I went to your link, here's more  detailed instructions.

How is it possible that both the attacker and the defender can lose over 50% of their units?

The battle mechanics of Raids vs Siege are different.

The siuation you describe i.e. both players losing >50% units cannot happen in raid battles - but can (and often do) happen in siege battles

Oberon is saying that you add the attacker and defender together and come up to a total power points to determine the outcome. 

So, your opponent’s percentage of the battle is not your loss? This would be the obvious calculation, right? If I make up 40% of the total I would lose 60% of my force? Raid/siege should matter not.  

However this is NOT true!!

Battle Mechanics (highly simplified)

Raid example 1.

Offense 100k vs. Defense 100k .. Castle Def Bonus = 0

Total force on battlefield (Off + Def) = 200k

Off = 50% force -> inflicts 50% casulaties on Def

Def = 50% force -> inflicts 50% casualties on Off

Both sides lose ~50k each .. pvp points wise - honours even .. battle report gives victory to side with fewest units lost.

Raid example 2.

Off 300k vs. Def 100k ... Castle Def Bonus = 0

Total force = 400k (Off + Def)

Off = 75% force -> inflicts 75% casualties on Def

Def = 25% force -> inflicts 25% casualties on Off

Off loses 75k .. Def loses 75k .. again pvp points - honours even .. battle report gives victory to side with fewest units lost.

Raid example 3

Off 300k vs. Def 100k .. Castle Def Bonus = 10k = 100% bonus to Def

Total force = 500k (Off + (Def x 2))

Off = 60% force -> inflicts 60% casualties on Def

Def = 40% force -> inflicts 40% casualties on Off

Off loses 120k .. Def loses only 60k (not 120k).. why? because Castle Def Bonus gives extra strength but does not add to Def unit combat stats! - in other words it is still only 100k Def for pvp points calculation!

PvP-wise Off scores ~1.5k ... Def scores ~3k .. (pvp points-wise Def wins).. battle report will give victory to side with fewest unit losses.

Siege example

Unlike Raids - siege battles are determined by both relative force and relative numbers.

Off 100k  vs Def 100k .. castle def bonus = 0

Off is largely infantry .. Def is largely Bestiary

Assume Off = 600 units and Def = 200 units (it makes calculation easy for this example)

Raid mechanics assume 50/50 losses here - but relative numbers must also be taken into account for sieges in this case Off outnumbers Def 3 -1 .. this aproximates to ~8% offset

i.e. Off loses 46k (50k - 8%) .. Def loses 54k (50k + 8%)

PvP scores: Off = ~1.3k .. Def = ~1.1k ... (points wise Off wins)

Battle report gives victory to side with fewest unit losses (in this specific example - Def)

Ask the Emps how they properly calculated the Battle for beacon 754

1. Have inside intel - nope

2. test hit and calculate - nope didnt do that either

3. Spy and calculate - Impossible

4. If you didnt do items 1-3 succesfully then you just send troops at it and calculate the loss % - nope didnt even do that. 47 attacks and the very last attack, they were still loosing 99.9% of the attacking offense. They lost 1.375 million dragons alone, an estimated 250k USD to revive @75% off. 

Other: It was a great idea to have leaguemates send troops the day before with a pike to slow travel and target a specific time, problem was you cant stop the attacks when the player isnt around who launched the day before, you had to go all in and loose it all

But hey folks, the Emps have the fastest time doing the tower to 100, and a 10% bonus from achievements for troops. guess that helps while your being mismanaged.