Author Archives: statsinthewild
Here are my first set of thoughts on my “radical redesign”.
- I think we need to introduce non-parametric statistics in intro stats. I basically had no idea about non-parametric statistics until I taught a course called non-parametric statistics in my first semester as a professor at Loyola. I’m totally sold on them. I think we do a disservice teaching all these parametric procedures, which were useful 50 years ago (I mean they are still useful) because the extra assumptions were greatly simplifying. But we have computers and don’t really need that extra level of simplification all the time now.
- I think we should mention the t-test as basically an after thought. My plan is to introduce hypothesis testing using simulation and directly examine the distribution of the test statistic with this simulation. Once you do that the fact that it’s a t-distribution (or whatever distribution it is) doesn’t even really matter as long as you have the distribution. Students get way too hung up on using t-tests like they are the end all be all of hypothesis testing. It should be presented as ONE test among many.
- I’m going to completely get rid of slides. I’m going to go into every class with a plan and a data set. All theory will be written on the board while trying to get students involved as much as possible. I will write simulations on the spot to show students examples of code. (I will keep the simulations simple). I will then do all data analysis on the spot. NO SLIDES.
- Something that I am on the fence about that I read in the GAISE report: dropping probability theory. In the section with a list of topics to potentially drop they include this. The more I think about it though, the more it makes sense. We already have other classes that will cover probability in much more detail and we don’t need much probability to actually do a lot of data analysis (we do need some though).
- Another note the GAISE report makes that I have been screaming about for years is getting rid of the F@#$ing tables. Students in my class aren’t allowed to use Z/T/whatever tables to look up probability. It’s an antiquated skill and it has been for like 30 years. Yet it’s still taught in so many intro stat classes. If I see students using a table, I reserve the write to rip up the table on the spot and throw the pieces into the air while yelling about how it’s 2020 not 1920.
Well, I’m probably going to get tenure in the Spring, which is a fairly big accomplishment. And it’s the end of a decade. So I’ve decided to look back on some people who have had a positive influence on me in my life. Here is a VERY INCOMPLETE list, with amusing anecdotes.
Roughly in chronological order:
Michael Kinsley: When I was a little kid, Mike lived next door. We were best friends. He moved to Pennsylvania when I was like 8. Devastating. Since then I’ve only seen him a handful of times (one weird day when we watched an XFL game in West Springfield, his wedding, once in Springfield at Sophia’s, etc), but most recently we met up in Chicago. We went to a barbecue place across from Wrigley, and he managed to get us a 50% employee discount because the new job he was starting was somehow tangentially related to something. It was truly masterful work.
He also once tried to play the word “re-re” in me in scrabble when we were like 10. “re-re”. As in short for retard (it was a different time).
Dad: My father gave me two pieces of advice when he dropped me off at college: 1) Don’t drink anything that you didn’t pour yourself and 2) When a woman asks how old she looks, always answer 22.
I wrestled in high school. At some point I wanted to box. My father wouldn’t let me. I am so thankful he never let me box.
Mom: My mom let me do everything that I wanted. She asked me if I wanted to play an instrument, and I told here maybe the drums. Just based on that I took lessons for like 10 years as a kid. Basically anything I wanted to try, I was encouraged to do. That’s awesome. Ellen Improv
Mark Franczyk: From basically the time I was born, our families were going on vacations together and doing various other things. We went to school together from K-8 but we for some reason were never in the same class. Year after year it was like some joke that the teachers were playing on us. I think in like 5th or 6th grade we ended up in the same class finally. Anyway, basically my entire childhood was spent with Mark.
Another random thought: Remember ski club? We used to do this thing in elementary school where like on Tuesday nights were would go to Mount Tom and ski. Mount Tom has been closed for like 20 years at this point. It’s hard to even imagine that there was a ski area in Holyoke at one point.
Mrs. Vosburgh: I had Mrs. Vosburgh in 3rd grade. She was the best teacher I had in elementary school.
Mrs. Lussier: She taught me math in 8th grade and I’ll always associate FOIL with her.
Also, she had us do this thing once because kids weren’t being nice to each other, and we had to write a nice word about everyone in class. Then she would compile the words for everyone. I remember using the word “kinky”, not fully understanding what it meant, to describe someone. I had to do my list over. So, I guess you could say that I learned the definition of “kinky” from my 8th grade teacher. Which is a very strange thing to say out of context.
