In reality, the manuscripts of the Bible are more like a tree. Imagine a tree with several branches coming off of the main trunk, splitting into other branches and then smaller ones yet. When the original copies of a Biblical letter—such as Paul’s letter to the Colossians—were written, other copies would be made for churches in other cities. Many copies would be made from the original and sent to various places in the Roman Empire. From those copies, other copies would be made for more Christians, and eventually to replace the old copies as they wore out. This means that there are multiple lines of transmission. This means that even if a change was made on one branch of the tree, it would not affect every other copy. Other branches would still be okay.
This also means—contrary to The DaVinci Code—that it would have been impossible for someone such as Emperor Constantine to change the text of the Bible, even if he had wanted to. There would be no way to gather and change all of these documents.
Scholars are able to determine where many manuscripts fit on this family tree by their age and shared characteristics. By comparing manuscripts, they are able to weed out any alterations and determine with great accuracy what the original text said.
In addition, there are several good reasons why the Bible is not like the telephone game.
1. The New Testament documents were in writing. They were not whispered one time, with the chance of mishearing one word for another. They were in writing and could be copied carefully and reviewed.
2. As mentioned, there were multiple lines of transmission. In the telephone game there is only one chain. The Bible has many branches. Even if someone got it wrong, other branches would get it right. Imagine a different version of the telephone game: One person whispers a message to four different people, and each of them whispers it to four more people, and so forth. Even if someone intentionally tried to sabotage the message, it would still be very easy to figure out what the original message was at the end of the game when you compared all of the final answers.
3. Bible scholars don’t just rely on the last version of the message. Imagine the same game of telephone from the paragraph above. Now imagine that not only do you get to hear the report from all the last people, you also get to hear other reports from many people early on in the tree. That would make it even easier to know with certainty what the original message was.
4. In addition to ancient manuscripts, we have over one million quotations from the New Testament by the early church fathers. Even if the entire New Testament was destroyed, it could be almost entirely reassembled just by using these quotes. Also, these quotes are from various points in history, meaning that changes in the Bible would also be reflected in these quotes. Further, in addition to the 5,700 Greek manuscripts that we have and the million plus quotations, we also have thousands of ancient translations of the Bible in languages such as Latin and Coptic. There are more than 10,000 manuscripts in Latin alone. Although these are translations, there are also very helpful witnesses to the original text.
5. Finally, there is a motivational difference between the New Testament scribes and kids playing the telephone game. Many kids—myself included—would intentionally try to garble the message in the telephone game. In contrast, the scribes were professionals who took great pride in their work. Copying these manuscripts by hand was painstaking work and they were motivated to do the best they could. They viewed these texts as sacred, not something to be careless with. The fact that many scribes would knowingly recopy a type-o, rather than fix it, shows that they were dedicated to copying the text as it was in front of them. Yes, sometimes there were mistakes as they looked at the wrong line, or a word with a similar ending. And there were times when the scribe would wrongly think that the text in front of him had a copying error in it, and by ‘fixing’ the ‘error’ would actually be making a copy error. But all of this shows that they were trying very hard to create an accurate copy.
In conclusion, the telephone game is a very bad and misleading analogy of how the Bible was copied.
Sources include Dan Wallace's debate with Bart Ehrman.