Sampling, because tracing every request is not affordable

Full-fidelity tracing on a busy service is a considerable volume of data and a considerable bill, and almost all of it describes requests that were fine.

// head-based: decide at the start, propagate the decision
$sampled = random_int(1, 100) <= 1;      // 1%

// tail-based: buffer, then keep what is interesting
//   every trace with an error
//   every trace slower than the p99
//   1% of the rest
//
// tail-based needs a collector that can hold a whole trace.

Head-based sampling is simple and throws away the slow requests along with everything else, which is exactly backwards — the interesting traces are the rare ones. Tail-based keeps what matters and requires a collector holding every span until the trace completes, which is real infrastructure. Propagating the sampling decision is what keeps a trace whole; a service that decides independently produces traces with holes in them.