This research aims to compare the accuracy of the expectation of Earnings per Share (EPS) resulting from two models of expectation which are: Random Walk and Random Walk with Drift (or with deviations). The study has been relying on historical data published by Amman Stock Exchange. The research sample is amounting to thirteen banks for the period between2005 to 2014. This research seeks to measure the external factors flexibility influencing in determining each share profits from the achieved (EPS). The research resulted indicated that the second model is more accurate in predicting the Earnings per Share , and both of the first and the second models were biased towards reducing their expectations, as the signal of average error in the forecast was negative. The research indicated that there are external factors affecting the Earnings per Share of the profit (EPS), factors such as (inflation, interest rate, indicators of shares prices).