Shaun McGrady: I met Shaun in high school. he was two years ahead of me. We had a study hall together I think. Years after we graduated we ended up playing poker together a lot. In fact, I met my wife, who was roommates at the time with his current wife, at one of his poker tournaments. Which leads me to to….
Bare Naked Ladies, the band: Shaun knew my wife because he ran some sort of BNL fan club. So I’m currently happily married to my fanatics wife as a direct result of the band Bare Naked Ladies. I don’t like it that much, but what are you going to do.
Rob Higney: This guy was the best man at my wedding. I once threatened to beat him up in high school before we were friends. He is without a doubt, the smartest person I know who also thinks that everything a 12 year old finds funny is still funny.
Dan McCarthy: My greatest achievement in life is when we won that midnight beer pong tournament on Christmas Eve with you drinking 75% of the beer. You are truly an inspiration.
JOC: Nearly all of my political views are based on conversations with this guy. Not sure he actually knows that. Specifically, my views on taxes.
Joanna: I didn’t know what her last name was for about 10 years. She’s the only person on earth I don’t think I have ever been annoyed with.
Ann Kellner: I took AP Calculus from Mrs. Kellner my senior year of high school. To this day it was the best class I have ever taken with the best teacher I have ever had. It was unbelievably well organized, and I still remember basically everything from that class.
Bonnie Moriarty: Dr. Moriarty was my english teacher junior and senior year of high school. My sophomore year of high school I was in “regular” English and I kept getting B’s and C’s because I was totally uninterested. I wanted to do honors and she let me in even though my grades weren’t the best. This is where I learned to write. I still use the process that she showed us in that class to this day. Also, fun fact: I once told this teacher that I didn’t need to know how to write because I was good at math. That is maybe the dumbest thing I have ever said. I write every single day.
Another thing that I will always remember from this class is this poem called “The Unknown Citizen”. When we were discussing the poem in class I said something like, “This guy’s life seems pretty good. He had everything he wanted”. She responded, “Oh, Greg. I hope you are joking”. I think about this basically every day.
Mike Cecere: Coach Cecere was my wrestling coach my first three years of high school. My junior year of high school I had just finished 4th at sectionals and the top 4 from Western Mass made it to states. So I was basically the last person in. On the day before the tournament after our last practice while I was waiting to get picked up he told me that there was no reason that I couldn’t place at this tournament. I didn’t really believe him. But I ended up finishing 4th. It’s the first time in my life I did something that I didn’t think was possible.
Mike Maynard: When I started wrestling my freshman year of high school, Mike was also a freshman. We basically beat the shit out of each other for 4 years. And the only reason I was any good at wrestling is because I had someone better than me to practice with every single day.
Dennis Fenton: Coach Fenton was my coach my senior year. His practices were unbelievable. I was never a better wrestler than I was at the end of my senior year of high school. And I’ll always remember the lazy man’s fire man’s carry (In my last victory in high school, I beat a guy who beat me at states using this move), the Peterson series, and the Penn State ride.
My wife: I mean I can’t say enough about this lady. She’s just the best. I love art because of her. It took here a decade, but she convinced me that art isn’t just scribbling with paint on canvas. I’ve basically had an entire art school education thanks for being married to her. She’s just great.
Anna Foss: Anna was probably my first friend in college. We lived on the same floor freshman year. I once went to her house in a car that she had borrowed from someone else. She told me that if her dad asked, I had to tell him it was my car. Her dad did ask and I told him it was my car. I said, “Oh. I don’t know. I’m not that good with cars.”
Scot Junkin: Scot lived next door to me freshman year of college. Freshman year of college was very fun. I want to be Scot when I grow up.
I went to visit Scot in Utah a few months before my first kid was born. He took me downhill mountain biking. It is one of the best experiences of my life. I think about it all the time.
Matt Houde: My roommate in college my Senior year. We used to set our alarms for 7am ready to attack the day and then snooze for like 4 hours before laying in bed for another hour an insulting each other. College was pretty good.
Jon Cahill: Jon is the nicest person I have ever met. I met Jon at college and now he hangs out with a bunch of my friends from high school without me.
Tejal Patel: At WPI there was a fraternity that almost of the wrestlers joined. I ended up joining a different fraternity in large part because of Tejal who wrestled, but wasn’t in the wrestling fraternity. So many of my best friends today I met in that fraternity.
