Saturday, October 13, 2012

Brees, Unitas and DiMaggio: 47-Game Streaks Fifty Years Apart, and that 56-Gamer, in Perspective.

by Jim Glass
Drew Brees is collecting well-deserved congratulations on breaking what many have long considered to be the greatest record in pro-football: the streak of 47 consecutive games with a touchdown pass thrown, set by John Unitas during the 1956 through 1960 seasons. In my youth that was often compared to Joe DiMaggio's famous "unbreakable record" 56-game hitting streak in baseball. Last week it was again.
Yet Brees tied-and-broke that record with no fewer than seven TD passes in his last two games, while looking as if he's going to "keep on going and going and going" like that trademarked battery-packed bunny.
So just how "unbreakable" should these records be considered to be?  With all the changes in the game that have occurred during the last 60 years, has Brees' streak really matched Unitas' as being "comparably unlikely," an equal achievement against the odds?  And how do these streaks actually compare to DiMaggio's.   Here's a quick take:

Running the Numbers
How unlikely were the Brees and Unitas 47-game streaks?   To adjust for the different styles of play of different times, a reasonable measure is the probability of the average team of each era (not quarterbacked by Brees or Unitas) scoring at least one touchdown by passing for that many consecutive games. 

The database informs us that during the Unitas streak (from game #10 of the 1956 season through game #10 in 1960) teams other than his Colts scored TDs through the air in 70.3% of their games, while during the Brees streak (game #5 in 2009 to game #4 in 2012) NFL teams apart from the Saints threw at least one TD pass in 78.3% of their games.
Passing yards per game in the NFL increased by a good 33% over that period (to 225 from 169) so this increase of only 8 percentage points (or by 11%) in the number of games with TD passes thrown may seem unexpectedly small.  But while teams throw much more often and for more total yards today, back in the Unitas era the fewer pass attempts generally were more aggressive and deeper, producing significantly greater yards-per-completion and TDs-per-attempt numbers than today (as detailed previously.)
The probability of the average team in each era scoring a touchdown by passing in 47 consecutive games by random chance, starting in any single given game, is simply the above percentages compounded to the 47th power.
  • Brees era probability: 0.783^47 = 1.01579E-05
  • Unitas era probabiity:  0.703^47 =  6.41062E-08

Those results are made more comprehensible by converting them into "Once per how many games", via dividing 1 by each result above. Giving...
  • Brees era:  Once per 98,446 games.
  • Unitas era:  Once per 15,599,107 games.
The Brees record is a very impressive, expected to be seen starting only once in near a hundred thousand games -- but Unitas' is once in 15.6 million. 
Those mere 8 percentage points make a serious difference when compounded 47 times.
Another way to look at these records is "Once in how many years".  A streak can start with every game played by every team.  Thus, the chance of one starting in any given season is the "once per how many games" number multiplied by the number of games in a season.  In today's NFL with 32 teams each playing 16 games, there are 512 games per season.   During the Unitas-streak era 12 teams played 12 games each season for 144 games.  (In 1960 Dallas joined the league as its 13th team, still playing a 12-game season.)  Applying these numbers we get...
  • Brees record:  Once in 192 years.
  • Unitas record when set:  Once in 108,327 years. (That is not a typo!)
  • Unitas record with today's 512-game season:  Once in 30,467 years.
As impressive as Brees's performance is -- and it is very impressive -- by the measures used here, it is simply not "comparably improbable" to Unitas' accomplishment.
How many consecutive games with a TD pass must Brees achieve for his record to match Unitas' as an equally improbable achievement?  By the methodology used here ... 68.  That would happen in the ninth game of the 2013 season, if he doesn't sit out any games before then. Set your DVR now to record it, so you don't forget.  With his talent and the offensive talent around him on that team, I'm not doubting that he can make it.
For more perspective on these two historically great sustained performances by these two great quarterbacks in very different eras of QB play, here are the numbers for each during their 47-game streaks.  
Since the average numbers for the two eras are so different, I've also added a three digit percent number comparing the average of each stat with the NFL average for all the non-Brees, non-Unitas teams during the period of each streak:  100 is average, 120 is 20% better than average (more than average, except for interceptions for which it is less than average), etc.
                                                      BREES  and UNITAS

