Chess! 2022 FIDE Candidates Tournament!

The 2022 FIDE Candidates tournament is being played right now with the winner facing Magnus Carlsen for a chance to become the world champion (or maybe not). Either way, the winner of this tournament will secure a spot in the World Championship Match (and possible the runner-up, if Magnus decides not to play).  The tournament consists of 8 players and who play each opponents twice, once as white and once as black, for a total of 14 matches.  Players get 1 for a win, 1/2 for a draw, and 0 for a loss and they are currently 9 games into the 14 total and are on a rest day.  (Why do they need a rest day in chess?  Because some of these games are like 8 hours long!?!?).

I’m also teaching a Bayesian class this summer, which gave me an excuse to use the data from the candidates tournament  in a Bayesian example.  So I showed the students a simple multinomial model for the three outcomes of (win, draw, loss).  And we got to have a nice discussion about what our priors should be.  I showed them that if we use a non-informative prior here and let the data dominate, we get kind of nonsense results because they’ve only played so few games in the candidates tournament.  But we have a ton of prior knowledge!  Since all these players qualified for this tournament, we are very confident that they are all very very good and also very very close in terms of skill.  In the model that we set up, the strength coefficients are all relative to each other so we put priors on the betas with mean 0 and HIGH precision (low variance) since we have confidence that these players are all very similar to each other.  We don’t want to let the result of a single game drastically change the regression coefficients.  I’ve included the JAGS model below and the full code can be found here.

Jags Model

"model {
for (i in 1:N){
##Sampling model
#y[i] ~ dmulti(p[i,1:J], 1)
y[i] ~ dcat(p[i, 1:J]) # alternative
for (j in 1:J){
log(q[i,j]) <- alpha[j] + inprod(X[i,], beta[,j])
p[i,j] <- q[i,j]/sum(q[i,1:J])

yrep[i] ~ dcat(ppred[i, 1:J])
for (j in 1:J){
log(qpred[i,j]) <- alpha[j] + inprod(X[i,], beta[,j])
ppred[i,j] <- qpred[i,j]/sum(qpred[i,1:J])

for (j in 1:3) {
alpha[j] ~ dnorm(0, 1)
for (k in 1:8) {
beta[k, j] ~ dnorm(0, 5)

for (m in 1:Npred){
ypred[m] ~ dcat(ppred2[m, 1:J])
for (j in 1:J){
log(qpred2[m,j]) <- alpha[j] + inprod(Xpred[m,], beta[,j])
ppred2[m,j] <- qpred2[m,j]/sum(qpred2[m,1:J])



Some model results

Given equally matched players the model predicts that the player with the white pieces will win 10.10%, the player with the black pieces with win 6.28% of the time and there will be a draw 83.62% of the time.  This all seems very reasonable. (Though the white win percentage in actual games exploded to about 27% given three with wins yesterday).  I also made some fun plots to see the differences in players.  The first plot is the the probability of the players winning vs drawing playing as white and the second plot is the same but for players playing as black.  The dashed lines represent expected values that are equal.  So for instance, in the first plot (players playing as white), Nepo is more likely to win as white and less likely than the others to draw, but his EV is near 0.55.  The only other player with a white EV above 0.525 is Fabi.  When playing as black, the model actually gives Caruana the highest probability to win, but Nepo’s draw probability is high enough that he still have the highest EV as black of almost exactly 0.5.



Expected Final Points

Based on the results of this model, I simulated the remaining games in the tournament 5000 times and then computed the final standings.  Here are the expected number of points for the final tournament standings, with 95% credible intervals:

  1. Nepo: 8.70 (7.5, 10)
  2. Caruana: 8.08 (7, 9)
  3. Hikaru: 7.03 (6, 8)
  4. Rapport: 6.99 (6,8)
  5. Duda: 6.49 (5.5, 7.5)
  6. Ding: 6.47 (5.5, 7.5)
  7. Radjabov: 6.38 (5, 7.5)
  8. Alireza: 5.87 (5, 7)


And I made a fun plot for the number of points that each player will end with.  The darker the colors the more likely that outcome.  (Is there a name for this type of plot?  It’s like a histogram with color.  Does this have a name?). What’s notable about this is that Rapport, Radjabov, and Firouzja are all stuck at 4/9 but the model is predicting that Rapport and Radjabov are likely to finish with more points of Firouzja.

Probability of winning the candidates

I’ve calculated two probabilities for every player: 1) The probability they win the candidates outright and 2) the probability that either win outright OR are part of a tie for first.

