A hypothetical statement is one that is speculative. It speculates on the consequences of a hypothetical event. It states what would occur if something that hasn't happened, were to happen.

Expressing hypotheticals in Italian (il periodo ipotetico) is somewhat tricky because it requires use of the subjunctive, a verb tense that takes getting used to. It is further complicated by making the chapter on this topic that you will find in textbooks overly long and confusing.

Here I will start with two solid reference points in English, so that you can see exactly what is going on. Then we'll go through some examples to see what it looks like in real world use.

Could

The first case is the could scenario.

- You've never scored a penalty.
- Yeah, but I could do it.

- You don't play the piano, do you?
- I could if I wanted to!

Got it? Okay, so we build our hypothetical from the could.  And the hypothetical describes what would happen if you did the thing that you "could do". (Or, in general, what would happen if the thing that "could happen", happened.)

- If I scored a penalty, I would celebrate.

- If I played the piano, I would play Beethoven all the time.

Here is what you need to know:

1. The action is described using the imperfect subjunctive (il congiuntivo imperfetto).
2. The consequence of the action is described using the conditional (il condizionale).

- Se segnassi un rigore, lo festeggerei.

- Se suonassi il pianoforte, suonerei sempre Beethoven.

Of course, you are not limited to talking about yourself.

- If it rained, they would not show up.
- Se piovesse, non si farebbero vivi.

Could have

The second scenario is all about could have.

- You lost the game!
- Yeah, but we could have won.

- Al Capone never jumped out of a window.
- Yeah, but he could have, he was that crazy.

Once again, the hypothetical starts from the thing that "could have happened".

- If we had won the game, we would have been champions.

- If he had jumped out of a window, he would have terrified his underlings even more.

In this case the tenses are different:

1. The action is described using the pluperfect subjunctive (il congiuntivo trapassato).
2. The consequence of the action is described using the past conditional (il condizionale passato).

- Se avessimo vinto la partita, saremmo stati campioni.

- Se si fosse buttato dalla finestra, avrebbe fatto ancora più paura ai suoi subalterni.

A slight variation on this is used if the consequence is one that is still felt today, in which case you use the regular conditional:

- If he had jumped out of a window, he would be even more famous.
- Se si fosse buttato dalla finestra, sarebbe ancora più famoso.

Examples

If you're not reading Leonardo then you really should, the guy is hilarious. In a recent entry he made a superb demonstration of the hypothetical.

I'll just quote one sentence here, but read the whole thing so you understand what is being talked about. The short version is that Berlusconi is alleged to have employed underage prostitutes, one of whom was nicknamed Ruby. Hiring a prostitute in Italy does not constitute a crime, but if the person is underage then it obviously does. Leonardo here is satirizing the kind of statements made in support of Berlusconi by various figures who more or less owe their position to him. A classic case of scandal and farce in Italian politics.

Il sesso coi cyborg non è ancora regolamentato per legge, e quindi Berlusconi (che è impotente) (e se non fosse impotente sarebbe fidanzato) (e se avesse tradito la fidanzata con Ruby, comunque non l'avrebbe pagata) (e se l'avesse pagata, comunque sarebbe maggiorenne) non può essere punito per aver fatto sesso con un cyborg.

- e se non fosse impotente sarebbe fidanzato
- and if he weren't impotent, he would have a girlfriend

- e se avesse tradito la fidanzata con Ruby, comunque non l'avrebbe pagata
- and if he had cheated on his girlfriend with Ruby, he still wouldn't have paid her for it

- e se l'avesse pagata, comunque sarebbe maggiorenne
- and if he had paid her, she would be of age anyway