We used a boundary line approach to enclose values on a scatter plot of treatment yield against control yield. The boundary line represents the maximum value of a dependent variable that can be achieved at different values of the independent variable. Existence of large number of points far below the boundary function is often associated with suboptimal field management. However, studies used in our study were designed and managed by researchers so the yield gap is mainly attributed to the omitted nutrient.

We determined, from the fitted yield response curve, the marginal maize grain yield increment for each additional kilogram of nutrient to determine the level of maximum nutrient application that is economically acceptable to farmers. This was based on the average nutrient/maize grain price ratios for the last 5 years (2008-2013). To be profitable, each kilogram of applied nutrient should result in at least 4.8, 14.5 and 5.4 kg additional grain for N, P and K respectively. The potentially profitable points are shown as shaded circles while the open circles are all unprofitable. Of the 328 fields tested, the potentially profitable ones (represented by shaded circle datapoints) with at least 100% MRR are 64% for N, 52% for P and 38% for K, while only 45%, 35% and 26% attain an MRR of 200%. There are 29-54 % and 10-48% of cases where K is profitable at value cost ratios of 1 and 2, respectively, and only two sites, Mbinga and Kasungu showed promise. For P, 22-77% and 17-60% of the cases were profitable at VCR of 1 and 2, respectively, with most responsive sites being Pampaida, Sidindi, Mbinga and Kasungu. For N, only one site, Kiberashi in Tanzania, had a much lower profitable cases than the other sites, being only 28% compared to at least 49% in the other sites. Even at a VCR of 2, profitability of N application reached upto 80% in Pampaida and 74% in Mbinga.

Yield gap attributed to omission of K (a), P (b) and N (c) at different levels of control yield within best preforming fields in SSA. Yield gap is gap between dotted line (the response under omission) and the continuous line (the response under NPK). Open symbols are NPK yields where N, P or K are not profitable and shaded circular symbols where these nutrients are potentially profitable (i.e., yield at least 0.48, 0.44 and 0.32 t/ha more yield than omission treatments for N, P and K, respectively). Plus symbols are omission treatment yields.