All the teams could encounter the last key shot to win/lose the games during the long season. And many great players have proved themselves under this situcation. I'm sure the player's mindset, the defense of opponent, the score ability of the player to take the last shot and so on all could influence the final result. Is there any stat. to show the %made of different ways of the last shot? And which position is the best choice?
The shot that goes in. It honestly, doesn't matter, you would want a sure thing like a post player, but getting it into them is not easy to do, especially if they are being doubled or guarded well. A perimeter player like a guard or forward are great, but usually all it does take for a hand to be raised in their general area or a rushed shot by way of nerves for things to not go down. So when it comes down to it, you want your star player taking that last shot, because they have usually had experience making all sorts of shots. The closest thing on our roster to that are Aaron Brooks, Carl Landry and Luis Scola. And only one of them can be considered such a threat thanks to his speed that he can get away from some good one on one defenders to get a cleaner look on his own.
The game changes on a last possession in some important ways. First, there is generally a timeout preceding it, so the opponent will sub in their best defensive unit for matchup purposes. Second, you are forced to score in an half-court setting, and the defense is set and usually well-organized. Third, the defense has an advantage because they usually know at what time you want to take your shot. Consider that on a usual possession, the offense will take the first good shot they can get (usually). But on a final possession, the offense wants to score with little time remaining. So you can't just run your standard offensive set. You want the ball in the hands of a player who can initiate the action at the appropriate time. For most teams, this will be some sort of pick and roll or isolation for a perimeter player.