My response to a recent comment:
To a certain extent, the commentor was correct in saying that everyone has their own individual hold; I have said the same. Just remember that every bowhold that we recognize as “Russian” or “Franco-Belgian” has its roots from that region’s way of originally teaching their bowholds.
Welcome to America, the great melting pot of cultures; we now run into people who still strictly hold to these traditions, therefore we run into slight differences in how the bow is held. Tradition is a powerful thing, and in the bowhold especially because, when a teacher discovers that his/her way of holding it works fabulously, they therefore doggedly teach it to their students (though some, like myself, tend to be more flexible and observant of the student’s personal make-up, individual progress, and comfort – still almost all of my students are bowing like I do; observation and imitation are powerful teaching-tools).
The bowhold is actually a very complex thing, because the bow is the part that is responsible for emotion (barring vibrato, slight pitch nuances, etc. in the left hand). That is why we spend such a huge amount of effort both teaching it and mastering it ourselves.
As for the work of the thumb, a lot of teachers spend time on this (I have found it to be most successful in myself and my students), and others spend a lot of time on the weight of the index finger (which I have also found to be successful) – all in combination with the efforts of the pinky, too! The reason we spend so much time on one or more of these digits is because they have a specific function in control of that awkward stick we call the bow. They help us keep the tip sounding as strong as the frog, they help in keeping the bow straight, in keeping the sound full and little scratches/wavery bounces out of the stroke, they help in control of dynamics, they help in more complex bowing techniques such as spiccato or ricochet, and much, much more.
This why we spend so much time agonizing over the bowhold. Each finger has a responsibility to contributing to the whole production of a player’s unique and individual sound.