HTTPS aims at securing communication over the Web by providing a cryptographic protection layer that ensures the confidentiality and integrity of communication and enables client/server authentication. However, HTTPS is based on the SSL/TLS protocol suites that have been shown to be vulnerable to various attacks in the years. This has required fixes and mitigations both in the servers and in the browsers, producing a complicated mixture of protocol versions and implementations in the wild, which makes it unclear which attacks are still effective on the modern Web and what is their import on web application security. In this paper, we present the first systematic quantitative evaluation of web application insecurity due to cryptographic vulnerabilities. We specify attack conditions against TLS using attack trees and we crawl the Alexa Top 10k to assess the import of these issues on page integrity, authentication credentials and web tracking. Our results show that the security of a consistent number of websites is severely harmed by cryptographic weaknesses that, in many cases, are due to external or related-domain hosts. This empirically, yet systematically demonstrates how a relatively limited number of exploitable HTTPS vulnerabilities are amplified by the complexity of the web ecosystem.