This is a rehosting of one of my GDSE answers.
This answer is me taking a gamasutra article and summarizing it with the question asked in mind. As with any soft science there are disagreements even among the experts on the field so I would recommend looking into the links to specific schools of though.
The Types of Players
The Fictionalists: They see the game's story and fictional world as the most central aspects of video games, and want the game worlds to look and sound exactly like the fictional worlds presented in film. They are negative to all features that disturb the illusion of a coherent world existing separately from our own. They want to immerse into the story world and find all interface elements to be disturbing for the ability to suspend disbelief.
The Systemists: They see the game as a formal system of rules and regard understanding the system as the most central and interesting game activity. They see the fictional environment as an overlay to the game system, and find the fiction to be present only as a supportive feature that is mainly unnecessary and only there to represent the system beyond. They accept the interface without question since it provides contact with the game system and presents information necessary for controlling and understanding the system.
The Relativists: They are in the middle ground between the Fictionalist and the Systemist, and appreciate both the fictional and the game system layers. They see attempts at integrating the user interface or fictionalizing it as elegant solution, but accept that certain kinds of information may be hard to include.
I believe this bit does a good job of clarifying the definition of a Relativists.
Necessity is therefore an important explanation for the Relativists. Although it may be more elegant to present all interface features as natural to the fictional game environment, there are many game system features that cannot be represented as such. For instance, verbal messages such as World of Warcraft's "I cannot cast that yet" and "Not enough rage" would appear as a negative intrusion for the Fictionalists, as they would argue that it makes no sense that the avatar would say that out loud, but for the Relativists this is perfectly acceptable.
Tying it All Together.
I would argue that displaying statics such as damage on screen in a manner such as Borderlands or Diablo deter Fictionalists who are "negative to all features that disturb the illusion of a coherent world existing separately from our own" and cater towards Systemists who "see the game as a formal system of rules and regard understanding the system as the most central and interesting".
Now to directly answer the question. Hiding statistics would attract Fictionalists and (so long as you are not leaving out needed information in your minimalizm) Relativists while also it would deter Systemists. It will attract people looking to immerse them selves in a new world but deter those looking to quantify and solve a new system.