Players who are saved to a raid have already received a loot roll (and potentially loot) from a boss, so therefore if they kill a boss again within the same reset (so each week), they will be illegible to receive loot from that boss.
So imagine you have a raid of 10 people (which is the minimum in normal/heroic, based on that is as low as a boss will scale), but 5 of those players are already saved to the first boss. When you kill the first boss, the game then rolls for 5 eligible players, not 10, as 5 players are illegible to receive loot. Therefore a maximum of 1 piece of loot will drop, as opposed to the 2 that would drop if no players were saved.
On the flip side, I see what you mean by chances of getting loot. If only 5 people are eligible for loot, then you have a 1/5 chance of getting the item (if all 5 players can use that item).
I guess maybe I should clarify that having people saved to bosses on a kill reduces the number of outcomes. If we take the above example, then the outcome for getting loot for myself is either receive 0 pieces of loot, or 1 piece of loot.
But if no one is saved in the example above, then the outcomes become 0 pieces of loot, 1 piece of loot, or 2 pieces of loot.
In either scenario, you’re % chance of getting loot remains the same - but this assumes that every person in your raid can use the item that dropped. In my PUG yesterday, a cloth helm dropped, but none of the 5 people that were unsaved could use the helm. However, in a 10man unsaved group, the loot may well have been usable by 1 person of 10. But of course, this purely comes down to raid composition.
It’s also worth mentioning that some loot that drops is not needed by players due to it not being an upgrade for them, or already having the item. If you have 10 people in a raid, and an item drops that only 3 players can use, but only 2 of those people actually need the item, then the chance of getting the loot is 50%, not 33%.
But the chance of getting that loot is still the same in a 10man, 5 saved, 5 unsaved group, if you assume that the same item drops, 3 players can use, only 2 people need, so the chance goes from 33% to 50% (if the 3rd player who doesn’t need the item, doesn’t need on the item). Similarly, if 2 of the 3 people who could’ve used the item are already saved, now your odds actually increased to 100% chance of receiving that item.
So why mention it if the chances in either scenario are the same? Because the chances of seeing an item you need is increased in the 10 player unsaved scenario.
My understanding of the loot table for a boss is that each item has a set percentage chance to drop. It is not decreased or increased based on what else drops. When the first item is rolled from the loot table, it has no greater or lesser chance of being rolled when the second item is rolled from the loot table.
Example A:
Boss has a loot table of 20 items.
Each item has an equal chance of dropping (I am aware that this is not the case for some bosses in DF (very rare loot table on some)).
First loot table rolls.
Second loot table rolls.
First loot table has a 1/20 chance of something I need rolling into loot.
Second table also has a 1/20 chance of something I need rolling into loot.
There is now a 2/20 chance, or 1/10, chance of something dropping that I need. This is a raid of 10 unsaved people, because there 2 loot rolls.
Example B:
Boss has loot table of 20 items.
First loot table rolls.
First loot table has a 1/20 chance of something I need rolling into loot.
Therefore, the chance of me seeing an item I need is now 1/20, as 5 players are saved and 5 are unsaved, so there’s only 1 loot table roll.
As you can see, in Example A I have a higher liklihood of seeing a piece of gear I want than in Example B, though the chance of me receiving loot is technically the same.
As mentioned above, the maths is very complicated as you have to take into account multiple extensive factors, such as the raid composition (could be any composition which will affect the likelihood of you getting loot when rolling against other players), and whether the players in your raid need the items that drop.
Generally speaking, and in my opinion, it is better to know that players in your group are saved or not, to manage the expectation of what loot may or may not be dropped and/or useable to the group you raid with, rather than expecting X number of pieces of loot to drop only to find it is X minus Y.
(Apologies for the wordy responce, I spent some time discussing the mathmatics behind this with a maths professor, and we both agreed that it is incredibly complex to calculate, but that it would be beneficial to know who in your group is saved and not saved from a clarity and raid building perspective)