I think if a manager plays numbers correctly all season long, and uses the highest percentages in high leverage situations, they have a better chance of winning. This isn't always the case, obviously, and sometimes it is known as micro-managing. But, for the most part, doing it this way is better.
The process of data-based decision making includes gathering and analyzing data to make a decision. Since most baseball players have stats from previous games, I believe this method can increase the odds of winning in a baseball game. Of course, if one team uses this method and the other does as well, it may be safe to assume that the odds are equal again.
They say that baseball is above all, a mental game. So while using data to help understand key stats of a player's overall performance, there are many aspects which the data cannot account for. For instance, if a really great player had gotten into a fight with his wife on the phone earlier that day. The data would not be able to show how this would impact his game.
Data-based decision making is a powerful tool, but it is only based on the raw data that has been input into it. You cannot program into a database things that are emotion-based. For example, one player might be having the game of his life, despite what the data from previous games shows. Another player might be excellent according to the statistics, but his dog just got run over and he is distracted. Coaches need to use data, but also know their players and ultimately go with their instincts.