Carlos Morales: Professor Morales was must undergraduate major project advisor and basically got me hooked on statistics. We did a project where we used a Bradley-Terry model to rank tennis players. I wanted to (and still want to) do a project where we analyzed wrestling data, but that data is not so easy to get. This is what got me hooked and I stayed at WPI after I graduated to do a M.S. in Applied Statistics.
Jayson Wilbur: Professor Wilbur took over my Master’s project after Professor Morales left to take a job in industry. He let me do a project on predicting NFL point spreads! That’s pretty awesome. I also had some really important conversations about doing a Ph.D. with Jayson that I will always be thankful for. I was a not so great master’s student, but he still wrote me a recommendation to do a Ph.D., and I’ll always appreciate that. I hope I haven’t let him down.
Andrew Swift: Professor Swift taught me Bayesian statistics at WPI. I also took a class called life contingencies with him because I was an actuarial science major (the best thing to ever happen to me was failing the actuarial exam. twice. Otherwise I might be n actuary……). I had a lot of conversations with him about statistics, and he was another professor who helped lead me toward statistics. Unfortunately, he’s a Dolphins fan……..
Peter Cook: My first job after school was at Brookstone in their direct marketing department segmenting catalog mailing lists. If that sounds awful to you, you are correct. I didn’t really like anything about this job except for Peter. He was my first boss, and I couldn’t have had a better experience with him. I learned so many practical things from him.
Story about him: For whatever reason, we were talking about something called a “death pool“. It’s not important why we were talking about this, but on his way out of work one day he mentioned that I should take “that alligator hunter” guy. Literally the next work day he got stung by that sting ray and he just walked into work in the morning and said “I told you you should have taken him”. I’m sure that not a totally accurate telling of that story, but that’s the version I’m sticking with.
He’s also the reason that I sign all my emails with “Cheers”. Cause apparently that’s what British people say. And he was very British.
Ofer Harel: Ofer was my Ph.D. adviser. Basically my entire professional academic career is thanks to him. It’s hard to over state the influence that he has had on my professional life.
Elijah Gaioini: Elijah taught me that everyone has a different loss function. Which basically changed the way I viewed the world whether he meant it to or not.
Brien Aronov: I’ve never met a person who baffles me so much. In grad school, I used to have really interesting conversations with Brien. No one views the world quite like this guy. He is genuinely one of the most interesting people I have ever met. I’ll never, ever understand him, but that’s the best part. And f$&^ing MOVE!
Paddy Harrington: I wouldn’t have made it through grad school without Paddy. We were two of the three Americans in the “remedial class” when we started our Ph.D. together. I believe that every single class I ever took, Paddy was in. I hope I help him half as much as he helped me in getting through those classes. I wish I talked to him more. Paddy, if you are reading this, CALL ME!
Mike Lopez: I “met” Mike Lopez online and through twitter because we were both writing sports statistics blogs. We finally met in person for this first time (I think) at JSM in Montreal. Since then we won a Kaggle contest and have written two papers together : one about the Kaggle contest and the other with Ben Baumer about competitive balance. The latter paper is probably my favorite paper that I have ever written. Now Mike works for the NFL, and he likes to remind me how much more successful he is than I am.* When I first writing about sports, I always felt like I had to sort of hide it because it wasn’t “real statistics” or “real research”. But getting to work with Mike has helped me embrace pursuing sports statistics as a “real” research topic.
*That’s completely untrue. Anyone who has ever met Mike knows he is incapable of this. He’s so nice it’s painful.
Andrea Foulkes: Dr. Foulkes was my post-doctoral adviser at UMass. I have my current job today because she took me on a post-doc and I’m eternally grateful for that. I didn’t know anything about genetics when I started working with her, and it was an incredible opportunity to learn something completely new. I’m not sure I will ever have another opportunity where I have just total time to focus on learning a new field.
Nick Reich: Nick started as a professor in the School of Public Health at Umass the same year (the year before?) I started as a post-doc. I found it really helpful to get to watch him on the tenure track. I also felt really comfortable around him enough to ask him “stupid questions”. I remember in my third year as a post-doc I started teaching, and I asked him “what do I even wear to teach?” I know it’s hard to imagine me asking that question because I dress so well now, but as a post-doc I was……fashion challenged.
