Joe D's Streak, You'll Never Beat (Probably)

In 1941, Joltin' Joe DiMaggio hit safely in 56 consecutive games.  It's staggering.  Mind-boggling.  It may never be repeated.  It's also attributable hugely to luck. 

In the aftermath of Jimmy Rollins recent hitting-streak attrition, many people have wondered aloud and in print whether anyone will ever break Joe DiMaggio's 56-game hitting streak.  The answer may well be "No."  To wrap one's mind around this, it is useful to look at the feat as a matter of probability.  Let's take a hypothetical hitter who would be the league leader in batting average most any year, and assume his seasonal batting average to be .350 (DiMaggio hit .357 in '41).  Since he is such a prodigious hitter, we will also assume that he bats in the upper third of the order and gets 600 at bats in the season and plays in 155 games for an average of 3.87 at bats per game.

In any given at bat, this hitter has a 35% chance of hitting safely, which means he has a 65% chance of making an out (or reaching on an error).  Thus the odds of this hitter NOT getting a hit in any given game can be calculated by taking 0.65 to the power of 3.87.  This comes out to 18.9%, so the odds of a .350 hitting GETTING a hit in 3.87 at bats are very good -- 81.1%.  Now, what are the odds of this hitter getting at least one hit 56 games in a row?  Well, to calculate the probability of consecutive occurrences taking place, we take the probability of a single occurrence and raise it to the power of the number of consecutive occurrences we are curious about.  For example, if we wanted to know the odds of a coin coming up heads three times in a row, we would take the single occurrence odds -- 1 in 2 or 50% or .50 expressed as a decimal -- and raise it to the third power (in other words, multiple it by itself three times):

0.5 x 0.5 x 0.5 = 0.125 or 12.5% or 1 in 8

For our purposes of the hypothetical hitter, we take the single occurrence odds of 81.1% (about 8 in 10) and raise it to the 56th power (multiply it by itself 56 times):

0.81121186759633^56 = 0.000008157 or 0.0008157%  or about 1 in 125,000

Needless to say, these odds are quite long.  For a mere .300 hitter, the odds are far, far longer -- 0.000009013% or about 1 in 11,000,000.  There are, of course, quite a number of players "attempting" the feat every year, but hardly any of them hit anywhere near .350, and before approaching a level where a larger clump of hitters is in the mix, the odds drop precipitously.  So every year, you have no more than a relative handful of players chasing a feat that they have about 1 in 11,000,000 odds of achieving with one or two thrown in whose odds are closer to 1 in 125,000. 

With this statistical backdrop, it's easy to understand how this has only been accomplished once.  And if it's not obvious at this point, the event was as much attributable to DiMaggio's good luck than it was anything else.  Without a doubt, his .357 hitting ability (also partly luck -- DiMaggio was a career .325 hitter) is what put him in that rarified echelon that allowed his odds to come down to about 0.001549% or about 1 in 65,000, making him approximately 170 times more likely than a .300 hitter to pull it off.  Still, Joltin' Joe could only expect to pull off this feat once for every 65,000 seasons he played (assuming he hit a career-high .357 every year).  It may not be better to be lucky than to be good, but it certainly helps to be both.

Not unrelatedly to his streak, DiMaggio won the MVP award in 1941, arguably robbing Ted Williams, who hit .406 on the season, of what should have been Williams's first such honor.  How could this happen, you ask?  Well, there are a number of reasons, one of which was DiMaggio's media darling reputation and the fact that he had been around the League (in heroic form) three years longer than Williams.  It also helped that the Yankees won the pennant and that the Red Sox finished second.

Two questions immediately come to mind: 1) Who had the better season? and 2) Which feat -- hitting safely in 56 consecutive games or hitting .406 on the season -- is the more impressive feat?  I won't engage in discussing whether Williams was more deserving of the MVP since the Yanks went to the playoffs and the Sox went home (nothing like last year's Ortiz-Rodriguez travesty). 

