MLB and the MLBPA have jointly released the results from the most recent batch of COVID-19/Coronavirus testing, which is for the week ending Thursday, July 16, 2020 (yesterday).
MLB says that of the 10,548 tests collected and sampled from people in the “Monitoring Testing” category — those who are not currently in the COVID-19 protocol due to a positive test or other issue — there were six new positive tests. Of those six, 5 were players and 1 was a staff member.
That is, I think, about as good a result as one could hope for, under the circumstances. The overall new positive rate is 0.05%, and if MLB can keep cases at or below that level going forward, the 2020 season would be much more likely to take place.
Of course, this is at a time when players are not traveling, and once traveling starts up, one would assume the risk of transmission would be higher, and positive rates would increase. At this point, though, all we can do is take it one week at a time.