Many observable Standard Model predictions have both experimental values and theoretically predicted values based on other Standard Model constants. The Higgs boson mass was the last (non-neutrino) constant in the Standard Model to be observed and this has allowed for a global fit of all of the electroweak force influenced observables in the Standard Model in a way that minimizes overall experimental measurement deviation from Standard Model predictions.
This analysis has now been done. All of the dozens of Standard Model observables in the fit are consistent with each other. A global fit nudges some of the mean values of the constants while reduciing the uncertainty in many of them significantly. Using a Higgs boson mass of 125.7 +/- 0.4 GeV (which is assumed to be a Standard Modle higgs boson), some of the values most notably nudged by the inclusion of the Higgs boson mass in the fits are:
W boson mass: 80.385 +/- 0.015 GeV => 80.367 +/- 0.007 GeV (change is 1.2 sigma)
Z boson mass: 91.1875 +/- 0.0021 GeV => 91.1878 +/- 0.0021 GeV (change is 0.14 sigma)
Top quark mass: 173.18 +/- 0.94 GeV => 173.52 +/- 0.88 GeV (change is 0.36 sigma).
The best fit for the strong force coupling constant at the energy scale equal to the square of the Z boson mass is 0.1191 +/- 0.0028.
The inclusion of the Higgs boson mass in the fits did not alter estimates of the charm quark mass or bottom quark mass.
The greatest tensions in the fits relate to b meson observables. One is 2.5 sigma above the Standard Model prediction and another is 2.4 sigma below the Standard Model prediction. The nineteen other observables included in the global fit were all within two sigma of the Standard Model prediction in a global fit of the experimental data and mostly much closer. These tensions are present with or without including the measured Higgs boson mass which slightly reduces those tensions.
Implications for possible Higgs boson mass formulas:
This makes the mean value of the quantity (2W+Z)/2 equal to 125.96 GeV +/- 0.004 and makes the value of (W+top quark mass)/2 equal to 126.94 GeV +/- 0.44. Both combinations have been suggested as Higgs boson mass formulas.
The former is 0.26 GeV from the measured Higgs boson mass, which is about 0.65 sigma, either considering only the uncertainty in the Higgs boson mass and considering all uncertainties combined since the W and Z boson masses are known so precisely.
The latter is 1.24 GeV from the measured Higgs boson mass about 3.1 sigma considering only the uncertainty in the Higgs boson measurement, and about 2.1 sigma considering all of the uncertainties, which are similar in size for both the top quark and Higgs boson mass values.