Interesting stat and trivia question re: Brady's streak

[ctpatsfan77]

In a Sport Science segment on SportsCenter, they stated that about 2.9% of all pass attempts in the NFL are intercepted. [I'm not sure how far back that number goes; if you look at just this year, the number's actually a bit higher, ~3.1%.]

In any case, using that number, they calculated the odds of a QB reaching Brady's streak of 319 passes without an INT is 1 in 11,947.

Of course, as most of us know, Brady is significantly more careful with the ball than your average QB. If you look just at the 2007 and 2009 seasons, you'd find the probability of Brady throwing an INT is about 1.8%.

So, here's the question: given that figure of 1.8 percent, what do you think is the likelihood of Brady's streak? [I was shocked when I figured out what the answer is.]

* * *

[As a hint: using the method to calculate the probability, which is not the same one Sport Science used, I get a somewhat larger figure; I actually get about 1 in 10,000 using the 2.9% figure.]

 

[Fencer]

Since 1.8 is a little more than 1/2 of 3.1, without looking it up I'd guess it's around the square root of your other figure -- i.e., somewhat over 100:1

That would suggest the chance of him doing it any time in his career (under the usual long list of oversimplifying assumptions) would be in the single digits of percent.

 

[DarrylS]

Listening to Kerry Byrne(sp) on the radio and he said something like if a team is intercepted there is something like a 20% chance the team will loose, conversely if a team is not intercepted then there is a 20% that team will win..

From his research interceptions are a very big deal..

Kerry Byrne of Cold Hard Football Facts..

 

[PatsWickedPissah]

Listening to Kerry Byrne(sp) on the radio and he said something like if a team is intercepted there is something like a 20% chance the team will loose, conversely if a team is not intercepted then there is a 20% that team will win..

From his research interceptions are a very big deal..

Kerry Byrne of Cold Hard Football Facts..

Brady has always had the rag on about picks. Hates it when he tosses one. Takes it personally. I'm certain that BB and he both understand the impact of INTs. That's one major reason BB soured on Bledsoe with his cavalier attitude with the ball and penchant for Red Zone picks, like his very last pass as a Cowperson under Parcells that led to the Romo error (sic).

 

[RobertWeathers]

That's one major reason BB soured on Bledsoe with his cavalier attitude with the ball and penchant for Red Zone picks, like his very last pass as a Cowperson under Parcells that led to the Romo error (sic).

I wouldn't say Bledsoe had a cavalier attitude with picks. Bledsoe's problem was that when things moved fast or if he was under pressure he made poor decisions and relied on his arm more than his brain. Thats what POed BB.

There is that story how BB and Weis got the QBs ready for the season. They gave them a HUGE test (written, white board and on the field). The test was based on decision making, speed of recognition, etc. I don't remember the exact scores but on the written tests, Brady, Bledsoe and Huard all did well, but when it came to defense recognition and changing the play, checking down, reading the D, etc. as a 2nd year player, Brady blew everyone out of the water. Huard did slightly better than Bledsoe.

 

[BlueString94]

I wouldn't say Bledsoe had a cavalier attitude with picks. Bledsoe's problem was that when things moved fast or if he was under pressure he made poor decisions and relied on his arm more than his brain. Thats what POed BB.

There is that story how BB and Weis got the QBs ready for the season. They gave them a HUGE test (written, white board and on the field). The test was based on decision making, speed of recognition, etc. I don't remember the exact scores but on the written tests, Brady, Bledsoe and Huard all did well, but when it came to defense recognition and changing the play, checking down, reading the D, etc. as a 2nd year player, Brady blew everyone out of the water. Huard did slightly better than Bledsoe.

That's interesting, never knew that. But, I do remember Brady saying that she was chastised for not reading D's quick enough (though I presume he did it well, just took too much time), and he saw the quarterback coach's notes lying somewhere, he read the bit about himself, and it was all about how he was slow in every aspect of the game.

Bledsoe was a gunslinger; whether that's good or bad, that depends on the offense, and it definitely didn't suit BB's offence.

 

[Rainy-Day Patriot]

If the probability of TB's throwing a pick on any given pass is 0.018, then the probability of his NOT throwing a pick on any given pass is 0.982. Raise 0.982 to the 319th power to get the probability of NOT throwing a pick in 319 passes.

0.982^319=0.003044841

That's a 0.3% chance of TB's throwing no interceptions over the course of 319 passes. If you like odds: the odds are the probability for divided by the probability against, which is 0.00305414.

The hugely oversimplifying assumption in all this is that each TB pass has the exact same probability of being intercepted, regardless of the type of pass, the game situation, the defense, what have you, and regardless of how many interceptions he has or hasn't thrown in the past.

 

[Patsfanin Philly]

I wouldn't say Bledsoe had a cavalier attitude with picks. Bledsoe's problem was that when things moved fast or if he was under pressure he made poor decisions and relied on his arm more than his brain. Thats what POed BB.

