I played a game of Hanabi with my fiance this weekend, I recently got her hooked on the game (which is surprising because she's usually not into board games, but the full-cooperative aspect is something that really appeals to her so I'm looking to Pandemic and the like) and we played some 3P and 4P games and wanted to try out 2P (I had tried it before and it seemed awkward). To my surprise we played one game and got a perfect score *very* comfortably. I mean, we're both pretty good players, but it didn't feel like we were really using clues very efficiently so we were both pretty surprised. So I tried thinking about Hanabi in a certain way to see if I could make sense of this.
IN A 3-PLAYER GAME (EXAMPLE)
There are 50 cards in the deck, and 15 of those cards start in hand, so when the deck runs out we've made 35 plays/discards and ideally you can get 3 more after that so that means you can have at most 38 plays/discards before time runs out. If 25 of those are plays, that means you can discard 13 cards at most over the course of the game and still have a shot at the perfect score.
You start with 8 clue tokens, let's say you get 13 from discards and (we'll be generous) 4 more from playing fives. This means you 25 clues to give in order to play 25 cards in the best case.
APPLYING TO THE GENERAL CASE
Using similar calculations for other numbers of players (which changes the number of cards that start in players' hands and also the number of plays after the deck is drawn) we have:
2 players: 29 clues
3 players: 25 clues
4 players: 25 clues
5 players: 22 clues
Now there are are ways to burn clues other than take the clue action -- explosions, not playing a 5 early enough (or at all), initiative issues at the end of the game that cause people to not effectively use all of their actions, so you can just count those as using this limited "clue" resource. But in the best case you get this number of clues to pass along enough information to play 25 cards.
It seems that as the number of players increases, you're expected to get the same information across using less clues, which means the game probably gets harder. Now there are mitigating factors, like the fact that it's probably easier to give better clues when people have less cards in hand and more cards are visible to more people. Also, initiative and sequencing can be awkward in 2P games sometimes. On the other hand, I've never played a 5P game of Hanabi without at least one person in the group who will never do anything except give a clue, no matter what happens, and endgame sequencing only gets harder with more people.
So the conclusion is that Hanabi gets more difficult to "win" the more players you add to the mix.
Also, the intuition that one clue -> play one card is kind of like the "Copper" of Hanabi; you need to use it to get things done, but a hand of all Copper is not going to get you a Province in the same way that this will not get you a perfect score in Hanabi -- you have to do better. You have to get more value out of your clues. (with the possible exception of 2P games).
Another interesting calculation to make has to do with one of the variants using the "Rainbow Cards" -- where it just acts as a sixth color and nothing else. This adds 10 more cards to the deck and 5 more plays to make, so it's 5 extra clues you get to make 5 extra plays, plus the possibility of playing another five to squeak out one more clue token. I've found that this variant makes the perfect score easier to get and in the context of this calculation that makes sense, since it seems to act as a "buffering" effect at the very worst.
2P: 29/25 -> 35/30 : 1.16 -> 1.17
3P: 25/25 -> 31/30 : 1.00 -> 1.03
4P: 25/25 -> 31/30 : 1.00 -> 1.03
5P: 22/25 -> 28/30 : 0.88 -> 0.93
You can look at it a lot of different ways, but even in 2P you get more wiggle room with this variant.