Other than in the countries where they have comprehensive testing (S Korea, China etc) the data on caseload is likely to be inaccurate because it completely depends on the country's testing criteria.
If they are only testing a certain sub population - those who end up in hospital or who have recently travelled back from an infected region (which is now basically everywhere) then once it becomes widespread, the official figures on cases will not be an accurate measure of the underlying caseload in the population.
But if the mortality rate from the disease (whatever it is) stays constant over time, you can use the number of deaths announced per day as a way to infer what is happening with the underlying caseload. If the average time from showing symptoms till death is 14 to 17 days, then the number of patients that die today tells you something about what the underlying caseload was 14 to 17 days ago.
The mortality rate may not stay totally constant over time - once the case load reaches a level where the health service is over capacity the mortality rate will rise and when it falls below that level it should fall down again. But it may be reasonable to assume these as one-off shifts at certain points, rather than the mortality rate varying a lot over time.
So to track the effectiveness of distancing measures brought in, look at what happens to daily deaths in about 2 to 3 weeks after they were brought in. What you hope to see is some change - if not a fall in absolute terms, at least a levelling off of the rate of growth, which suggests you've got it under control.
As we are still in the early stages this might be a 'noisy' indicator in that from day to day the numbers might bounce around a lot and also there will be some patients who became sick in the early stages and who have been in ICU for a long time and ultimately die several weeks later, so for a few weeks there will still be some deaths from the 'pre-measures' point, coming up in the daily death rates.
I think we should expect to see some very sharp rises in the daily death rates in the next couple of weeks, which will be alarming, but if the growth rate starts to fall after that, even if the deaths keep rising, that will suggest that the measures are starting to work, and should hopefully level off, and then start falling.