I'll dispatch with the better season question first.  As always, let's take a look at the numbers:

Williams

143 G, 456 AB, 135 R, 185 H, 37 HR, 120 RBI,  2 SB,  4 CS, 147 BB, 335 TB,
.406 BA, .553 OBP, .735 SLG, 1.288 OPS

DiMaggio

139 G, 541 AB, 122 R, 193 H, 30 HR, 125 RBI,  4 SB,  2 CS, 76 BB, 348 TB,
.357 BA, .440 OBP, .643 SLG, 1.083 OPS

At the outset, I should point out that these are both MVP-level seasons in any year (at least when Barry Bonds isn't juicing to the performance-enhanced tune of a 1.450 OPS).  We see that the two all-time greats drove in and scored similar numbers of runs, though these are objectively poor, albeit popular, metrics of individual performance.  Williams and DiMaggio both had a lot of opportunites to drive in runs hitting the middle of their respective orders with plenty of opportunity to be driven in themselves once on base.  From a team standpoint, however, these are the only offensive stats that matter because they represent how many times the team scores.  In that sense, then they may be valid measures for consideration in MVP voting since the MVP award is supposed to be awarded to the player who was most valuable in helping his team win ballgames. 

But we asked who had the better season, not who should have been the MVP, so what about the numbers that do matter to that determination?  Defense and baserunning aside, it really all comes down to OPS.  As any astute student of the game (or maybe even just a reasonably intelligent person who was just given the rules of the game but was previously locked away in a fallout bunker from birth with zero exposure to baseball or its writing and reporting) can tell you, the most important thing to do when you are at bat (certain necessary sacrifice situations notwithstanding) is not make an out.  For that reason, on base percentage, or the percentage of time one does not make an out, is of paramount importance.  Beyond that, it is better to homer than it is to triple, which is better than it is to double, which is better than it is to single or walk.  After all, the closer you are to home, the easier it is for you to score a run, which is the ultimate goal.  For that reason, slugging percentage, or the number of total bases one achieves per at bat, is also of great importance.  Adding the two together to get OPS (On-base Plus Slugging), as has become chic in recent years, provides a nifty snapshot of offensive total value.  Even OPS is not perfect, however, as it too incorporates data that is attributable significantly to luck (i.e., hits), but it is the best non-adjusted, readily available stat that's out there.

With a staggering 1.288 OPS, Williams recorded the seventh highest single-season OPS in history -- and, more significantly, the fourth highest ever when we subtract out Barry Bonds's drug-induced performances of 2001, 2002, and 2004.  The only other player to record a higher OPS than Williams in 1941 was Babe Ruth.  (Of note, Williams's career OPS was 1.1155; Ruth's was 1.1638.)  DiMaggio, at 1.083, is not even in the top 100 all-time, single-season performances.  (For his career, DiMaggio ranks 14th at .9771.)  Incredibly, Williams could have not drawn a single walk the entire season (in fact, he drew 147) and still finished with a higher OPS than DiMaggio on the back of that .406 batting average.  Williams's .553 OBP is the third highest in history behind only Bonds tainted performances of 2002 and 2004, and his .735 slugging ranks 17th (with four Bonds-owned, tainted performances as well as one from McGwire in 1998).

In short, there is little question that Williams had the better season.  Based on his titanic OPS, it was arguably among top five most historic of all-time to boot -- and this is without giving additional weight to being the last man to hit .400!

Now, for the second question.  What's more impressive -- hitting .406 or a 56-game hitting streak?  Well, it depends on how you define "impressive."  If you are impressed by people winning millions of dollars in the lottery, then you may be more jazzed about the streak.  If on the other hand, you are more impressed by someone who earns millions of dollars through hard work and skill, then surely you are more impressed by the .406 mark.  The truth is, a .406 hitter with 600 at bats actually has a 0.0333% or about 1 in 3,000 chance of hitting in 56 consecutive games, though Williams actually saw far fewer at bats per game because of his walks, which actually bring his chances into line with a .350 hitter getting 600 AB. 

In any case, DiMaggio just got plain lucky in 1941.  Hitting at a .406 rate over the course of an entire season is far more impressive than hitting .357 over the same span.  Of course, it's also reasonable to assume that both hitters were relatively lucky that year in that they achieved career-high BAs substantially above their career averages.  Making good contact is the fundamental objective of hitting, but good contact hardly guarantees a hit.  Most of that is attributable to the good fortune of hitting the ball to an area where it cannot be caught on the fly or where it can be fielded for a putout.  Thus, in any given season, a hitter or a pitcher may be more or less lucky with respect to where the ball falls, resulting in substantial variance in BA and ERA (hence their less favored status predictive performance metrics).

An old baseball proverb advises, "Hit 'em where they ain't."  As anyone who's ever played the game knows, getting this done at all, much less once or more per game 56 times in a row, is up to the fickle gods of baseball.