I found the first part of this discussion with the first chart confusing. What is expected value? Is it the number of 4 and 5 star funds expected based on the number of Vanguard Funds? The observed is the actual number?
Your statement - "What does the chart suggest? Vanguard is less likely to be “spectacular” than the numbers would suggest but more than twice as likely to be “really good.” Four stars means really good.
You conclude that there results are not spectacular? If my interpretation of your terms and chart are correct then I would argue that landing 65 funds in 4 and 5 star territory, when statistically only 34 are expected, is a rather spectacular result. 18 rather then 7 since 2002 is also impressive. Considering that the presence of low expenses is the one factor that it is most consistent and reliably related to performance makes Vanguard one of the best fund families.
I'm not a big Vanguard investor because of the other issues with their administration of accounts - making you open two accounts, one for Vanguard funds and one for non-Vanguard funds and stocks. Some silly practices: Requiring you in your Vanguard fund account to treat a purchase as an exchange when you use funds from a money market account; when you make a purchases of a non-Vanguard fund it is not an exchange and you just indicate the amount you want to purchase; calling holdings held in an account "accounts."
Nevertheless there funds performance is damn good overall.
Comments
There is a user guide which you will find under the "Resources" heading in the blue bar, above. I suggest that you consult that guide to find out how to properly reply to an existing discussion.
"Expected value" is just the number of four and/or five stars you'd expect from any random collection of funds comparable in size to Vanguard's offerings. If you took any random collection of 112 funds, you'd expect to find 11 five-star and 36 four- or five-star funds in the pot. (Some of Vanguard's funds are as-yet unrated fund, which is why the "expected" number in the chart is a bit lower than the quick calculation above.)
"Spectacular" was shorthand for "five star." "Really good" was a shorthand for "four star." I could accept "damn good" as a description as well.
As ever,
David