The Tokai to Kamioka (T2K) long baseline neutrino oscillation experiment was designed to make precise measurements of neutrino oscillations. It uses a muon (anti-)neutrino dominated beam produced at the Japan Proton Accelerator Research Complex (J-PARC) on the east coast of Japan, aiming towards the Super-Kamiokande (SK) detector 295 km west. The neutrino beam is sampled by the two near detectors ND280 and INGRID, 280 m downstream of production. These measure the neutrino flux and interaction cross-sections to reduce the impact of systematics for oscillation analyses. The work presented herein details the process of using ND280, INGRID, and external data to best constrain the predicted event rates at SK. The analysis proceeds by using a Markov Chain Monte Carlo method which simultaneously fits ND280 and SK data without assumptions on the underlying posterior probability density function. The two analyses detailed herein reduce event rate uncertainties at SK from 12-14\% to 2-4\%, enabling world-leading oscillation parameters to be extracted from T2K. Numerous run-by-run and detector-by-detector studies were performed and alternate models investigated, all of which were deemed compatible within uncertainty. This body of work has been included in the official T2K results presented in 2017 and 2018, and its use continues beyond that.