If the size of a Patronus doesn't influence its power, why was Umbridge's Patronus less effective?

Question

I guess the title makes it clear: if the effectiveness of a Patronus doesn't depend on size or shape, as per this question and the answers to it

why is Umbridge's Patronus less effective in HP7 (The Muggle-Born Registration Committee)?

The stag's light, more powerful and more warming than the cat's protection, filled the whole dungeon as it cantered round and round the room.
_{The Muggle-Born Registration Committee, Harry Potter and the Deathly Hallows}

I hope my question is clear and can be answered using canon sources (including Pottermore, excluding Harry Potter Wiki)!

Answer 1

One possible reason seems to be that Umbridge's patronus was not meant to protect anyone other than herself, Yaxley, and Mafalda (Hermione).

The patronus might have been cast intentionally in a way (supposing that's possible) so that its positive effects are limited to the prosecutors. At the very least, these three would not have found it "weak".

The moment he had passed the place where the Patronus cat patrolled, he felt the change in temperature: It was warm and comfortable here. The Patronus, he was sure, was Umbridge’s, and it glowed brightly because she was so happy here, in her element, upholding the twisted laws she had helped to write.

Harry Potter and the Deathly Hallows, Chapter 13

Other than this, it could be because Harry was much more determined than Umbridge, given that his goal was to actually ward off all the dementors. He was also acting out of uncontrolled anger on hearing Umbridge lie.

It was Umbridge’s lie that brought the blood surging into Harry’s brain and obliterated his sense of caution — that the locket she had taken as a bribe from a petty criminal was being used to bolster her own pure-blood credentials.

Harry Potter and the Deathly Hallows, Chapter 13

Notably, the two patronuses are being compared at different points of time, when their purposes were different. Umbridge's patronus was to protect the prosecutors while ensuring that the accused received no warmth, while Harry's was to actually fight off dementors. Moreover, Umbridge's patronus was gone before Harry cast his - as he had already stunned Umbridge by then. It is not as if both partonuses were around simultaneously, with Harry's overpowering Umbridge's.

Answer 2

Because of how a Patronus is formed, Harry's might have more power than Umbridge's.

A Patronus is created from positive feelings, like hope and happiness.

“The Patronus is a kind of positive force, a projection of the very things that the Dementor feeds upon – hope, happiness, the desire to survive – but it cannot feel despair, as real humans can, so the Dementors can’t hurt it. But I must warn you, Harry, that the Charm might be too advanced for you. Many qualified wizards have difficulty with it.” _{^{- Harry Potter and the Prisoner of Azkaban, Chapter 12 (The Patronus)}}

Conjuring a Patronus successfully requires focusing on a happy thought to give the Patronus its power.

“And how do you conjure it?’

‘With an incantation, which will work only if you are concentrating, with all your might, on a single, very happy memory.’ Harry cast about for a happy memory.” _{^{- Harry Potter and the Prisoner of Azkaban, Chapter 12 (The Patronus)}}

Harry theorizes that the Patronus that Umbridge cast was powered by her happiness enforcing the laws against wizards born to Muggles.

“The Patronus, he was sure, was Umbridge’s, and it glowed brightly because she was so happy here, in her element, upholding the twisted laws she had helped to write.” _{^{- Harry Potter and the Deathly Hallows, Chapter 13 (The Muggle-Born Registration Commission)}}

Harry's, while this time what thoughts he uses to cast his Patronus are not described, is probably fueled by a more "noble" sort of happy memory than Umbridge's would be. The happy thoughts he's used previously have been things like flying on a broomstick for the first time and when he found out he's a wizard, which are quite "innocent" happy thoughts. It's like the Cruciatus Curse - a bit of righteous anger won't cause nearly as much pain as someone who really means it, who really wants to cause pain. The motivation behind the Patronus likely affects how well it works.

