In 2008, June 3 was the last day of primaries. Clinton won South Dakota and Obama won Montana, but neither had enough pledged delegates to clinch the nomination outright. That cycle, the target was 2,117 delegate votes necessary for a majority at the Democratic National Convention. By the end, Obama had 1,794½ pledged delegates to Hillary's 1,732½ -- a difference of only 62 pledged delegates. However, Obama had the support of 478 superdelegates to Hillary's 246, and their numbers helped to put him well over the magic number of 2,117 delegates. That evening, all the news programs were calling Obama 'the presumptive nominee,' and four days later (June 7), Hillary conceded from the race.
This year, the last primary is being held on June 14 (Washington, DC), though many pundits agree that Hillary would become the presumptive nominee a week earlier, on June 7, when NJ and CA vote. This cycle, the target is 2,383 delegates. Hillary currently has 1,768 pledged delegates to Sanders' 1,497 -- a difference of 271 pledged delegates, which she looks to expand in the remaining contests left. Also, she has the support of 537 superdelegates to Sanders' 42, and with their numbers she just needs 78 delegates.
Anyway, the OP's point was that, If Sanders were to follow Clinton's example, he would also concede four days after the last primary on June 14, which would be June 18.
Furthermore, when Hillary dropped out on June 7, 2008, that gave the party 2 1/2 months to regroup and for the Clinton supporters to lick their wounds, until the convention in late August. If Sanders drops out on June 18, that only gives the party one month to collect itself, since the convention is in late July this year. But still, a month is better than nothing.
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