If anyone is genuinely interested, I would suggest you read the gospel of John, and decide for yourself if you believe what it says.
https://www.biblegateway.com/passage/?search=John%201%20&ver...
0. http://www.scientificamerican.com/article/do-the-eyes-have-i...
In this case; however, we're talking events like person X gave a speech and said Y. This is much more likely to have been heard by many people, so the likelihood of it have happened in the way it was relayed is much higher.
The Torah claims a million witnesses for the revelation at Sinai. I don't see anyone rushing off to become Jewish.
It occurs to me that "number of purported eye-witnesses" may not be a good evidentiary standard.
Of course, the larger problem isn't the anonymity of the authors. It's why the bible should be accepted over any other text. Perhaps it should, but that would have to be argued separately.