Odds of Rizzi Getting Permanent Job and, If So, What Type of Contract
I will make a few more assumptions.
First, my odds assume the Saints will go 1-2 over the next three games. If we lose all three, the odds plummet. If we win all three, the odds soar. If we go 2-1, the odds are higher.
Second, as I indicated in my original post, Loomis will likely be picking the next head coach if he remains as GM, and the likelihood is high that he remains GM. Gayle will have to approve, but the Saints are an incredibly insular organization, Gayle already has a relationship on some level with Rizzi, and usually after the season the players rally around and promote the interim coach to get the permanent job. See Antonio Pierce in Las Vegas.
Third, the players should never pick their new coach. It is one thing to listen to what the players have to say. If they say negative things, that's really important and a big red flag. But the players cannot be the dominant voice in the process.