The simple answer for the best time to place a bet is whenever you think there is value in the line. However, there are other variables to keep in mind. This article is about when the best time to place a bet is, however to understand my conclusion you need to learn a little about line movement first.
Recall, a traditional UFC betting line takes the following form:
Nate Marquardt: -300
Yoshihiro Akiyama: +240
A correctly set line from the bookie's perspective means that regardless of who wins the fight, the bookie will make a profit. In the example of the above line, this occurs when roughly 73% of the money goes on Marquardt, and 27% is on Akiyama. If however the distribution of money on each fighter was split 50/50, and the bookie kept this line, then the bookie would lose money if Akiyama were to win.
Assuming the bookie is not in the business of gambling and is only interested in guaranteed profits, if the bookie observes that the distribution of bets will not allow itself to make a guaranteed profit at the present line, it will shift the line until it can make that guaranteed profit. In our above example, if significantly more money was coming in on Akiyama than Marquardt, then the line might shift to Marquardt -200, Akiyama +140. We can call such a shift vertical line movement.
There is a second way that lines can move. Again, let's assume that the line is Marquardt -300, Akiyama +240, and the distribution of bets is very strong in the 73% range for Marquardt, and 27% for Akiyama. As the time of the fight closes in, the bookie may want to attract additional holdouts to place a bet. They can do this by shifting the lines horizontally. This would be reflected in a movement from a line of Marquardt -300, Akiyama +240, to a line of Marquardt -290, Akiyama +250.
Note the difference between vertical and horizontal line movement. With vertical line movement, the line on one fighter improves and the other line gets worse, while with horizontal line movement the lines on both fighters improve.
So, how can any of this be applied?
The first conclusion is this: When you think a line is off, you should bet right away. At +240 Akiyama is being given a 29% chance of winning. If you are confident that his actual chances of winning are much closer to 40%, then you should capitalize on the +240 line right away. By not doing so, you risk the chance that the public will bet on Akiyama before you and move his line to +140, which to you is a line that has no value and warrants no bet.
The second conclusion is that when you feel the line set by the bookie is about right, you should hold off on betting. Assume you believe Akiyama has about a 30% chance of winning and the line is at +240. If you are risk neutral or risk taking and you really want to bet on it, then you should wait until closer to the fight to place the bet.
As the date of the fight approaches, and assuming you are correct that the line will not move vertically, you can only benefit by a horizontal line movement. (ie: If Akiyama is +240 a week before the fight and there is no vertical line movement, you can likely get him at +250 the day of the fight by virtue of horizontal line movement).
A final practical caveat to note is that most vertical line movement takes place very soon after the initial line is released. So, if you missed the opportunity to take advantage of vertical line movement as soon as the line was released, then it is almost always worthwhile to wait to place your bet until the day of the fight to take advantage of horizontal movement.