“EXPECTO PATRONUM!’ The silver stag soared from the tip of Harry’s wand and leapt towards the Dementors, which fell back and melted into the dark shadows again. The stag’s light, more powerful and more warming than the cat’s protection, filled the whole dungeon as it cantered round and round the room.” _{^{- Harry Potter and the Deathly Hallows, Chapter 13 (The Muggle-Born Registration Commission)}}

It's possible that his thoughts were focused on getting to his friends, since that's what he reminds himself of to will himself to fight the Dementors' effects when he can't conjure a Patronus without revealing his presence.

“Fight it, he told himself, but he knew that he could not conjure a Patronus here without revealing himself instantly. So he moved forwards, as silently as he could, and with every step he took numbness seemed to steal over his brain, but he forced himself to think of Hermione and of Ron, who needed him.” _{^{- Harry Potter and the Deathly Hallows, Chapter 13 (The Muggle-Born Registration Commission)}}

Umbridge's thoughts of being able to write and enforce laws against wizards who were born to Muggles were strong enough to create a corporeal Patronus, but probably weren't as strong as whatever Harry's thought was.

The power of the happy thought behind it does affect the power of the Patronus cast.

When Harry isn't able to focus on his happy thought, and is thinking instead about his fear of the Dementors and dread of losing Sirius, he's unable to conjure a strong or effective Patronus.

“A thin wisp of silver escaped his wand and hovered like mist before him. At the same moment, Harry felt Hermione collapse next to him. He was alone … completely alone … ‘Expecto – expecto patronum –’ Harry felt his knees hit the cold grass. Fog was clouding his eyes. With a huge effort, he fought to remember – Sirius was innocent – innocent – we’ll be OK – I’m going to live with him – ‘Expecto patronum!’ he gasped.” _{^{- Harry Potter and the Prisoner of Azkaban, Chapter 20 (The Dementors' Kiss)}}

However, if his happy thoughts are strong enough, they will form a strong Patronus.

“He summoned the happiest thought he could, concentrated with all his might on the thought of getting out of the maze and celebrating with Ron and Hermione, raised his wand and cried, ‘Expecto Patronum!’ A silver stag erupted from the end of Harry’s wand and galloped towards the Dementor, which fell back, and tripped over the hem of its robes …” _{^{- Harry Potter and the Goblet of Fire, Chapter 31 (The Third Task)}}

The strength and power of the thoughts used to create the Patronus directly affects the power and strength of the Patronus that's created. Even once the thoughts are strong enough to create a corporeal Patronus, it's still controlled by how strong the thoughts behind it are.

Answer 3

The happiness for Umbridge's Patronus comes from her own self-righteousness. Therefore is likely that her happy memory is not as strong as Harry's and therefore the charm is not as effective.

In addition the story is from Harry's point-of-view, so he is remembering/feeling the happiness that allows him to cast the Patronus in the first place.

From The Patronus Charm writing on Pottermore.

As a pure, protective magical concentration of happiness and hope (the recollection of a single talisman memory is essential in its creation) it is the only spell effective against Dementors. The majority of witches and wizards are unable to produce Patronuses and to do so is generally considered a mark of superior magical ability.

In spite of a long association with those fighting for lofty or noble causes (those able to produce corporeal Patronuses were often elected to high office within the Wizengamot and Ministry of Magic), the Patronus is not unknown among Dark wizards. While there is a widespread and justified belief that a wizard who is not pure of heart cannot produce a successful Patronus (the most famous example of the spell backfiring is that of the Dark wizard Raczidian, who was devoured by maggots), a rare few witches and wizards of questionable morals have succeeded in producing the Charm (Dolores Umbridge, for example, is able to conjure a cat Patronus to protect herself from Dementors). It may be that a true and confident belief in the rightness of one’s actions can supply the necessary happiness. However, most such men and women, who become desensitised to the effects of the Dark creatures with whom they may ally themselves, regard the Patronus as an unnecessary spell to have in their arsenal.

Answer 4

Other answers have already given good reasons why Umbridge's Patronus may be weaker.

However, I think the direct answer to your question is that you are making an invalid assumption. The fact that "the effectiveness of a Patronus doesn't depend on size or shape" means just that. It does not mean that a smaller Patronus should be more effective than a larger one.

In this case, Harry's Patronus is more effective than Umbridge's. That fact that it is also larger is just a coincidence.