Surprisingly, I haven't been able to get any reliable numbers on this point. Of the ~5.9 million Jews that were murdered in the Holocaust, how many died from conditions in concentration camps and ghettos (starvation, disease, being worked to death, etc.) and how many died from mass murder (e.g. the Einsatzgruppen, gas chambers, etc) ?
I found numbers for the Einsatzgruppen (apparently it was ~1.3-1.5 million Jews, depending on which source you look at), but once you get to the camps nobody seems to have concrete numbers. Is this an answerable question? I would have thought you could get a rough estimate by comparing death statistics from labour camps (e.g. Buchenwald, Sachsenhausen) with death statistics from death camps (e.g. Treblinka, Belzec). Although, Auschwitz complicates things, since it was both.
Does anyone know if there are statistics on this?
If there is a lack of distinction in some sources that is likely due to the fact that "death because of poor conditions" is not the same as "the death of the person was not wanted or just due to circumstance". Extermination in the context of the Holocaust does not only refer to an act of murder taking place. The term extermination when talking about the holocaust also means "Vernichtung durch Arbeit" ("Annihilation/extermination through work") meaning that people dying due to starvation or exhaustion from hard labor was no accident but intended. This is also mentioned in the infamous protocol of the Wannsee-conference.
Under proper guidance, in the course of the final solution the Jews are to be allocated for appropriate labor in the East. Able-bodied Jews, separated according to sex, will be taken in large work columns to these areas for work on roads, in the course of which action doubtless a large portion will be eliminated by natural causes. The possible final remnant will, since it will undoubtedly consist of the most resistant portion, have to be treated accordingly, because it is the product of natural selection and would, if released, act as the seed of a new Jewish revival.
So I'm sorry for not being able to provide some numbers but I hope explaining the terminology helps making more sense of how the numbers came to be.
Source:
Roseman, Mark - The Villa, The Lake, The Meeting: Wannsee and the Final Solution. (2002)