"improve something" and "improve on something"

[Daruma]

Hello.

Bertorelli has scored 165 points, and I don't think anyone will improve on that.

It's wrong to use improve instead of improve on, isn't it?

Thank you.

[PROESL]

Hello.

Bertorelli has scored 165 points, and I don't think anyone will improve on that.

It's wrong to use improve instead of improve on, isn't it?

Thank you.

In your example sentence "improve on" means "do better" or "exceed that point total". Using "improve" alone means to make the point total better, which would be an illogical thing to say in this context.

Bertorelli has scored 165 points, and I don't think anyone will improve on that. = Bertorelli has scored 165 points, and I don't think anyone will do better than that.

Bertorelli has scored 165 points, and I don't think anyone will improve that. = Bertorelli has scored 165 points, and I don't think anyone will make that better (that point total better).

So it's not a question of structure or grammar in this case. Right or wrong here has to do with what one really means to say, as well as what would be logical to say.