There is that story how BB and Weis got the QBs ready for the season. They gave them a HUGE test (written, white board and on the field). The test was based on decision making, speed of recognition, etc. I don't remember the exact scores but on the written tests, Brady, Bledsoe and Huard all did well, but when it came to defense recognition and changing the play, checking down, reading the D, etc. as a 2nd year player, Brady blew everyone out of the water. Huard did slightly better than Bledsoe.

Keyshawn Johnson was on NFL Network recently talking about the 14 QBs he played with and he said maybe 4 were very smart. He described one as having the pedigree, the big time program, the build but he would hold the ball too long and get sacked or make really bad throws at the worst time and cost his team games, he said this QB was great on the chalkboard but couldn't make decisions on the field....I have a feeling that he was referring to his fellow Cowboy ( and former Patriot) with whom he played in 2005. I wish I could find the video of it....

 

[RobertWeathers]

That's interesting, never knew that. But, I do remember Brady saying that she was chastised for not reading D's quick enough (though I presume he did it well, just took too much time), and he saw the quarterback coach's notes lying somewhere, he read the bit about himself, and it was all about how he was slow in every aspect of the game.

Bledsoe was a gunslinger; whether that's good or bad, that depends on the offense, and it definitely didn't suit BB's offence.

I believe that story.

A coaches job is to push a player to be their best. We all know BB maximizes a player's talent. When you mix that with a 6th round pick who has talent, is a perfectionist, hungry, very smart and has a great work ethic, you have the perfect storm.

It wouldn't surprise me in the least that TB recognized defenses faster than 99% of the QBs in the NFL but BB and Weis knew he could do better.

 

[RobertWeathers]

Keyshawn Johnson was on NFL Network recently talking about the 14 QBs he played with and he said maybe 4 were very smart. He described one as having the pedigree, the big time program, the build but he would hold the ball too long and get sacked or make really bad throws at the worst time and cost his team games, he said this QB was great on the chalkboard but couldn't make decisions on the field....I have a feeling that he was referring to his fellow Cowboy ( and former Patriot) with whom he played in 2005. I wish I could find the video of it....

It's a fascinating discussion. I don't want to come across bashing Drew because I liked him as a player. He did a lot for the franchise, good family guy and is a class act. I am glad he wore a Patriots uniform (although he did drive me nuts sometimes ). Drew had a solid NFL career that he can be proud of.

I do think that the major differences b/t/w TB and DB were the ability to process information quicker and a greater desire to improve their overall game (accuracy, footwork, film study, etc).

 

[hambone1818]

If the probability of TB's throwing a pick on any given pass is 0.018, then the probability of his NOT throwing a pick on any given pass is 0.982. Raise 0.982 to the 319th power to get the probability of NOT throwing a pick in 319 passes.

0.982^319=0.003044841

That's a 0.3% chance of TB's throwing no interceptions over the course of 319 passes. If you like odds: the odds are the probability for divided by the probability against, which is 0.00305414.

The hugely oversimplifying assumption in all this is that each TB pass has the exact same probability of being intercepted, regardless of the type of pass, the game situation, the defense, what have you, and regardless of how many interceptions he has or hasn't thrown in the past.

Can this be taken a step further to say that with a .003 chance of reaching 319 straight un-intercepted passes you could take each of his 319 pass 'streaks' over his career and figure out the probability, given the number of times he's thrown 319 straight passes, he'd actually hit that mark over his present career?

In other words, he's thrown 4,694 passes in his career, and thus has (4,694 - 318) = 4,376 'streaks' of 319 straight passes (1-319, 2-320, ... , 4,376-4694). With 4,376 streaks of 319 straight passes what are the odds, given his 1.8% interception rate, that he'd have a streak this long at this point in his career? I'm far too removed from my econ and stats courses in college to figure it out, can someone help me out (or am I way off base with the theory)?

Either way, this is yet another example of Brady playing chess while everyone else is playing checkers. Best QB of this generation, hopefully every Pats fan realizes this because it's not gonna last forever.

 

[Rainy-Day Patriot]

hambone1818, great question.

I feel like I should be able to figure out the answer to your question. I can see how to answer it empirically with a simulation. Simulate 4,694 passes each with a 1.8% chance of being an interception. Count the number of interceptionless streaks equal to or greater than 319. Assign a 0/1 dummy such that 1 if the count is non-zero, and 0 if the count is 0. Repeat, say, 50,000 times, to obtain 50,000 dummy values. Take the average of the dummy to obtain the probability of TB streaking 319+ over the course of his career so far.

The probability will be much greater than .3%!

Here's a psychological fact: people are terrible at guesstimating the length of the longest streaks. We generally underestimate the probability of long streaks. For example, in the casino, we tend to underestimate the likelihood of long losing streaks, and of course the casinos love us for it!

