The year 1914, which is the year that the Gentile Times (aka Appointed Times of the Nations) ended, was determined though a study of the Bible along with no doubt some holy spirit given to the brothers that were able to discern this information.
There are quite a few scriptures involved in coming to the year 1914, one of them from Ezekiel about "Lifting off the crown and it will be no one's until he who has the legal right comes". So that is the starting point, which was 607 BC, when Jerusalem fell to Babylon. Then another significant scripture is from Daniel chapter 4 which showed the appointed times of the nations would be "seven times". Then to figure out what the seven times means we need to go to Revelation chapter 12 which notes that 1,260 days are 3-1/2 times. Making the 7 times equal to 2520 days. So doing the math, 607 BC plus 2,520 days comes to the year 1914.
Studying the Bible is one of my most satisfying endeavors. It never gets boring for me.