In voting with ranked ballots each agent submits a strict ranking of the form a > b > c > d over the alternatives, and the voting rule decides on the winner based on these rankings. Although this ballot format has desirable characteristics, there is a question of whether it is expressive enough for the agents. Kahng et. al. address this issue by adding intensities to the rankings. They introduce ranking with intensities ballot format, where agents can use both >> and > in their rankings to express intensive and normal preferences between consecutive alternatives in their rankings. While Kahng et. al. focus on analyzing this ballot format in the utilitarian distortion framework, in this work, we look at the potentials of using this ballot format from the metric distortion view point. We design a class of voting rules coined Positional Scoring Rules, which can be used for different problems in the metric setting, and show that by solving a zero-sum game we can find the optimal member of this class for our problem. This rule takes intensities into account and achieves a lower distortion. In addition, by proving a bound on the price of ignoring intensities, we show that we might lose a great deal in terms of distortion by not taking the intensities into account.