Those are two stellar sets of numbers.
The greater aggressiveness of Unitas' passing (and that of his era) is seen in the fact that while he had 31% fewer attempts than Brees in their 47-game sets -- Brees had as many completions as Unitas had attempts -- and a completion percentage that was 22% lower than Brees', his yards-per-completion was 34% higher than Brees's and his touchdowns-per-completion fully 66% higher than Brees'.
There's a common belief that the rule changes that have so opened up the passing game in recent years have made offense more aggressive and increased scoring.  But in reality, the rule changes have led to a big increase in conservative, short, ball-control passing, replacing the former running game.  As the average pass has become shorter and safer, the running game has been evaporating, but scoring hasn't increased as much as many think.  In 1958 NFL teams averaged 22.6 points a game -- during the middle of Unitas streak as the Colts won the title behind his passing.  Last year, 2011, the league averaged fewer, 22.2 points, in spite of all the passing records that were set and all the breathless journalism about them.  But that's another story.

The question seems more appropriately asked about the Unitas streak, but let's look at  the DiMaggio s streak to see, using the same methodology as above as closely as it can be applied to a very different sport.
DiMaggio hit safely in 56 consecutive games during the 1941 MLB season.  The Baseball database tells us that during that season the overall batting average for non-pitchers was .274,  and that each of the nine slots in the batting order had an average of  3.83 at bats per game.
The chance of the average batter getting a hit in the average game is the inverse of that of not getting a hit in any of his at bats.  Using the numbers above, the probability of not getting a hit in any one at bat is .726, and thus 0.726^3.83 gives a .293 probability of not getting a hit in the average game -- and a .707 likelihood of getting a hit.
As it happens, the Unitas and DiMaggio streaks were very comparable on a per game basis, with a nearly identical per game chance of "success" of .703 for quarterbacks and .707 for batters.  But DiMaggio's streak ran nine games longer.   How much difference does this make?
Repeating the methodology above, the probability of each streak starting in any given game for the average player...
  • DiMaggio streak:  0.707^56 = 3.69392E-09
  • Unitas streak:  0.703^47 =  6.41062E-08
Which gives....
  • DiMaggio streak:  Once per 270,715,316 games (!!)
  • Unitas streak:  Once per 15,599,107 games.
Wow.  As great as the Unitas streak is, DiMaggio's is a good deal even more so as a "starting from any given game" event.
But there is another way to look at it. There are many more games in a baseball season than in an NFL season, so the "once in how many years" baseball record will be correspondingly reduced.
In a single season during the Unitas-record era a starting QB played 12 games a season, and so had 12 chances to start a streak.   In 1941 baseball batter played a 154 game season, and so had 154 chances.  Thus, first, the probability of a given single average player starting a record streak in a given season...
  •  DiMaggio streak:  Once in 1,757,892 seasons.
  •  Unitas streak:  Once in 1,299,926 seasons.
By this measure they are nearing equal.
Then again there is the "Once in how many years" will the streak be expected occur for the entire pro sport given how it is organized.
In 1941 there were 16 MLB teams playing a 154-game season, and for the purpose here I count eight batters in the lineup per game (disregarding pitchers).  Multiplying those numbers out gives 19,172 chances for some batter on some team to start a hitting streak in the 1941 season.
Today's MLB plays a 162-game season with 30 teams, of which 16 are the National League for which I again count eight batters each, and 14 are in the American League with nine batters each (thanks to the designated hitter).  Multiply those out and we get 41,148 chances for some batter to start a streak each season, which gives...
  •  DiMaggio record when set:  Once in 14,120 years.
  •  DiMaggio record, today's MLB season:  Once in 6,579 years.
Compared to, as we have already seen...
  •  Unitas record when set:  Once in 108,327 years.
  •  Unitas record with today's 512-game season:  Once in 30,467 years.
Now the Unitas streak looks the more impressive.
So it depends what measure one judges by.  The DiMaggio hitting streak is significantly more impressive -- improbable, against the odds -- in terms of an individual player's starting such a streak in any given game.  But because so many more hitters play so many more games in major league baseball each year, giving so many more chances to break the DiMaggio record,  it is the Unitas streak that seems to be the one more likely to last "for the ages" before matched by another of equal improbability.
So which record is the "greatest"?  That's subjective, you decide. 
And don't forget to set your DVR to record those Saints games in weeks #9 and #10 of the 2013 season.


