Wheat is a staple crop that is critical for feeding a hungry and growing planet, but its nutritive value has declined as global temperatures have warmed. The price offered to producers depends not only on yield but also grain protein content (GPC), which are often negatively related at the field scale but can positively covary depending in part on management strategies, emphasizing the need to understand their variability within individual fields. We measured yield and GPC in a winter wheat field in Sun River, Montana, USA, and tested the ability of normalized difference vegetation index (NDVI) measurements from an unoccupied aerial vehicle (UAV) on spatial scales of ~10 cm and from Landsat on spatial scales of 30 m to predict them. Landsat observations were poorly related to yield and GPC measurements. A multiple linear model using information from four (three) UAV flyovers was selected as the most parsimonious and predicted 26% (40%) of the variability in wheat yield (GPC). We sought to understand the optimal spatial scale for interpreting UAV observations given that the ~ 10 cm pixels yielded more than 12 million measurements at far finer resolution than the 12 m scale of the harvester. The variance in NDVI observations was “averaged out” at larger pixel sizes but only ~ 20% of the total variance was averaged out at the spatial scale of the harvester on some measurement dates. Spatial averaging to the scale of the harvester also made little difference in the total information content of NDVI fit using Beta distributions as quantified using the Kullback-Leibler divergence. Radially-averaged power spectra of UAV-measured NDVI revealed relatively steep power-law relationships with exponentially less variance at finer spatial scales. Results suggest that larger pixels can reasonably capture the information content of within-field NDVI, but the 30 m Landsat scale is too coarse to describe some of the key features of the field, which are consistent with topography, historic management practices, and edaphic variability. Future research should seek to determine an ‘optimum’ spatial scale for NDVI observations that minimizes effort (and therefore cost) while maintaining the ability of producers to make management decisions that positively impact wheat yield and GPC.