Number of visits before and after is in fact a good metric, imo.
It could merely indicate that the "SEO" had purchased 'hits' from some pointless "website traffic scheme"
It's about as much use as reporting that "We have greatly improved your Alexa rank" while neglecting to also point out that the Alexa toolbar had been installed on all the computers used by company staff and their 'home page' is set to the company website.
Traffic "before and after" statistics is merely fluff number UNLESS it is qualified with corresponding increase in conversions for the same period.
I could write a simple 'bot' with a set of user agent ID strings that used rotating proxies such as the 'Tor network', to visit a URL or series of URLs to simulate an "increase in visitors".
Without a qualifier that determines it as being useful traffic it is just a number. A truly clued up client would be asking "How much extra income are you creating for my business"
Bank managers and accountants don't give a toss about traffic numbers, toolbar PR and 'back links', they deal in tangibles. When the "Star Trek" utopia happens and no one cares about monetary wealth, THEN you can consider such ephemeral numbers as being the "currency of success". Until then real world currencies rule the roost.
Would YOU accept you client saying that they told an extra one hundred people about you this month, and that's your payment for getting my site more people looking at it???
Funny how that works isn't it?
Go to google.com and search it for " 5 Ways to Prove to the Client that the Traffic Will Come" that is a very useful post from Moz Blog. And I think the title of this post is enough to admire this post
Then you are truly misguided.
MoZ articles are there to persuade you to buy their "tools", you know ... the ones you have to part with REAL money for, thus improving the MoZ bank account.