We used to play chess at lunch, and he would generally smoke me. But those games helped me get through a tough time in my life when I started having panic attacks again. I also remember one time where I showed up in his office having a panic attack, and I was just like “talk to me”. That really helped. Thank you.
When I was a post-doc I wrote a blog post critical of a Grantland article. I didn’t really know what to do with it, but in talking with Nick he encouraged me to submit it to Deadspin. At the time Tommy Craggs was at Deadspin and Nick had worked with him in the past, and Nick wrote an email supporting my post getting put on Deadspin. I really appreciate that. Thanks for that.
The advice I’ll always remember him giving me was “Don’t let the perfect be the enemy of the good.” This is so true.
Nick is also the first person to buy my art. Guy has good taste.
Ben Baumer: I met Ben at a talk he gave at UMass. He had started as a professor at Smith the same year I started as a post-doc. I went up to him after the talk, and asked if he wanted to work on a project with him on baseball. I was thinking that we would do something small. Ben was like “Let’s re-do WAR”. That’s a big project. Well, we developed openWAR (with Shane Jensen), and it won a SABR award. The moral here is go big.
Tim O’Brien: Every time I have a question about something at Loyola, I go ask Tim. He’s been incredibly helpful, and it’s an absolute pleasure working with him.
Peter Tingley and Emily Peters: Peter and Emily are a married couple who work in the Math Department with me at Loyola. When I first moved out to Chicago, they invited my wife and I over for dinner. Which was nice because we knew basically no one in the Chicago area. Peter and Emily are two of the big reasons why I’ll never leave Loyola. They are fantastic colleagues and they are both pretty good at math #understatement.
Everyone in Loyola’s Math Department: I could just list everyone here, but that’s a lot of people. I’ve never met even a single person in this department who isn’t fantastic. I really like this department. Special shout out to Agnes, who is the best.
Harry Pavlidis: I met Harry almost right away when I moved to Chicago at a conference at Northwestern. He’s one of the head honchos over at Baseball Prospectus. The community that he has created and the people I have been able to meet through him has been absolutely fantastic. And he’s an all around great guy.
David Montgomery: I did the Second City Improv program from level A-E and my group wanted to keep going. So we kept taking classes with David. Our group has been together for 4 years, and it’s been one of the great experiences of my life. And David has been
The Emeralds of Saigon: Denny O’Malley, John Retterer-Moore, Jackie Hilmes, Michaela Choy (and Sweet Sarah and Michael Cho): I’ve been doing improv with these jokers for almost exactly 4 years. I hope I do improv with them for another 40 years. Also, I know that I say that we aren’t friends all the time. But secretly I consider myself friends with you.
Brian Seguin: Brian got hired a year after I did at Loyola. I’ve learned more at our weekly lunches at IDOF than I did in 4 years of college. Brian is also largely influential in me learning about functional data analysis and shape analysis and is always very helpful with teaching me the right notation. He’s also a pro at deck drinking in the summer.
- I need a new example of Simpson’s Paradox. Anyone got any ideas?
- I think we need to talk much more about sampling methods in intro stats courses. I don’t know how much other people talk about this, but I usually mention it in like 15 minutes in one class and then we never talk about it again.
- I want to employ the “theory, simulation, example” for all the topics that I am going to cover. So for instance, for a one sample t-test we would talk about what the form of the t-test is (in more advanced classes we could derive it using the idea of ancillary statistics), then using R simulate the test statistic over and over again to see the actual distribution of the test statistic, then get an actual set of data and do an example. Theory. Simulation. Example.
- I think ethics should be included in every intro stats course. I’ve never formally done it before, I want to include it in this, and I have no actual idea how to include it. Anyone have any thoughts?
- I’m heavily relying on the GAISE report for ideas about what to include in my course. Instead of traditional chapters from a book, I think I’m going to use their nine goals as 9 modules in my course. And then I’ll put the appropriate techniques into each of those modules. Only issue is that I want software to appear in all of the modules so I’ll need to re-order that goal from 8 to like 2.
- I really like the distinction that the GAISE report makes between CONSUMERS and PRODUCERS of statistics. I’m teaching STAT335, which is Introduction to Biostatistics. These students will be about 50% consumer and 50% producers. The course should be tailored to that. In our STAT 103 course, the students are going to be 95% consumers of statistics. We need to revamp that course to account for that. I’ve never really thought about that distinction before in terms of developing course material for an intro stat course.