Probability of winning the candidates outright

  1. Nepo: 67.76%
  2. Caruana: 10.44%
  3. Hikaru: 0.58%
  4. Rapport: 0.5%
  5. Duda: 0.06%
  6. Ding: <0.02%
  7. Radjabov: <0.02%
  8. Alireza: <0.02%

Probability of finishing with at least a piece of first place

  1. Nepo: 87.94%
  2. Caruana: 29.46%
  3. Hikaru: 2.26%
  4. Rapport: 2.02%
  5. Duda: 0.38%
  6. Ding: 0.12%
  7. Radjabov: 0.38%
  8. Alireza: <0.02%

Probabilities of most likely outcomes

  1. Nepo wins outright: 67.76%
  2. Nepo and Caruana two way tie: 16.88%
  3. Caruana wins outright: 10.44%
  4. Nepo, Caruana, Hikaru three way tie: .76%
  5. Nepo and Rapport two way tie: .64%
  6. Hiarku wins outright: 0.58%
  7. Nepo and Hikaru two way tie: 0.52%
  8. Nepo, Caruana, Rapport three way tie: .52%
  9. Rapport wins outright: 0.5%
  10. Caruana and Hikaru two way tie: 0.26%
  11. Caruana and Rapport two way tie: 0.2%
  12. Nepo and Duda(!!!) two way tie: 0.16%
  13. Nepo and Radjabov two way tie: 0.14%
  14. Nepo, Caruana, and Radjabov three way tie: 0.12%
  15. Nepo, Caruana, and Duda three way tie: 0.12%
  16. Nepo, Caruana, Hikaru, and Rapport FOUR WAY TIE: <0.1%
  17. Duda wins outright: <0.1%
  18. Nepo, Caruana, and Ding three way tie: <0.1%
  19. Nepo and Ding two way tie: <0.1%
  20. Nepo, Caruana, Hikaru, and Radjabov FOUR WAY TIE: <0.1%
  21. Nepo, Caruana, Rapport, and Radjabov FOUR WAY TIE: <0.1%
  22. Nepo, Rapport, Radjabov, and Ding FOUR WAY TIE: <0.1%
  23. Nepo, Caruana, Rapport, Ding, and Duda FIVE WAY TIE(!!!): <0.1%
  24. Nepo, Duda, Radjabov three way tie: <0.1%
  25. Nepo, Duda, Rapport three way tie: <0.1%
  26. Radjabov and Rapport two way tie: <0.1%




Data Art Talk Video

Here is a link to the talk on Data Art that I gave at the University of Oregon.




Greg’s wildly uninformed opinion about the NCAA Men’s basketball tournament

Since I started paying attention to NCAA basketball two days ago, I am now an expert.  I’ve done my “research” and I will now tell you exactly what is going to happen in the tournament.

Some things:

  • Worst 1 seed: Arizona
  • Best 2 seed: Duke
  • Best 3 seed: Purdue
  • Best 4 seed: Illinois
  • Best 5 seed: Iowa
  • Best 6 seed: Texas
  • Best 7 seed: Michigan St
  • Best 8 seed: UNC
  • Best 9 seed: TCU
  • Best Double digit seeded teams: Michigan, Virginia Tech, Indiana, Iowa St, San Francisco, Notre Dame, Miami FL, Rutgers, Loyola Chicago (Go Ramblers!)
  • Worst single digit seeds: Murray St, Creighton, Boise St, Colorado St, Providence, Marquette, Seton Hall
  • Teams that are under seeded: Purdue, Texas,  Michigan, Virginia Tech, Indiana, UNC, Iowa St
  • Teams that are over seeded: Villanova, Arizona, Wisconsin, St. Mary’s, USC, Providence, Colorado St, Marquette, Boise St, Davidson, Creighton, Murray St
  • Why is Murray State a 7 seed?
  • Best team to miss the tournament: Wake Forest
  • Worst At-Large Bid: Wyoming.  (More like WHYoming, amirite?)

My current top 100 rankings (seed) Qualified for NCAA tournament:

