Tl;dr: About 80% of heroin users started on prescription opioids. This sounds bad, but actually the conversion rate from opioid on-label use to abuse is pretty low and the conversion from pill abuse to heroin is even lower.
* Rate of conversion from on-label opioid prescription to addiction ("opioid use disorder") is lowish; this metastudy[1] claims 8-12% on average, but the 95% CI is anywhere from 3-17% and I'm not sure what they're measuring the percentage of (i.e., long-term prescriptions might both be more represented in the data and have higher conversion rates) — I doubt 8-12% of people who get 3 days of vicodin for their wisdom teeth extraction develop an opiate use disorder. They also point out that some studies showed misuse rates below 1% and "significant variability remains in this literature." We should expect these rates to fall as tighter prescription quantities from the last several years impact "leftover" pill rates.
* The rate of conversion from prescription opioid addiction to heroin is low; 4-6% per the government.[2]
* Overall opioid-involved overdose annual deaths in the US rose from 8000 in 1999 to 47600 in 2017; of those, the prescription-involved number rose by 13600 deaths (+300%), from 3400. Conversely, the non-prescription-involved deaths rose from by 26000 deaths (+465%), from 4600.[3](Figs 3-4) 26000/39600 = ~66%. (The population has also grown about 17% over that period, but that doesn't change the calculus too much.)
* Therefore: the overall growth pattern in opioid deaths in the last two decades is largely accounted for by heroin and other non-Rx use, which are a tiny population with a very high (and rising) death rate. The rising death rate is mostly due to the surge in black market sale of fentanyl as "heroin."[3] (esp. figures 4-5 and associated text) (Perhaps as a result of DEA and other restriction on the supply of the relatively safer, but less dense, heroin, and restriction on supply of the vastly safer prescription opioids.)
* Notably, the number of non-fentanyl-involved prescription opioid-involved deaths has actually been in decline since 2011![3] (fig. 4.), despite a rising population. Let me echo that since it's really important: prescription opioid-involved overdose, ex fentanyl, both in number and per capita rate, HAS BEEN IN DECLINE SINCE 2011! Why doesn't any news story on opioids in the US headline with that? The primary reason the overall prescription opiate-involved death rate hasn't tracked that decline is rising co-(ab)use with illicit fentanyl, and its relatively higher death rate.
If we could wave a magic wand and wipe (illicit) fentanyl off the earth, our annual opioid death rate would fall by something like half.
[1]: https://www.ncbi.nlm.nih.gov/pubmed/25785523
[2]: https://www.drugabuse.gov/drugs-abuse/opioids/opioid-overdos...
[3]: https://www.drugabuse.gov/related-topics/trends-statistics/o...