I thought a White Labs vial had 70-90 billion cells. For 5 gallons of 1.068 wort wouldn't one need more like 250 billion cells? Mark, are you saying this isn't true? Or is the yeast from White Labs so healthy and ready to go that the cell count doesn't doesn't matter? Or am missing something else? Will there be 250 billion cells by the end of the lag phase? If so, why is it considered best practice to make starters?
If we are talking about achieving maximum cell density in a 5-gallon (19L) batch, well, it's a lot more than 250 billion cells, more like 3.8 trillion cells (200 billion cells per liter). That's why I take the values that are quoted by yeast calculators with a grain of salt.
Most home brewers assume that yeast biomass growth is linear when it is actually exponential. Yeast cells bud into two cells roughly every 90 minutes after the exponential phase has been entered. The difference between 90 billion cells and 250 billion cells is log(250 / 90) / log(2) = ~1.5 replication periods after pitching, where a replication period is roughly 90 minutes long.
If the maximum cell density for 5-gallons (19L) batch is 3.8 trillion cells, then the amount time necessary to reach maximum cell density starting with 90 billion cells is:
log(3,800 / 90) / log(2) = ~5.4 replication periods or 5.4 x 1.5 = 8.1 hours
If the maximum cell density for 5-gallons (19L) batch is 3.8 trillion cells, then the amount time necessary to reach maximum cell density starting with 250 billion cells is:
log(3,800 / 250) / log(2) = ~4 replication periods or 4 x 1.5 = 6 hours
What pitching a larger number of cells does when pitching high gravity wort is allow for cell loss due to osmotic pressure. Osmotic pressure is a phenomenon that causes water to be drawn to the side of a semi-permeable membrane that has the highest level of solute, which is the wort. This loss of water causes the cells to lose something known as turgor pressure. The loss of turgor pressure is known as plasmolysis. Turgor pressure pushes the cell membrane against the cell wall. Loss of turgor pressure causes the cells to shrink, resulting in shock, if not outright death.