  1. Gonzaga (1)
  2. Baylor (1) 
  3. Kansas (1) 
  4. Purdue (3)
  5. Duke (2)
  6. Arizona (1) 
  7. Kentucky (2) 
  8. Auburn (2) 
  9. Texas Tech (3) 
  10. Illinois (4) 
  11. Tennessee (3) 
  12. Texas (6) 
  13. Iowa (5)
  14. UCLA (4) 
  15. Villanova (2) 
  16. Arkansas (4) 
  17. Ohio St (6)
  18. Alabama (6) 
  19. UConn (5) (Go Huskies!)
  20. Michigan (11)
  21. LSU (6) 
  22. UNC (8)
  23. Wisconsin (3) 
  24. Virginia Tech (11)
  25. Michigan St (7) 
  26. Wake Forest
  27. Indiana (12)
  28. Oklahoma
  29. Nicholls St (Wisconsin, a 3 seed, beat Nicholl’s state by only 3 points!)
  30. Xavier
  31. Florida
  32. Oklahoma St
  33. Virginia
  34. Iowa St (11)
  35. San Francisco (10)
  36. USC (7) 
  37. St. Mary’s (5) 
  38. Miss St
  39. TCU (9)
  40. San Diego St (8)
  41. Seton Hall (8)
  42. Notre Dame (11)
  43. UAB (12)
  44. Miami FL (10)
  45. West Virginia
  46. Rutgers (11)
  47. Loyola Chicago (10) (Go Ramblers!)
  48. Kansas St
  49. Providence (4) 
  50. Marquette (9)
  51. Colorado St (6)
  52. Oregon
  53. Washington St
  54. Northwestern
  55. BYU
  56. St. Johns
  57. Maryland
  58. Clemson
  59. North Texas
  60. Texas A&M
  61. Boise St (8)
  62. Florida St
  63. Penn St
  64. Davidson (10)
  65. VCU
  66. UC Irvine
  67. Vermont (13)
  68. Syracuse
  69. Vanderbilt
  70. Dayton
  71. UCSB
  72. Creighton (9)
  73. St. Bonaventure
  74. South Dakota St (13)
  75. St. Louis
  76. Utah St
  77. Colorado
  78. SE Louisiana
  79. Belmont
  80. Murray St (7) 
  81. Richmond (12)
  82. Texas A&M CC
  83. New Orleans
  84. Toledo
  85. SW Missouri St
  86. Louisiana Tech
  87. NC St
  88. NM St (12)
  89. Mississippi
  90. South Carolina
  91. Louisville
  92. Wyoming (12)
  93. Furman
  94. Chattanooga (13)
  95. Drake
  96. Call Riverside
  97. CS Fullerton (15)
  98. Iona
  99. Fresno St
  100. Western Kentucky




I know everyone wants to know what I think about Joe Rogan and Neil Young. So I wrote this.

Joe Rogan issued an apology about the whole Neil Young/Spotify/Covid Misinformation kerfuffle.  And since I know the world is dying to know what I think about the whole thing, I have written down some thoughts about apology.

If you are living under a rock, you can read about the whole slap fight here.  Basically, Neil Young (then Joni Mitchell) wanted his music removed from Spotify is they were going to keep Joe Rogan’s podcast on the platform.  People are pissed at Rogan for spreading some misinformation about Covid, and other people are pissed at Young et. al. for trying to “cancel” Joe Rogan while they vaguely yell “Free speech”.  (Some people are even trying to compare calls for Rogan being removed from Spotify to a Tennessee school board banning the Pulitzer Prize winning book “Maus”.  They are not at all the same, by the way. Just think for 2 seconds about the entity trying to do the banning in both these cases to figure out why.)

Anyway, Joe Rogan has issued and apology.  You can view the apology here:

I’ve written my thoughts in response to the apology with time stamps addressing specific comments that Rogan makes:

0:35: He mentions the two episodes that people have particular issues with.  The guests in question are Dr. Peter McCullough and Dr. Robert Malone.  

For sure, both of these guys are highly credentialed in their fields.  But Peter McCullough’s field is cardiology.  He’s not an expert epidemiology or vaccines.  Yet on the podcast, McCullough makes a bunch of objectively incorrect statements about the vaccines, masks, how the virus spreads, and he even claims the pandemic was planned.  He also does not seem to understand VAERS very well and how the data is collected.  You can read a nice summary of the claims, complete with why they are incorrect, here.

Robert Malone’s story is a wild one.  I won’t summarize it in this post, but I encourage you to read all about it here.

1:40: Rogan says: “8 months ago if you said if you get vaccinated you can still catch covid and you can still spread covid.  You would be removed from social media.  They would ban you from certain platforms.  Now that’s accepted as fact.”   

No no no no no.  No vaccine is 100% effective.  All vaccines can do is lower the risk of catching a disease, which also lowers the risk of spreading it.  The original efficacy of the Pfizer vaccine for instance was 95%.  Which means that some vaccinated people got Covid.  It’s literally in the journal article describing the study.  It’s right in the abstract.  This statement is complete nonsense.   (Update: A commenter pointed out that Biden was saying things like “You’re not going to get COVID if you have these vaccinations,” and “If you’re vaccinated, you’re not going to be hospitalized, you’re not going to be in the ICU unit, and you’re not going to die.”  This was never true.  All vaccines do is lower your risk.  In this case these vaccines lower your risk a lot.  Side note: One of the biggest failures of this entire pandemic is the communication from public health organizations to the public.  It has been absolutely awful.  It was awful under Trump and awful under Biden.  Public health officials need to totally rethink how they communicate top the public because its been an un mitigated failure.)

And “I don’t think cloth masks work.  You would be banned from social media.   Now that’s openly and repeatedly stated on CNN.”