Anonymous said...


Only 256 games per season.

Jason said...

I think using the average team/batter to determine per season results doesn't work well here. Especially for comparisons between sports.

In football you have two ways to score so you'd get some teams built for rushing and some built for passing. I'd guess this split was more pronounced in 1941 (but that's just my guess). So while the hypothetical average team is unlikely to score passing TDs in consecutive games, the likely hood that one of the 'passing' teams does so would be much greater.

I looked at the 1957 season and (excluding Baltimore) 2 teams scored passing TDs in 10 games and 2 teams scored passing TDs in 9 games. So 18% of teams had a 83% success rate and 36% had a rate over 75%. The average success rate you gave for the whole sample was 70.3%.

An 83% success rate in baseball would be the equivalent of hitting .370. Only 1 batter out of 268 did this (0.3%) - Williams .406. Only 24 players hit .303 or better (9%).

So I don't think using the average team works well for football. I have no idea what would work better but I'm sure there must be something.

Jim Glass said...

Dude: Only 256 games per season.

Um, 32 teams play 16 games each, 512 total.

I think using the average team/batter to determine per season results doesn't work well here. Especially for comparisons between sports. In football you have two ways to score so you'd get some teams built for rushing and some built for passing...

The average team number is just a common "yardstick" to measure by. It's not the actual probability of setting the record. Clearly great QBs on top passing offenses designed to score passing TDs by the bunch, and batters who hit .357, have much, much better probabilities of setting such a record. Otherwise we wouldn't see such a record set in 10,000 years, literally.

The yardstick illustrates the relative scale of the accomplishments, it doesn't calculate their actual improbability. There are much more sophisticated calculations to do that.

And of course when comparing achievements between different eras during which so much has changed -- not to mention between entirely different sports as well -- there's a whole lot of subjective judgment involved.

(Baseball fans still argue over whether Mickey Mantle or Willie Mays was "better", and they played the same position in the same sport in the same city at the same time.)

All this is just information for those who might be interested, FWIW.

Steve said...

Jim, what he was saying was that each team plays 8 home games so its 32*8=256 games. If you count the away games (16 games) you are double-counting games you already counted as others team's home games.

But in this context you're looking at "game-QB" pairs so 512 is still the right number.

Jason said...

-The average team number is just a common "yardstick" to measure by. It's not the actual probability of setting the record.
-The yardstick illustrates the relative scale of the accomplishments, it doesn't calculate their actual improbability.

Of course. What I'm saying is that the average team number is not a good yardstick for football and does a very poor job of illustrating the relative scale of the accomplishments.

James said...

Another way of looking at it is given that he threw 114 TDs in 47 games how do you work out the probability that he threw at least one in every game.I cant figure it out.

And how many players have thrown 114 TDs over a 47 game period as Brees did.

Just looking at Brady's season stats he threw 100 TDs from 05-07 (48 games) and 103 from 09-11 Manning threw 108 from 04 to 06 so if you start moving a window of 47 games they might come close.

James said...

I estimate that Brees had a 4.1% chance of a 47 game streak given that he threw 114TDs, Unitas had a 1% chance as he only threw only 102.

I assumed 11.5 possessions per game which means Brees threw a TD on 21% of possessions. So the probability of throwing none in a game is (1-21%)^11.5=6.6% so the probability of him scoring in a game is 93.4%. I then replaced the average scoring rate of .783 in the original post with .934 which is Brees’ scoring rate to get 4.1%.

So really Brees’ streak is more a product of his high TD numbers rather than a miracle of consistency and Unitas’ streak is more unlikely as he threw fewer TDs.

DiMaggio is a different kettle of fish

DiMaggio during his 56 game streak hit .406 with an average of 3.98 ab per game.
So his probability of having a hitless game was (1-.406)^3.98=12.3% so the probability of the 56 game streak was (1-12.3%)^56 =0.06% so given how good DiMaggio was his streak was almost 100 times less likely than Brees TD streak given how good Brees was. I am sure there have been many players who have batted over .400 in a 56 game window but to get a hit in every game is much harder than to score a TD in every game if you are throwing 2.2 TDs a game as BRees was.

If Brees keeps scoring at this rate his streak won’t be as unlikely as DiMAggio’s until around 75 games which is another 28 games or early in the 2015 season.

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