Our earlier article, Boundaries of the Prediction Model in Tax Law’s Substantial Authority, analyzed the substantial-authority standard, identified factors that taxpayers and their advisors can consider in determining whether substantial authority supports a reporting position, distinguished substantial-authority predictions from other types of predictions, and considered how substantial authority affects advisors’ ethical responsibilities. In short, that article presented a qualitative analysis of substantial authority. This Article presents a quantitative model of tax law’s substantial authority that introduces the concepts of horizontal substantiality and vertical substantiality. The prediction model places substantial authority and the other reporting standards on a zero-to-one horizontal scale that depicts the likelihood that a position will be upheld. Support for a reporting position satisfies horizontal substantiality if it provides the reporting position the required threshold likelihood of being upheld, which is generally thought to be around 40%. Vertical substantiality derives from substantial authority’s weight-of-authority method (i.e., the weight of positive authority in relation to contrary authority). The Article shows how to determine a value for vertical substantiality and convert it to a value on the horizontal scale and apply the well-reasoned method to determine whether substantial authority supports a reporting position. The Article presents the substantial-authority prediction model in a simple formula: H=V/(V+1)+R. The Article then illustrates how taxpayers and their advisors might consider applying the prediction model. That exercise reveals some of the model’s shortcomings, which provide opportunities for additional work in this area, but, more importantly, demonstrates how the model clarifies the concept of substantial authority and some of its various components.