I’m pretty sure no one was banned from social media for saying that cloth masks don’t work.  Can anyone find ANY example of this?  (Update: So I was wrong.  Apparently Rand Paul was banned from YouTube for 7 days for saying that  “Most of the masks you get over the counter don’t work. They don’t prevent infection,” adding that “cloth masks don’t work.”  While cloth masks certainly don’t guarantee that you won’t get Covid, they definitely work in lowering the risk of spreading covid.

“If you said, I think it’s possible that Covid 19 came from a lab.  You would be banned from many social media platforms.  Now that’s on the cover of Newsweek.”

Newsweek is a “zombie magazine” peddling right wing and alt-right conspiracy theories.  It’s trash now.

2:31: He totally admits to getting things wrong.  And he does admit when he’s wrong.  Somegtimes.  He says: “whenever he gets something wrong, he tries to correct it”

I’ve listened to my fair share of Rogan podcasts and he does admit when he’s wrong.  A lot.  But he seems to just double down on Covid mistakes.  It’s odd.  Because he’s so open to being wrong about other things.

2:37: “Cause I’m interested in telling the truth.  I’m interested in finding out what the truth is”

There are some people out there who are all like “He’s a comedian.  You shouldn’t be getting medical advice from a comedian”.  This is very true.  But in the context of this podcast, he isn’t a comedian.  He’s not telling jokes or performing.  He even says himself, he is trying to find the truth.  So he’s not acting like a comedian in this context.

2:46: “I’m interested in having conversations with people who have differing opinions”.  

Sure.  Fine, but some of these people’s “opinions” are factually wrong.  And just because someone has a differing opinion doesn’t make them worth talking to.  Flat-earthers have a different “opinion”, but they aren’t worth talking to because they are factually wrong.  And some of his guests are simply factually wrong about stuff.

3:20: I’m interested in finding out what is correct”.

Again, he’s not a comedian here!

3:55: He talks about the Spotify disclaimer.

He’s totally open to the Spotify disclaimer.

5:25: He tells a Neil Young story.

The Neil young story is great.  He even references Mansfield, MA and Great Woods!

7:35: “I’m not trying to promote misinformation”.

I genuinely believe him.  The issue here is that he has the largest podcast in the world.  And he seems to not understand what they means.  Millions of people are listening to this stuff and he seems totally unprepared for that.

7:55: “the podcast started of as  just fucking around with my friends.  and having fun and talking”

He even seems to admit this.  He just wants to talk to people.  The problem, again, is that millions of people listen to this podcast, and he is giving people a MASSIVE platform to share their ideas.  This podcast is HUGE.  So, I think it’s probably not a responsibility he ever wanted, but he probably needs to think a bit harder about who he gives his platform to.

8:50: “It’s a strange responsibility to have this many viewers and listeners.  It’s very strange.”

It is VERY strange.

9:26: “Thank you to the haters.  It makes you assess what you’re doing”.

I wish I had as many haters as he did.






My dream NFL season

There is a crazy scenario this week where the Jaguars (somehow) beat the Colts and then the the Raiders and Chargers could both make the playoffs with a tie on Sunday night football.  I for one want to see 60 minutes of kneel down, kneel down, kneel down, punt.  I would watch every second.

I live for stuff like this.  My favorite sports moments include the time the lights went out at the Super Bowl and the time Gurley accidentally scored a game losing touchdown.   And of course there is the all time greatest soccer game: Barbados vs Grenada where Barbados had to defend BOTH GOALS for three minutes.

So this got me thinking about one of my favorite topics: How bad can an NFL team be and still make the playoffs?  If you assume no game ends in a tie, an NFL team can theoretically go 3-14 and make the playoffs.  They would actually HOST A HOME GAME in this scenario.  But I wanted to see what this full season would look like, so I wrote some code to simulate the 2021-22 season (with the real schedule) with the caveat that NFC North teams lose all of their out of division games and split evenly with all teams in the NFC North.  I also required there to be an 8 win wild card team in the NFC, which is the lowest number of wins I could get for a wildcard team with all NFC North teams winning only 3 games.  So without further adieu, here is what that season could really have looked like in my dream world (there are many scenarios with this, here is one of them):



Dolphins 12-5

Patriots 8-9

Jets 7-10

Bills 6-11


Ravens 13-4

Browns 12-5

Steelers 10-7

Bengals 7-10


Texans 12-5

Jaguars 11-6

Titans 10-7

Colts 5-12


Raiders 13-4

Chiefs 10-7

Chargers 10-7

Broncos 5-12



Washington Football Team 13-4

Giants 11-6

Eagles 7-10

Cowboys 6-11


Bears 3-14

Lions 3-14

Packers 3-14

Vikings 3-14


Buccaneers 10-7

Panthers 8-9

Saints 7-10

Falcons 5-12


Cardinals 14-3

Seahawks 13-4

Rams 8-9

49ers 7-10




  1. Raiders 13-4
  2. Ravens 13-4
  3. Dolphins 12-5
  4. Texans 12-5
  5. Browns 12-5
  6. Jaguars 11-6
  7. Steelers 10-7

Things get fun here!