- At Loyola we have essentially 3 intro stats courses: 103, 203, and 335. Right now that are largely the same intro stats course with different students and slightly difference math requirements. My goal long term is to totally re-design these so that 103 is geared towards consumers, 203 is geared towards producers, and 335 is right in the middle for consumers and producers.
- The GAISE report in incredible.
Wild Card Round
Texans (55.95%) over Bills, 23-20
Patriots (56.47%) over Titans, 24-20
Saints (65.16%) over Vikings, 28-20
Seahawks (53.52%) over Eagles, 24-22
Ravens (69.03%) over Texans, 29-20
Chiefs (65.5%) over Patriots, 28-21
Saints (60.61%) over Packers , 28-22
49ers (64.6%) over Seahawks, 28-21
Conference Championship Games
49ers (51.52%) over Saints, 25-24
Ravens (50.5%) over Chiefs, 26-25
Ravens (52.19%) over 49ers, 24-22
I don’t think Kanye is a very good rapper. Other people disagree with me. So I said I would name 100 rappers better than Kanye. Here is my list:
7-16. All of the Wu Tang clan
17-19. Beastie Boys
23. Aesop Rock
25. Kendrick Lamar
26. Snoop Dog (barely)
28. Danny Brown
29. Chris Webby
31. Pigeon John
34. Dr. Dre
35-36. Run the jewels
37. Mc Chris
38. Ice Cube
41. 50 Cent
42. Most Def
44. Talin Kweli
45. Black Thought
46. Q Tip
48. Busta Rhymes
49. Lauren Hill
50. Missy Elliot
51. Lil Kim
52. Childish Gambino
53. Nate Dogg
54. Phife Dog
55. Ali Shared Muhammed
56. Jarobi White
58. Chance the Rapper
60. Kid Cudi
61. Wiz khalifa
64. MF Doom
66. Nicki Minaj
67. Immortal Technique
68. Obie Trice
69. Brother Ali
70. J Dilla
71. Del the Funkee Homosapien
75. Deacon the Villain
77. 21 savage
78. Pusha T
79. Kodak Black
80. Meek Mill
81. Lil Baby
82. Gucci Mane
83. Jay Rock
85. Nipsey Hustle
86. Grandmaster Caz
87. Melle Mel 8
88. Big daddy Kane
92. Rick Ross
93. 2 Chainz
94. Cardio B
95. Queen Latifah
Here is a fun plot that I made showing number of wins vs probability (according to fivethirtyeight.com). The 7-6 Bears, who just beat the 6-7 Cowboys last night, are probably going to miss the playoffs. The, let me repeat this, 6-7 Cowboys are probably going to HOST a home playoff game. I love it. What I’m really rooting for though is for Washington to win the NFC East, get a home playoff game, and get blown out by 80. That’s what I want for Christmas. Thought what I really want to see someday is a team get a home playoff game with a 3-13 record! It’s theoretically possible!
Alright. I’m really excited about this new series, which I’m calling the “Google Image Search Series”. Below you’ll see some examples from this series and a brief explanation of how these are created.
How are these images made?
First, I choose a word or phrase such as “celebrity” or “famous person”, and I do an Google image search for that word. I then take screen shots of the top 20 or so results. This set of images becomes my training data.
The images are then converted from an image array to a vector with the first third of this vector representing the intensities of the red channel, the second third corresponding to the green channel, and the last third the blue channel. So if the image was, for instance, 400 pixels x 400 pixels, the vector would be of length 400*400*3 = 480000 (because there are three color channels).
I then build one model for each element of this vector. Every element in the vector is the response variables once, and everything else acts as predictor variables in a model. Because of the n <<< p nature of this penalized regression models such as LASSO, Ridge, and elastic net were my first choice. Once I have all of the models, I then use them to predict the red, green, and blue intensities at each pixel with initialized values of all intensities being 0. Essentially this means starting with a solid black square and then letting the models modify each pixel accordingly. Some of the results can be seen below:
I think the images above are amazing. But others weren’t that interesting. A lot of these ended up just looking like blurry messes. So I kept experimenting with different models.
