Calculating the Casualties[]
Unfortunately, I don't know of any official statistics for the battle, so I had to go with what I could see onscreen. The two fleets are never shown in their entirety, so a lot of the calculations were based on estimates.
There is a scene in Luft Vanship where Claudia Units are shown rising up to the Guild arbiter. There are 21 units shown onscreen; therefore, 21 ships have been sunk up to that point. Unfortunately, it is impossible to tell how many of them were Anatoray and how many Disith. I will assume that 11 were Disith (destroyed in the early stages of the battle, when Anatoray had the advantage) and 10 were Anatoray (destroyed by the reinforcement fleet). This is the estimation with the least evidence behind it.
Casualties
Following the point where the Claudia Units are shown, one Anatoray ship is sunk onscreen by the Disith (the Parthelon) and 4 Disith ships are sunk onscreen (one by Tatiana, three by the Silvana). That puts the losses at 11 Anatoray, 15 Disith.
Anatoray ships carry 2,987 men (2,267 crew + 760 musketeers). Disith ships carry 2,708 men (1,988 crew + 720 musketeers). These figures were used to calculate the casualties, which I rounded to two significant digits. Thus, the casualty figures do not include any of the casualties on the damaged ships (musketeers killed in the opening salvo or crew killed by artillery hits) because there is simply no data for how many casualties occurred that way.
Three Disith ships in the reinforcement fleet were sunk in the Grand Stream by the Silvana in First Move, but I have not included these, as the battle had not actually begun at that point.
Initial Force Strength
At the end of Luft Vanship, 10 Anatoray ships are shown escaping. Add the 11 that were sunk -- plus one for the Goliath, which fled earlier -- and Anatoray started with 22 ships.
When the ships are initially lining up for battle, 15 Disith ships are visible. When the reinforcements arrive, 30 are visible through the Anatoray scopes. Thus, not counting any ships that may have been present but off-screen, Disith started with 45 ships. (Any ships lost in the crossing of the Grand Stream, such as the three-shot down by the Silvana, are again not included).
Lore video on The Third Battle of Minagith
I created a video on the Battle of Minagth and intended to make two more videos on the Lore of Last Exile. Not sure it is appropriate to include it in the wiki article itself
The Third Battle of Minagith (Last Exile Lore)