  1. Cardinals 14-3
  2. Washington Football Team 13-4
  3. Buccaneers 10-7
  4. Bears 3-14
  5. Seahawks 13-4
  6. Giants 11-6
  7. Rams 8-9

In the NFC this would lead to the following wild card games:

Rams 8-9 at Washington 13-4

Giants 11-6 at Buccaneers 10-7

Seahawks 13-4 AT BEARS 3-14(!!!) (This is theoretically possible!!!)

All I want for next Christmas is the 3-14 Bears to HOST the 13-4 Seahawks in a playoff game.  The Seahawks deserve to be that team to have to go to the 3-14 team after they hosted a playoff game withe a losing record (and then won!).



Chiropractic is still bullshit

Subluxation, as defined by chiropractors, is simply not a scientific concept.  And it even divides practitioners within the chiropractic community.  But look, it’s still taught in schools of chiropractic.  Like Palmer College of Chiropractic (named after the founder of chiropractic, D.D. Palmer).  Just look at the third trimester sample schedule:

Chiropractors can talk all they want about how they have made progress and what not, but they are still teaching this objectively unscientific concept in the top chiropractic schools.  It’s complete insanity.

Some of the other fun classes that are in their curriculum for whatever reason include embryology, toggle (whatever that is), obstetrics/pediatrics (please don’t take your kid to a chiropractor) and cervical technique.  Cervical technique!

If you are in pain and suffering, please go see an actual medical doctor who went to a real medical school.



