Phillies outfielder and former Mariner, Raul Ibañez, was the subject of a now-infamous blog post that hinted at the possibility of him using steroids. Indeed, his home run numbers are jumping off the page, and that generally doesn’t sit well with fans in the steroid era. However, when statistics are applied correctly, this nothing out of the ordinary.
Ibañez is one of 42 players at least 34 years old that has reached 100 plate appearances so far this year. Entering the twilight of their careers, these players are often the target of steroid suspicions. I recorded each of these player’s home run paces this season in terms of how many standard deviations their pace was above their career averages (a standard deviation is a measure of how much a player’s stats are likely to vary). Of these 42 players, only one joins Ibañez in relative home run productivity, Johnny Damon at about 2.5 standard deviations above average.
Statistically, it’s tempting to crank out the probability that a player will match what Ibañez or Damon has done this year – that likelihood is less than 1% – and then question these players’ morals. But it should be noted that both these players have experienced a change in venue to ballparks that have proven to be more home run friendly. Bombs are flying out of Yankee Stadium at an unprecedented pace, boosting Damon’s true power this year by by enough to explain his surge. The change from Safeco Field to Citizens Bank may have influenced Ibañez’s home run figures by about 1.1 according to ESPN’s home run park factors, leaving his standard deviation score, known as a Z score, at 2.1.
Assuming that individual home run numbers follow a normal distribution (the bell curve), Ibañez’s theoretical likelihood of hitting homers at this scorching pace is about 1.7%, but the collective story is what is important. Before the season started, I would have been willing to bet (just a gentleman’s bet, mind you) that we would see at least one of these 42 players performing at this high a level in 2009, no steroids attached. That likelihood is about 50%. The fact that we’re not seeing more than one oldie hitting home runs at Ibañez’s rate shows that players are aging as we would expect them to.
While it is rare that a given player performs at an extremely elevated level of play, the likelihood that some player from a sample of many performs at this level is actually quite high. This year it just so happens to be Raul Ibañez.