During our work, we developed a new, simple method to show the effects of fertilization on yield, which can both be applied over the long term as well as in series of independent experiments.
During the testing of this method, at the experimental farm of the Debrecen University Center for Agricultural Sciences at Látókép on a chernozem soil with lime deposits, we examined the fertilizer reaction of maize hybrids between 1989 and 1994. The treatments were: winter tillage, plant density of 70-80 thousand, unfertilized, N 120, N 240 kg/ha fertilized treatments, long term experiments using Dekalb 524 and Volga SC hybrids in long term experiments.
Four parameters are shown in the model. In the examined period TRmax represents the greatest yield in the fertilized treatments, NT the yield in unfertilized treatment, k the „efficiency of fertilizer” to NT and b the depression-coefficient, where the expected value is zero. The expected grain yield of the fertilized treatments (Y), in the function of the unfertilized grain yield (x) is the following:

The parameters were determined using the Monte Carlo method, in the optimizing process the sum of deviation square was minimized. The correct conformation of the functions was determined by the greatness of the R-value and the standard error. We found that during six years of testing, the tendency of fertilization efficiency was similar in the case of both hybrids. There was an unfavorable weather interval and, in these years, the yields were low, fertilization did not have an effect and moreover, in extremely bad conditions resulted in an obvious yield decrease. With the  improvement of conditions, which in the case of our country means an increase in precipitation, the efficiency of fertilization increases and reaches its peak at 13-14 t/ha. At this point, the yield increasing effect of fertilization is 4-4,5 t/ha. If the yield of the unfertilized treatments increases from 8-9 t/ha, then the efficiency of the applied fertilizer decreases.
Most likely, the k and b parameters depend on the soil of the experimental location (nutrient and water management) and on the amount of  pplied fertilizer and the characteristics of the  hybrid. With the increase of fertilizer dosage the k-parameter also increases. The greater value though does not obviously mean a more favorable situation. It is true that in medium and good years this means great fertilizer efficiency, but in low or extreme precipitation conditions it also means greater risk. With the increase of the k-parameter, the yield deviation also increases which, from a cultivation point of view, is quite unfavorable. If the value of the b-parameter is other than, zero then the effect is clearly unfavorable, because with the increase of this value, the yield decrease is also greater. The fertilizer reaction of the two examined hybrids can be well characterized by these two hybrids.
Examining the six years, our created model estimated the effect of fertilization on the yield accurately and with a high degree of safety. Both in highly unfavorable and extremely good years, it gave an exact estimate. In our opinion, it can be used well to evaluate the effects of fertilization on yield in the future.