The graph above shows the mass of the W boson and the mass of the top quark according to the recently determined world average of the most precise measurements to date, with the red ellipse showing the one standard deviation range of those masses given current uncertainty in the world average measurements. This is about a factor of four to five more precise than measurements as of the year 2000.
For complicated reasons related mostly to interactions between the Higgs boson, the W boson and the top quark in the Standard Model of Particle Physics, there is a linear relationship between the W boson mass and the top quark mass that depends upon the mass of the Higgs boson.
The blue line cutting diagonally across the chart shows the expected linear relationship of the W boson mass to the top quark mass at a currently estimated Higgs boson mass. The diagonal line in the chart above shifts to the right at higher Higgs boson masses, and to the left at lower Higgs boson masses. But, the location of the blue line in the chart isn't terribly sensitive to the Higgs boson mass. The blue line shown in based on the currently estimated Higgs boson mass which is known with about a 1% precision - which is allows for considerable accuracy because a roughly 20 GeV error in the Higgs boson mass translates to a roughly 1 GeV shift on the top quark mass axis above, and so the uncertainty in the Higgs boson mass measured shifts the blue line only about +/- 0.05 GeV on the top quark axis in the chart above.
Since the one standard deviation red ellipse around the current best estimates of the W boson and top quark masses touches the blue line, this means that the relationship between these three experimentally measured physical constants is within one standard deviation of the theoretically expected relationship, confirming the Standard Model.
This relationship also suggests that we should expect more precise future W boson mass measurements to favor the low end of the current error bars on this measurement (a difference from the central world average value of about 0.03%), while future measured top quark mass may be just a tad higher than the current best estimate (which is known with a precision of +/- 0.6%), although probably not quite as close to the error bar boundaries for that measurement. This is because, with greater precision, I expect that the data will more precisely confirm, rather than contradict the Standard Model prediction.
But, if the world average values of the W boson mass doesn't shift a bit lower as measurements of this value become more precise, this may be a signal of beyond the Standard Model physics. However, if the average value remained unchanged, the error margins would have to shrink by another factor of five (as much as they did in the last twelve years or so), in order for this discrepancy to meet the threshold for considering an experimental result a new discovery, and this is likely to take more than twelve years to happen again given the kinds of experiments that are on the drawing board today.
Note that the top quark mass estimate is actually much less precise on a percentage basis than the W boson mass determination by a factor of about twenty or so. It doesn't intuitively look that way on the chart because the X and Y axis have different scales even though they are both in the same units.