NFL Predictions – Week 7

Season Total – W/L 29-20, Spread 29-20, O/U 25-24

Week 1  – W/L 9-7, Spread 11-5, O/U 8-8

Week 2 – W/L 11-5, Spread 9-7, O/U 8-8

Week 3 – W/L 8-8, Spread 8-8, O/U 9-7

Week 4 – W/L 1-0, Spread 1-0, O/U 0-1

Week 5 – W/L 1-1, Spread 1-1, O/U 1-1

Week 6 – W/L 0-0, Spread 0-0, O/U 0-0

Week 7 – W/L 1-0, Spread 1-0, O/U 0-1

Denver at Cleveland

Outcome: Browns 22-20

Spread: Browns -1.5

Total:  Over 40.5

Washington at Green Bay

Outcome: Packers 28-21

Spread: Washington Football Team +8.5

Total:  Over 48

NY Jets at New England

Outcome: Patriots 22-17

Spread: Jets +7

Total:  Under 42.5

Carolina at NY Giants

Outcome: Panthers 21-20

Spread: Giants +3

Total:  Under 43

Kansas City at Tennessee

Outcome: Chiefs 31-25

Spread: Chiefs -4

Total:  Under 59

Cincinnati at Baltimore

Outcome: Ravens 28-21

Spread: Ravens -6

Total:  Over 46

Philadelphia at Las Vegas

Outcome: Raiders 28-23

Spread: Raiders -2

Total:  Over 48.5

Detroit at LA Rams

Outcome: Rams 32-19

Spread: Lions +16.5

Total:  Over 50.5

Houston at Arizona

Outcome: Cardinals 31-15

Spread: Texans +20

Total:  Under 47.5

Chicago at Tampa Bay

Outcome: Buccaneers 29-17

Spread: Bears +12

Total:  Under 47

Indianapolis at San Francisco

Outcome: 49ers 25-21

Spread: 49ers -3.5

Total:  Over 42

New Orleans at Seattle

Outcome: Saints 24-22

Spread: Seahawks +4.5

Total:  Over 42.5

NFL Predictions – Week 6

Season Total – W/L 29-20, Spread 29-20, O/U 25-24

Week 1  – W/L 9-7, Spread 11-5, O/U 8-8

Week 2 – W/L 11-5, Spread 9-7, O/U 8-8

Week 3 – W/L 8-8, Spread 8-8, O/U 9-7

Week 4 – W/L 1-0, Spread 1-0, O/U 0-1

Week 5 – W/L 1-1, Spread 1-1, O/U 1-1

Tampa Bay at Philadelphia

Outcome: Buccaneers 30-22

Spread: Buccaneers -7

Total:  Under 53

Miami at Jacksonville

Outcome: Dolphins 23-20

Spread: Dolphins -3

Total:  Under 47

Minnesota at Carolina

Outcome: Vikings 25-24

Spread: Panthers +2.5

Total:  Over 45.5

Green Bay at Chicago

Outcome: Packers 26-20

Spread: Packers -5.5

Total:  Over 44

Houston at Indianapolis

Outcome: Colts 26-16

Spread: Texans +11.5

Total:  Under 44.5

Cincinnati at Detroit

Outcome: Bengals 25-21

Spread: Bengals -3.5

Total:  Under 46.5

LA Rams at NY Giants

Outcome: Rams 29-20

Spread: Rams -7.5

Total:  Under 49

LA Chargers at Baltimore

Outcome: Ravens 25-23

Spread: Chargers +3

Total:  Under 51

Kansas City at Washington

Outcome: Chiefs 29-23

Spread: Washington Football Team +7

Total:  Under 54

Arizona at Cleveland

Outcome: Cardinals 25-23

Spread: Cardinals +3.5

Total:  Under 48

Las Vegas at Denver

Outcome: Broncos 25-21

Spread: Raiders +5

Total:  Over 44.5

Dallas at New England

Outcome: Cowboys 25-24

Spread: Patriots +3.5

Total:  Under 50.5

Seattle at Pittsburgh

Outcome: Seahawks 24-23

Spread: Seahawks +5

Total:  Over 43

Buffalo at Tennessee

Outcome: Bills 27-24

Spread: Titans +6

Total:  Under 53.5

An Open Letter to the residents of East Longmeadow, the Town Council and Town Manager of East Longmeadow, and the East Longmeadow Board of Health

To whom it may concern:

Recently it has come to my attention that Justin McCarthy, an East Longmeadow resident, has filed a petition the the Town Council that has 160 signatories (or just over 1.25% of registered EL voters) “demanding an end to the defunct Health Board’s mask mandate”.

Justin lays out his arguments in a blog post from October 6, 2021, “Why the East Longmeadow Town Council Can and Should End the Mask Mandate.

I am not an expert in the law, therefore I will not comment on the strengths or flaws in Mr. McCarthy’s legal arguments, however, it is my understanding from talking to several other lawyers that his legal arguments are without merit.

However, I do have expertise in statistical analysis.  My training includes an M.S. in Applied Statistics from WPI in 2005, a Ph.D. in Statistics from the University of Connecticut  in 2011, a postdoctoral research fellow in the School of Public Health at the University of Massachusetts from 2011-2014.  Since 2014 I have been at Loyola University Chicago in the Department of Mathematics and Statistics where I am an Associate Professor of Statistics with tenure and the Director of the Data Science Program.  Given my particular background, I feel I am qualified to comment on Mr. McCarthy’s contention that the statement from the Health Board that was used to justify the mask order is not supported by any sort of data or evidence.  Specifically, Mr. McCarthy states in his blog post from October 6, 2021:

The Health Board justified its mask order by stating “we know that masks slow or prevent transmission of all COVID-19 variants so far.”  (See the third paragraph of the order.) The statement is not supported by any sort of data or evidence.

To put it bluntly, this statement is patently incorrect, and I will provide comprehensive support for masking policies later.  Before that, however, I want address he shortcomings in Mr. McCarthy’s framing of masking efficacy in relation to COVID-19.  Mr. McCarthy cites a single paper, Guerra and Guerra (2021) in International Research Journal of Public Health (DOI: 10.28933/irjph-2021-08-1005). (Note: Mr. McCarthy states in his October 6 blog post that Dr. Damien Guerra is a “bio-statistician [sic]”.  This is another incorrect statement.  Dr. Guerra is a trained biologist focusing on cell and molecular biology who appears to have taught biostatistics courses in the past.  It is unclear what his formal training in statistics is, if any.)  In that article, the authors conclude:

We did not observe association between mask mandates or use and reduced COVID-19 spread in US states. COVID-19 mitigation requires further research and use of existing efficacious strategies, most notably vaccination.

After reading the full article, it is my professional opinion that the statistical analysis performed in this article are extremely weak.  They used observational data (true randomized control trials (RCT), the gold standard for evaluating efficacy of a treatment are difficult to conduct for mask usage due to practical and ethical concerns) aggregated at the state level and looked for differences in growth rates associated with mask mandates.  However, the statistical methods that they chose to use are elementary and in my opinion not appropriate for this type of analysis (I am happy to elaborate if there is interest).

Curiously, one of the authors of this study, Damian Guerra, has written a letter to the East Longmeadow Town Council and Town Manager offering the following summary points based on an annotated bibliography: 

  • COVID-19 is a serious pandemic disease that warrants precautionary measures.

  • The best protections against COVID-19 are vaccination, ventilation, and generally good health (e.g., vitamin D repletion).

  • General civilian mask use and mask mandates likely do not reduce rates of COVID-19 transmission.

  • Studies purportedly demonstrating mask efficacy have used small sample sizes, have lacked comparison groups, or have omitted key information.

