Haymitch is a drunkard, a friend, a mentor, and a victor. He's still really good at strategizing but he's no longer good at going out into the field. For most of his time in District 13, he's forced to be sober, but as soon as he's around alcohol, he can't keep his hands off it. He needs liquor just as Johanna needs morphling. It's how both of them cope with the trauma of being in the Games. Apart from the occasions when he's completely wasted, though, Haymitch is still able to provide advice and help the rebels strategize.
A lot of the time, Haymitch can see more clearly than other people. He's the first to say that a dressed-up, fake Katniss won't be able to film convincing propos. He's also the one who helps Katniss see that Peeta isn't her enemy, but is engaged in fighting his own demons. It's Haymitch who lets Katniss know what Johanna really endured as a prisoner of the Capitol. And he's the one who needs to be there on the other side of Katniss's earpiece, giving her advice from the bird's-eye view.
Despite all that, Haymitch and Katniss have a love/hate relationship. Part of the problem is that Haymitch and Katniss are just too similar to get along. The other part is that Haymitch is a broken man from his dealing with the Capitol, and he'll probably never recover. Sadly, Katniss worries in Chapter 12 that he doesn't have anyone to love or be loved by. In his own way, we think that Haymitch really might love Katniss. At the end of Mockingjay, Haymitch is the person who takes Katniss home to District 12, and, though it isn't confirmed in the book, we can't help but hope that Katniss and Peeta will looking out for him.