You can determine your odds of getting a permit for all permit rivers during the permit season by going to this link.
There you will find graphs that I created and turned over to Chris Shackleton of Dreamflows to perpetuate going forward since he has an excellent engine for graphing historic river flow averages. He did an amazing job replicating and automating my work.
Your odds can be determine by consulting the blue line with blue dots. That graph line uses the right axis. Note that the right axis ranges from 0% chance at the bottom to 100% chance at the top. The odds were originally calculated by Richard Ferguson of the Rocky Mountain Canoe Club then recalculated by Chris Shackleton using updated numbers in about 2015.
For example, the Middle Fork of the Salmon graph is shown below and can be linked by the below address.
For the Middle Fork your chances of getting a permit during the permit season(between the solid brown vertical lines) are defined by the "U" shaped blue line ranging from near 0% up to 33% at the end of the permit season. Your odds are very poor during the peak permit season(dashed brown vertical lines).
Good river flows are identified as between solid green horizontal lines. Optimal river flows are identified as between dashed green horizontal lines.
Other significant details and dates are included on each graph for each river.