  • Among masks, only properly fitted KN95 (or related N/R/P95 type) respirators have demonstrated protection against viral infection.

  • Enhanced building ventilation is more effective than mask wearing at aerosol dispersion.

I agree with the first two bullet points wholeheartedly, but the third statement statement “General civilian mask use and mask mandates likely do not reduce rates of COVID-19 transmission” is simply not supported by evidence.  The fourth bullet point may have been at least partially true earlier in the pandemic, but at this point (October 2021) this is simply false.  The fifth bullet point is false, and the sixth bullet point is true, but simply wearing a mask is a much more easily implementable prevention measure than modifying existing building ventilation.

I will now address the contention from Guerra that “General civilian mask use and mask mandates likely do not reduce rates of COVID-19 transmission”.  Early in the pandemic, the evidence that masking reduced the the spread of COVID-19 was mixed.  There simply were not many good studies evaluating the effectiveness of mask at preventing the spread of COVID-19 because this is a novel virus that was only recently identified. However, as of October 2021, this is no longer the case.

(Note: In Guerra’s letter to the East Longmeadow, he mentions Vitamin D repletion as a “proven strategy for Covid-19 mitigation”.  Recent work from McGill University was unable to find any link between Vitamin D Covid mitigation.  The Authors state in their conclusion: “In this 2-sample MR study, we did not observe evidence to support an association between 25OHD levels and COVID-19 susceptibility, severity, or hospitalization. Hence, vitamin D supplementation as a means of protecting against worsened COVID-19 outcomes is not supported by genetic evidence. Other therapeutic or preventative avenues should be given higher priority for COVID-19 randomized controlled trials.”)

In January 2021, a review article entitled “An evidence review of face masks against COVID-19” by Howard et. al. was published in the Proceeding of the National Academy of Sciences of the United States of America (PNAS).  This article presents an even handed review of the available evidence of the efficacy of mask use in limiting the spread of COVID-19.  They conclude:

Our review of the literature offers evidence in favor of widespread mask use as source control to reduce community transmission: Nonmedical masks use materials that obstruct particles of the necessary size; people are most infectious in the initial period postinfection, where it is common to have few or no symptoms (4546141); nonmedical masks have been effective in reducing transmission of respiratory viruses; and places and time periods where mask usage is required or widespread have shown substantially lower community transmission.

(Note: In a separate blog post, Mr. McCarthy, who, I will remind you, is not an economist, contends that the mask mandate is having a negative impact on local businesses.  He offers basically no evidence of this beyond a few scattered anecdotes, but if he is concerned about the economy, Howard et. al. mentions that “Economic analysis suggests that mask wearing mandates could add 1 trillion dollars to the US GDP.”)

For more evidence the use of masks in limiting the spread of COVID-19, the CDC has compiled (as on May 7, 2021) a list of studies evaluating the efficacy of masks.  In their conclusion, they state:

Experimental and epidemiological data support community masking to reduce the spread of SARS-CoV-2. The prevention benefit of masking is derived from the combination of source control and wearer protection for the mask wearer. The relationship between source control and wearer protection is likely complementary and possibly synergistic14, so that individual benefit increases with increasing community mask use. Further research is needed to expand the evidence base for the protective effect of cloth masks and in particular to identify the combinations of materials that maximize both their blocking and filtering effectiveness, as well as fit, comfort, durability, and consumer appeal. Mask use has been found to be safe and is not associated with clinically significant impacts on respiration or gas exchange. Adopting universal masking policies can help avert future lockdowns, especially if combined with other non-pharmaceutical interventions such as social distancing, hand hygiene, and adequate ventilation.

Notice that the CDC says “Further research is needed to expand the evidence base for the protective effect of cloth masks and in particular to identify the combinations of materials that maximize both their blocking and filtering effectiveness, as well as fit, comfort, durability, and consumer appeal.”  This is a sign of good, solid science.  When something is unknown and more evidence is needed, that is stated.  

As of the writing of that CDC summary (May 7, 2021) there is a preponderance of observational and epidemiological evidence that mask wearing effectively limits the spread of COVID-19.  However, there was no randomized controlled trial evaluating the causal effectiveness of masks in limiting COVID-19 spread, but just recently a large randomized-trial was performed to study exactly the question of mask efficacy.

On September 1, 2021, a working paper entitled “The Impact of Community Masking on COVID-19: A Cluster-Randomized Trial in Bangladesh” was published online. The authors of that study describe their experiment:

A randomized-trial of community-level mask promotion in rural Bangladesh during COVID-19 shows that the intervention tripled mask usage and reduced symptomatic SARS-CoV-2 infections, demonstrating that promoting community mask-wearing can improve public health.

