0) Hezen Vengeance, Legendary Rocket Launcher
(0) Thunderlord, Exotic Machine Gun
(0) Gjallarhorn, Exotic Rocket Launcher
(0) Truth, Exotic Rocket Launcher
[b]Armor[/b]
(3) Helmet
(1) Cloak, Bond or Mark
(0) Gauntlets
(4) Chest Armor
(1) Leg Armour
[b]Other[/b]
(3) Chatterwhite, Legendary White Armor Shader
(1) XV0 "Timebreaker", Legendary Sparrow
(0) "Glass Minuet", Legendary Jumpship
(4) "Aspect of Glass", Legendary Jumpship
(~ 42) Ascendant shards
(~ 48) Ascendant Energies
[i]ps. ~ approximation[/i]