The distribution of point differentials at the end of NBA basketball games shows that a tie is more than twice as likely as either team winning by one point. A possible simple explanation from the comments:
1. Teams down by 2 late are most likely to take a 2 point shot, while teams down by 3 will most often take a 3 point shot. The team's choices make ties a likely outcome.
2. A Tie is a stable equilibrium, while other scores aren't. If a team leads with the ball, they will be fouled, preventing the game from ending on that score. IF a team has the ball with a tie, they'll usually be allowed to wait and take the last shot, either winning the game or leaving it as a tie.
Update: This study about golf putting seems to have something in common with the overtime finding.
Even the world's best pros are so consumed with avoiding bogeys that they make putts for birdie discernibly less often than identical-length putts for par, according to a coming paper by two professors at the University of Pennsylvania's Wharton School. After analyzing laser-precise data on more than 1.6 million Tour putts, they estimated that this preference for avoiding a negative (bogey) more than gaining an equal positive (birdie) -- known in economics as loss aversion -- costs the average pro about one stroke per 72-hole tournament, and the top 20 golfers about $1.2 million in prize money a year.