The effectiveness of small ball, as a general philosophy, totally depends on the strength of your pitching staff. If you don't have pitchers who can limit your opponents' runs, small ball is likely not going to win you a lot of games. Texas did not play as much small ball last year because they didn't have the pitching to support it. This year they do, so they're using the sac bunt more often.
On an inning to inning basis, it's better to use small ball in early innings when you don't have a specific number of runs to score. It puts the defense on its heels early, it gets the pitcher thinking about fielding and not just throwing the ball, it gives you a psychological advantage if you score early, etc. But it's not as likely to be successful later in the game if you are down a significant number of runs. For instance, the odds of small ball scoring 4 or 5 runs in 2 innings are not great. So in that situation, you're going to start trying to make up most of that deficit the normal way and then go to small ball if you still have outs on your side.
But the reason Augie has been so successful with it is that he doesn't just sacrifice his worst hitters. He will sacrifice any hitter in his lineup if the situation calls for it. If it's going to be a major part of your approach, then every hitter on your team has to be willing and able to execute a sac bunt, and as a coach, you have to be willing to ask a guy batting .400 to do it when all the indicators suggest that you'll get a run from it.
Small ball obviously works best on a team that has great pitching AND big bats because you don't see a lot of runs scored on safety squeezes. You have to have guys to drive in the runs that sac bunts are putting in scoring position. But if you have both of those things (good pitching and solid hitting), small ball is a highly effective method of putting runs on the board. It exactly how Texas dominated Florida, a quintessential SEC gorilla ball team, in the championship series in Omaha in 2005, even though Texas only scored 10 runs over 2 games in that series.