For fun, I took some random players- Cristian Guzman, Ryan Zimmerman, Chipper Jones, Orlando Hudson, Mark Teixeira, Miguel Cabrera, Nick Johnson (2006) and Dmitri Young (2007)- and figured out at what clip they scored runs other than the times they hit HR's. Most scored runs somewhere between 24 and 28%. Cabrera and Young were the lowest at around 24%, I believe Zimmerman and Jones were 25%, Jones and Hudson were around 28%. NJ came out to around 32% and Guzman 34%.

Considering that Dunn's number was roughly 18%, I think tomterp is correct and some of his runs went to players who came in to pinch run for him late in games. Corey Pattrson's percentage was 42 so I think that may reflect tomterp's suggestion.