The Long-Range Connective Sandpile (LRCS) model was applied to the Italian seismicity. The Hurst exponent and the power-law slope of the frequency-size distributions for the avalanches in the LRCS model and for earthquakes in Italy are investigated. This study shows the transition of the correlation coefficient between b and H values with different calculation window length. The result shows similar behaviors in the LRCS model and the Italy catalogue. The negative correlation between b and H values can be clearly seen when an appropriate window length is employed for various time series. We suggest that the negative relationship is caused by the increasing correlation length as the system accumulates enough energy. Also the calculation window length is an important index to display the intensity of the negative correlation between these two exponents. The appropriate window length can be related to the period time for the avalanches with various sandpile and seismicity time series.