In the public sector, contracting depends on the competition principle; the selection of contractors is based on bidding price. Since the bidding with the lowest price is the winner, the contractors' thoughts that the probability of winning increases by decreasing the bid price. Studies have proven that many factors can improve the probability of winning, as: the total bid price, the number of bidders, knowing the competitors, and the project size. This study aims to build a statistical mathematical model to improve the contractor's opportunity award bidding for governmental construction projects in Jordan, and will be conducted as a quantitative study that includes literature-based research and a questionnaire. In addition, a sample of bidding documents for 30 construction projects collected from the governmental tendering department as a case study are examined. The questionnaire results generate sample checklists for factors that affect the probability of winning. Based on the governmental tendering data, a multiple stepwise regression applied to construct a mathematical model can help any contractor win a bid. The results of questionnaire shows that the probability of winning is directly affected by the total bid price, while the model results shows that the probability of winning is reversely affected by the number of competitors and the number of common contractors with no intention to the total bids price. This research has three limitations: the sample size limitation, in statistical analysis considering the curve as a normal distribution curve while it may be not , and finally the number of projects collected from governmental tendering department consider as a third limitation. More of this study may be beneficial to the construction industry regarding projects of greater value and to help more companies win more bids.