Online rating system serves as an indispensable building block for many web applications such as Amazon, TripAdvior and Yelp. It enables production quality estimation via aggregate ratings (a.k.a. wisdom of the crowd) as well as product recommendation via inferring user preference from ratings, etc. Previous studies showed that due to assimilate-contrast effects, historical ratings can significantly distort user's ratings, leading to low accuracy of product quality estimation and recommendation. To understand assimilate-contrast effects, an "accurate'' model is still missing as previous models do not capture important factors like rating recency, selection bias, etc. Furthermore, an analytical framework to characterize product estimation accuracy under assimilate-contrast effects is also missing. This paper aims to fill in this gap. We propose a mathematical model to quantify the aforementioned important factors on assimilate-contrast effects. Our model attains a good balance between model complexity and model accuracy, such that it is neat enough for us to develop an analytical framework to study assimilate-contrast effects. Based on our model, we derive sufficient conditions, under which the product estimation and collective opinion converges to the "ground-truth''. These conditions reveal important insights on how the aforementioned factors influence the convergence and guide the online rating system operator to design appropriate rating aggregation rules and rating displaying strategies. To demonstrate the versatility of our model, we apply to rating prediction tasks and product recommendation tasks. Experiment results on four public datasets show that our model can improve the rating prediction and and recommendation accuracy over previous models significantly.