 

[ctpatsfan77]

If the probability of TB's throwing a pick on any given pass is 0.018, then the probability of his NOT throwing a pick on any given pass is 0.982. Raise 0.982 to the 319th power to get the probability of NOT throwing a pick in 319 passes.

0.982^319=0.003044841

That's a 0.3% chance of TB's throwing no interceptions over the course of 319 passes. If you like odds: the odds are the probability for divided by the probability against, which is 0.00305414.

The hugely oversimplifying assumption in all this is that each TB pass has the exact same probability of being intercepted, regardless of the type of pass, the game situation, the defense, what have you, and regardless of how many interceptions he has or hasn't thrown in the past.

Ding-ding-ding . . . . sort of.

Since INTs are in a manner of speaking "rare events" (i.e., much closer to 0 than 1 or even 0.5), a Poisson distribution is appropriate (basically, it's a statistical tool for modeling rare events over a fairly large number of trials).

If you work it out, over a 319-pass span, Brady should toss about 5.7 INTs; the Poisson distribution works out to a probability of about 0.303%, or a likelihood of 1 in ~330. [This is also where I get a value of about 1 in 10,000 for the average QB, instead of Sport Science's 1 in 12,000.]

 

[patchick]

Can this be taken a step further to say that with a .003 chance of reaching 319 straight un-intercepted passes you could take each of his 319 pass 'streaks' over his career and figure out the probability, given the number of times he's thrown 319 straight passes, he'd actually hit that mark over his present career?

That does seem a more meaningful question than asking the probability that a given arbitrary 319-pass string will be INT-free. In fact, I'd like to see that calculated for the average career of all NFL QBs who throw a significant number of passes.

 

[Rainy-Day Patriot]

The Poisson approximates the binomial, when the instances are rare (i.e., the probability of "success" is small, where "success" means an interception in this case, go figure). Yes, your approximation is good, but it is still just an approximation...for my number!

 

[patchick]

I'd just like to state my general appreciation for patsfans.com being such a geek-safe space.

 

[hambone1818]

[Lot's of nerdiness ahead, you've been forewarned!]
So in digging for an answer to my question I found that Brady's regular season interception precentage is 2.2%, not 1.8%--maybe Sports Science used the playoffs as well? Either way, that changes the odds a bit:

100 - .022 = .978^319 = .000828123, or a .082% chance of him reaching 319 straight. To calculate the odds you'd use this formula: X*Y = Z, where Z is the chance of it happening (or 1), X is the number of chances, Y is the probability; therefore: X*(.000828123)=1, or X=1/.000828123, or 1,208 (1 in 1,208 odds for Brady); this works for the Sports Science example as well: .971^319 = .000008374, 1/.000008374 = 11,941.68.

The whole 'taking it a step further' question I posed is a bit more difficult to figure out, I've spent half my unproductive-at-work morning trying to figure it out. I keep coming back to (probability of success) * (number of chances) or .000828123 * 4,376 = 3.6, but that just can't be right, can it?

My head hurts...anyone have an idea how to come up with an answer?

 

[Krugman]

I wouldn't say Bledsoe had a cavalier attitude with picks. Bledsoe's problem was that when things moved fast or if he was under pressure he made poor decisions and relied on his arm more than his brain. Thats what POed BB.

There is that story how BB and Weis got the QBs ready for the season. They gave them a HUGE test (written, white board and on the field). The test was based on decision making, speed of recognition, etc. I don't remember the exact scores but on the written tests, Brady, Bledsoe and Huard all did well, but when it came to defense recognition and changing the play, checking down, reading the D, etc. as a 2nd year player, Brady blew everyone out of the water. Huard did slightly better than Bledsoe.

Good post,RW.I recall that year many(myself included)noted that Brady was ahead of Huard on the depth chart,and that was a surprise.Many on the board speculated that Brady had the situational awareness and ability to make quick reads of the defence which Bledsoe lacked.I was curious as to the process by which that was determined,other than training camp scrimmages.

 

[ctpatsfan77]

[Lot's of nerdiness ahead, you've been forewarned!]
So in digging for an answer to my question I found that Brady's regular season interception precentage is 2.2%, not 1.8%--maybe Sports Science used the playoffs as well? Either way, that changes the odds a bit:

As I noted in the OP: 1.8% is the number from Brady's last two complete seasons, 2007 and 2009 (21 INTs on 1143 attempts).

 

[WaterfallJumper]

I'd just like to state my general appreciation for patsfans.com being such a geek-safe space.

Absolutely. I'm loving this discussion. I started studying statistics earlier this year through an online service (ALEKS), and I'm enjoying the opportunity to expand my understanding of numbers and probability. This is a great real-world example. I'm not very far along yet, but I at least understood this discussion, so that was very cool.

Thanks, guys.