Sorry to add an addendum to my own post.
The number of horses entering the Derby and the Preakness with previous negative numbers have shrunk substantially over the last 5 years compared to the previous 5 year period.
From 2010 to 2014 there were a total of 9 Derby entrants and only 6 Preakness entrants with a previous negative number.
From 2005 to 2009 there were a total of 18 Derby entrants and 19 Preakness entrants with a previous negative number.
The generic numbers show twice as many horses with previous negative numbers were entered in the Derby in the 2005-2009 years versus the last 5 years.
The generic numbers show three times as many horses with previous negative numbers were entered in the Preakness in the 2005-2009 years versus the last 5 years.
So, in the last 5 years, only 15 horses entered the Derby and Preakness with a previous negative number.
The previous 5 year period, 2005-2009 there were 37 horses entered in the Derby and Preakness with a previous negative number.
Sorry to get so convoluted.