Chance, Spread and What to Expect
A Table Instead of a List
Last timeHow Far From Expected
Two quantities at once need a table of weights rather than a list, and independence is the strong claim that the table is nothing more than its own two margins multiplied.
Everything so far has concerned one quantity. In practice there are always
several, and the interesting questions are about how they relate. Does a slow
request make the next one slow? Does a user who clicked once click again? Does a
model that is confident tend to be right?
The object needed is a small extension of the first lesson. With one quantity the
outcomes formed a list. With two, an outcome is a pair, so the weights form a
table.
| next was fast | next was slow | next failed | row totals | |
|---|---|---|---|---|
| request was fast | 0.45 | 0.10 | 0.05 | 0.60 |
| request was slow | 0.15 | 0.12 | 0.03 | 0.30 |
| request failed | 0.02 | 0.03 | 0.05 | 0.10 |
| column totals | 0.62 | 0.25 | 0.13 | 1.00 |
The two rules are unchanged. No entry is negative, and the whole table sums to
one. Everything there is to know about the relationship between the two
quantities is already sitting in that table; the rest of this lesson is about
reading it.
Margins
Often only one of the two quantities is wanted. What is the chance this request
is slow, regardless of what the next one does? That is the sum of a whole row,
and the row and column totals are called the margins, from the practice of
writing them in the margin of the table.
The margins are what most reporting shows. A dashboard that gives the failure
rate for this hour and the failure rate for the next hour has shown two margins
and thrown the table away, and the discarded part is exactly the part that says
whether failures arrive in clusters. Two services with identical margins can
behave completely differently: one fails at random moments and the other fails in
bursts that take out a whole minute. The hourly numbers are the same. The
experience of using them is not.
The lesson stops here
4 more paragraphs to go
You have read the opening. The rest of the argument, the problems that check whether it landed, and the lines worth keeping at the end all come with a plan.
The first lesson of every course in the library reads the whole way through, free, so you can see exactly what the rest of them are.
See the planThe contentsThis is the reading half
Starting the course gives you your own copy of it. Every idea on every page has problems standing under it, marked with a reason rather than a tick, and any sentence you do not believe can be opened and argued with. None of that can happen on a page nobody owns.
The contents