Como os pontos da Casa são tabulados / rastreados?

A resposta é mágica. Meu entendimento é que qualquer pessoa com autoridade para recompensar ou deduzir pontos (professores, prefeitos, monitora-chefe e monitora-chefe) ao declarar o ajuste de pontos que o sistema automaticamente tabula.

Do Wiki de Harry Potter duvidoso:

Exactly how points are tabulated and recorded is not explained in detail. It is implied in several books that simply stating the addition or subtraction of points magically adjusts the score accordingly. It's not certain if this occurs in all cases, such as when Dumbledore adjusts the scores at the end of Harry Potter and the Philosopher's Stone. The four giant hourglasses, however, seemingly adjusts their contents accordingly to the house points granted or retracted by the teachers' wordings.

Há ampulhetas com jóias para documentar os pontos. Em Harry Potter e a Ordem da Fênix, Harry está perto das ampulhetas quando Snape tenta tirar dez pontos dele e vê que a Grifinória não tem mais pontos. McGonagall então passa e dá a Harry, Ron, Hermione, Neville, Ginny e Luna cinquenta pontos cada por suas ações no ministério, e uma grande quantidade de rubis caem no fundo da ampulheta da Grifinória, e safiras caem no fundo da o da Corvinal. Então os dez pontos que Snape queria tirar de Harry faz com que dez rubis voassem do fundo da ampulheta da Grifinória até o topo.

‘Right then,’ said Professor McGonagall, looking up at the hourglasses on the wall. ‘Well, I think Potter and his friends ought to have fifty points apiece for alerting the world to the return of You-Know-Who! What say you, Professor Snape?’
‘What?’ snapped Snape, though Harry knew he had heard perfectly well. ‘Oh – well – I suppose …’
‘So that’s fifty each for Potter, the two Weasleys, Longbottom and Miss Granger,’ said Professor McGonagall, and a shower of rubies fell down into the bottom bulb of Gryffindor’s hour-glass as she spoke. ‘Oh – and fifty for Miss Lovegood, I suppose,’ she added, and a number of sapphires fell into Ravenclaw’s glass. ‘Now, you wanted to take ten from Mr Potter, I think, Professor Snape – so there we are …’

_{^{Harry Potter and the Half-Blood Prince / CHAPTER THIRTY-EIGHT — The Second War Begins}}