How is the home field determined in MLB playoff tiebreaker games?

This afternoon, the Minnesota Twins and Detroit Tigers will play a tiebreaker game for the last spot in the MLB playoffs. It looks like the game is going to be played at the Metrodome in Minneapolis.

How did the Twins win home-field advantage? Was a coin flipped or is based on some regular season statistic? Since there aren’t games at any other ballpark today, wouldn’t it be more fair to play at a neutral location?