Jeter and Bautista Defying the Odds
April 29, 2004
With Derek Jeter enduring the slump of his career and Danny Bautista surprising everyone except maybe himself, it's time to churn the numbers to examine the rarity of these feats.
Derek Jeter's slump, currently at 0 for 32, got me thinking about the odds of such a thing. Assuming all other things constant (pitchers, ballpark effects, etc.), a simple calculation reveals that a hitter like Jeter, with a .315 career batting average, only has a 0.000552% chance of going hitless in 32 straight ABs. In other words, over his career, the odds of going hitless in any sequence of 32 consecutive ABs (even if it spans 2 seasons) for Jeter (or any .315 hitter) is just 1 in roughly 180,000.
Do those odds sound too high? Think of it this way - a .315 hitter only has a 32% chance of going 0 for 3 (failing to get a hit 68.5% of the time 3 consecutive times = 0.3214). 0 for 6? Just a 10% chance. 0 for 10? Only a 2.3% chance. You can see how fast the odds diminish. Keep in mind that 1 in 180,000 doesn't mean that only 1 in 180,000 .315 hitters will accomplish this feat. It means that in 180,000 sequences of 32 consecutive ABs, a .315 hitter will only go hitless once. So, if Jeter stuck around 300 years and kept hitting .315, the odds are that he WOULD endure an 0 for 32 slump (which would be understandable given the likely arthritic problems of a 300 year old).
Since Jeter is a little shy of 5,000 career ABs, the odds that HE would have endured this 0 for 32 slump in HIS CAREER so far (assuming he constantly hit .315) is just 1 in 36, or 2.8%. This number is much easier to register but still very small. Needless to say, Derek Jeter, in all his greatness (Red Sox fans may have a different opinion on that), is truly defying the odds here.
On the opposite end of the spectrum is Arizona outfielder Danny Bautista. Finally putting the "potent" in "potential," Bautista is currently involved in a 20 game hitting streak. Using the official TCO Hit Streak Calculator, first introduced in an article on June 23, 2003, we can see just how rare Bautista's streak is for someone of his caliber. Because Bautista has always been a platoon player, never coming close to playing in 162 games, we will still assume that his seasons consist of 162 games because if he kept getting hits every day, they wouldn't take him out of the lineup. He is currently in his 12th season and likely has a few more left, but we will assume in his career that he will maintain his current levels for only 10 seasons (this helps to discount the platoon years and the inevitable tailing off at the end of a career).
Admitting to some large assumptions, we can at least get a ballpark figure of the chances for Bautista to accomplish this streak. Using the calculator, Bautista has a 1 in 46 chance of hitting in a 20-game hitting streak over his career (or just a 1 in 460 chance to do it in a given season). This may seem low, but remember that we gave him the benefit of the doubt on most factors, especially playing time. Playing devil's advocate, if Bautista played 10 seasons at his level but we considered his seasons to be 130 games (since he doesn't play every day and therefore has less chance to put together long streaks during a single year), it would only change the odds to 1 in 48.
Again, while this may seem low, remember that there are only about 420 hitters on the 25-man rosters in a given year. A majority of them remain the same year after year, and a majority of them post stats better than Bautista. Over the last ten years, maybe 50 to 100 hitters have comparable stats to Bautista (platoon player who sticks around for a decade because he can hit .270 and offer some potential), so it's not really a surprise in terms of odds that SOMEONE like Bautista accomplished this feat. It's surprising to us because we are dismissing the first 45 "Danny Bautistas" who haven't had a 20-game hitting streak this decade and instead are focusing on THE Danny Bautista who is doing it right now.
Now for the real questions. In a career, what are the odds that Bautista can get a 30-game hitting streak? 40-game? 56-game? Feel free to use your own assumptions in the calculator, but here is ours:
Odds for hitting streaks over Danny Bautista's career:
30-game: 1 in 1,000
40-game: 1 in 22,000
56-game: 1 in 3,000,000