What I realized is that I wanted a model that would do a BAD job recreating these images, because that would look more interesting. So I turned to CART models. CART models aren’t necessarily bad, but they certainly will not be complex enough to accurately capture all of the complexities of an image. Also, as an additional way to further obscure the images, rather than working with the raw data as predictors, I’m using only the principle components as predictors. This produces some really stunning images:
And here is the exciting part! I’ve just recently added these to my store and they can be purchased here and here (I needed to create two separate listings because I ran out of variants in the first). Let me know if there are words or phrases you want to see. Just send me a message on twitter @statsinthewild.
So far this year, through 8 of 17 weeks (121 of 267 games) (i.e. less than half of the season), there have been EIGHT games in the NFL where the spread was 15 points or greater (and TWO(!!!) with spreads greater than 20):
- Vikings (16.5) vs Washington Football Team (October 24, 2019)
- Bills (-17) vs Dolphins (October 20, 2019)
- Patriots (-16.5) vs Giants (October 10, 2019)
- Patriots (-16.5) AT Washington Football Team (October 6, 2019)
- Chargers (-15) AT Dolphins (September 29, 2019)
- Cowboys (-21.5) vs Dolphins (September 22, 2019)
- Patriots (-21) vs Jets (September 22, 2019)
- Patriots (-18) AT Dolphins (September 15, 2019)
This seems like a lot! So I went and checked back through 2006. Turns out, this is a lot. The most there has ever been in a FULL season is 14 in 2007. Nine of those games were the Patriots during their undefeated season. The next most in a season was 2009 with seven such games (mostly involving the Raiders…). In 8 of the last 14 seasons, there were at most 3 such games (3 in 2006, 2011, 2016, 2017, 2018, 1 in 2014 and 2015, and ZERO(!) in 2010).
So we are ALREADY at 8 games and we are LESS THAN HALFWAY (there are NINE weeks left!) through the season.
Through 121 games 8 of them (or 6.61%) have had spreads of 15 or more. The next two highest rates occurred in 2007 and 2009 at 3.75% and 2.62%, respectively. No other season since 2006 has had more than 2% of games with spreads that large. The plots below show survival curves of the spreads with all past seasons in blue and 2019 in red with the plot on the right zoomed in. (The way to read this plot is that the height of the curve tell you the proportion of games played where the spread was LARGER than the x-value.)
You can also see the increase in the number of high spread games in this plot below, which shows the density estimates of the absolute value of the spreads.
Notice that the proportion of games with spreads around 10 are actually lower than most years, but as you get out past 15, you see a big jump in the density. If instead we look at the actual spread rather than the absolute value, we get the plot below.
Here, negative values correspond to a home team being favored and positive values indicate an away favorite. 2019 is shown in black. Notice the difference in the behavior in the tails of the distribution in 2019. There are both more big home favorites but also more big AWAY favorites. The big away favorites are particularly interesting. Since 2006 there have only been 8 total games where the away team was favored by 15 or more points and SIX of those games involved the Patriots:
- Patriots (-16.5) at Washington Football Team (October 6, 2019)
- Chargers (-15) at Dolphins (September 29, 2019)
- Patriots (-18) at Dolphins (September 15, 2019)
- 49ers (-16) at Jaguars (September 15, 2013)
- Patriots (-15.5) at Buccaneers (October 25, 2009)
- Patriots (-19) at Ravens (December 3, 2007)
- Patriots (-16.5) at Bills (November 18, 2007)
- Patriots (-16) at Dolphins (October 21, 2007)
So, in summary, between 2006 and 2018 we witnessed 5 total games where the away team was favored by 15 or more. That’s an average on ONE game every 2.6 seasons, but this season we are seeing an away team favored by 15 or more once every 2.67 WEEKS!
We’ll see if this trend continues for the rest of the 2019 season, but so far we are seeing a lot more extremely lopsided games than usual.
So I’m way behind on updating these. I blame my kids. Go Bears.
You can view my predictions here. Go Bears.
Season: SU: 38-24-1, Spread: 34-29, O/U: 31-29-3
Week 5: SU: 1-0, Spread: 0-1, O/U: 1-0
Prediction: Chiefs 28-25
Prediction: Rams 27-26
Prediction: Bills 29-12
Prediction: Jaguars 21-20
Prediction: Texans 25-22
Prediction: Vikings 23-21
Prediction: Packers 27-17
Prediction: Giants 25-23
Prediction: 49ers 27-19
Prediction: Titans 21-20
Prediction: Bears 23-17
Prediction: Seahawks 22-21
Prediction: Cowboys 24-23
Prediction: Patriots 27-12