It's very hard to predict, I heard an article yesterday that said that the magma chamber is so large the volcano could erupt without an outside cause (e.g. earthquake). It definitely would affect the world too! After the Tambora eruption in 1815 lowered the global temperature by nearly a degree the next year was nicknamed "The Year Without a Summer" as snow fell in the summer in the Northern hemisphere. There's no doubt that Yellowstone would do the same.
Its quite possible that it will affect the world, and even living on the West Coast (Vancouver, BC), my prof who was teaching (EOSC114) Natural Disasters included as part of how it might affect "Cascadia" or us.
That said these are super rare, but the chances of it erupting is quite possible. Like all disasters, they are hard to predict but the more devastating, the longer the return period (time between 2 similar-events)