Monica Rathbun explains what happens when statistics go wrong:
Over Estimations of Rows (Actual > Estimated) leads to:
– Selection of parallel plan when a serial plan might be more optimal
– Inappropriate join strategy selections
– Inefficient Index Navigation (scan verses seek)
– Inflated Memory Grants
Read the whole thing. The optimizer doesn’t get to look at actual data when determining plans (save for something like adaptive query join processing, but that’s pretty rare), so statistics are its link to reality.