Hi there, didn't see this until just now.
The metric that is improving is the latency experienced by a user.
Imagine that you have a web app that takes one second of server CPU time to render a page, and you have three servers which process three hits a second in total. All three servers are thus on 100% CPU load, dealing with one hit a second each.
Each time somebody visits your site, they are going to experience a 1 second latency (in addition to communication latency), as they wait for one of your servers to build the page.
If you then optimize your code so that it completes in a third the time, 333ms, then your servers are going to suddenly be at 1/3 load; they execute their one query for 333ms, and then sleep for 667ms.
Not just that; but the user now only has to wait for 333ms for the page to render on the server, so the site gets a lot more snappy for them.
Then you can shut down two servers leaving one; it will sit on 100% load, but you still keep the shorter 333ms latency experienced by your users.
You are doing the same amount of work as before - 3 hits a second. But previously, when the tasks took 1s each, three would be running in parallel, each being completed more slowly. With the faster run time, they are running in series, being completed quickly before switching to the next one.
Now, this does not apply if your requests are queuing. Because you're not able to do any more work than before (after shutting down the other two servers), if your hits/s exceeds the capacity of your servers to deal with them, the backlog will grow just as fast as it normally would have, and the latency caused by this will sky rocket.
Your example doesn't fit because multiple machines aren't ever used to process front end web requests in parallel; you don't render half of a template on one machine, and the other half on another, for example. If you can set up a system like this and see gains from it, then what I've written above will not apply.