This article finds statistically significant reductions in the spread of COVID-19 in villages where masks were worn compared to villages where masks were not worn.  In addition, they demonstrate that cloth masks also significantly lowered the spread of COVID-19 compared with villages that were not wearing masks.  It should be noted that the reduction in COVID-19 with cloth masks was smaller than the reduction observed when surgical masks were worn.  In the authors’ words:

We present results from a cluster-randomized controlled trial of a scalable intervention designed to increase mask-wearing and reduce cases of COVID-19. Our estimates suggest that mask-wearing increased by 28.8 percentage points, corresponding to an estimated 51,347 additional adults wearing masks in intervention villages, and this effect was persistent even after active mask promotion was discontinued. The intervention led to a 9.3% reduction in symptomatic SARS-CoV-2 seroprevalence (which corresponds to a 103 fewer symptomatic seropositives) and an 11.9% reduction in the prevalence of COVID-like symptoms, corresponding to 1,587 fewer people reporting these symptoms. The effects were substantially larger (and more precisely estimated) in communities where we distributed surgical masks, consistent with their greater filtration efficiency measured in the laboratory (manuscript forthcoming). In villages randomized to receive surgical masks, the relative reduction in symptomatic seroprevalence was 11% overall, 23% among individuals aged 50-60, and 35% among those over 60.

It is important to point out that currently, this article has not been peer-reviewed.  However, in my reading of the manuscript, it appears to be a well designed from a statistical perspective and the statistical methods are appropriate.  The Johns Hopkins School of Public Health made he following statement regarding the study (I would encourage everyone to read the full statement, including limitations that were identified):

This was a very large and well-designed cluster-randomized controlled trial of a multi-pronged intervention program to encourage mask-wearing in rural and peri-urban Bangladesh from November 2020 to April 2021; it was available as a preprint and is thus not yet peer reviewed. The study found that the intervention package (which included mask distribution, public role-modeling, and encouragement to non-mask-wearers in public settings) more than tripled public mask usage behaviors (from 13% to 42%) without diminishing observed physical distancing.


If the results are valid, they imply that near-universal mask wearing would be associated with much larger reductions in transmission.

In conclusion, there is very strong observational and epidemiological evidence that mask use, both cloth and surgical, in public reduces community spread of COVID-19, and I would recommend that local municipalities too continue to comply with state and federal masking guidelines, put in place by experts in public health, epidemiology, and medicine, as a part of a continued effort, along with vaccinations, social distancing, and basic hygiene, to combat COVID-19.  I would encourage everyone to read the American College of Pediatrics statement endorsing the use of facemarks for children 2 years of age and older.

Finally, while masks are an important par of COVID-19 prevention, the best weapon in our fight against this virus, and I think Dr. Guerra and I can both agree on this, is the safe and effective COVID-19 vaccine.  I would encourage everyone to get vaccinated and to say up to date on emerging guidelines for booster shots.

Stay safe.


Gregory J. Matthews, Ph.D.

NFL Predictions – Week 5

Season Total – W/L 29-20, Spread 29-20, O/U 25-24

Week 1  – W/L 9-7, Spread 11-5, O/U 8-8

Week 2 – W/L 11-5, Spread 9-7, O/U 8-8

Week 3 – W/L 8-8, Spread 8-8, O/U 9-7

Week 4 – W/L 1-0, Spread 1-0, O/U 0-1

Week 5 – W/L 1-1, Spread 1-1, O/U 1-1

LA Rams at Seattle

Outcome: Seahawks 28-27

Spread: Seahawks +2.5

Total:  Over 54.5

NY Jets at Atlanta

Outcome: Falcons 26-22

Spread: Falcons -3

Total: Over 45.5

Philadelphia at Carolina

Outcome: Panthers 25-23

Spread: Eagles +2.5

Total:Over 46

Green Bay at Cincinnati

Outcome: Packers 24-21

Spread: Packers -2

Total: Under 50

New England at Houston

Outcome: Patriots 27-16

Spread: Patriots -8

Total: Over 39

Tennessee at Jacksonville

Outcome: Titans 27-21

Spread: Titans -4.5

Total: Under 48.5

Detroit at Minnesota

Outcome: Vikings 28-21

Spread: Lions +10

Total: Under 49.5

Denver at Pittsburgh

Outcome: Broncos 19-18

Spread: Steelers +1.5

Total: Under 39.5

Miami at Tampa Bay

Outcome: Buccaneers 30-17

Spread: Buccaneers -11

Total: Under 48

New Orleans at Washington

Outcome: Football Team 21-20

Spread: Football Team +2.5

Total: Under 43.5

Chicago at Las Vegas

Outcome: Raiders 25-18

Spread: Raiders -5.5

Total: Under 46

Cleveland at LA Chargers

Outcome: Chargers 27-26

Spread: Browns +2.5

Total: Over 47

San Francisco at Arizona

Outcome: Cardinals 25-24

Spread: 49ers +5

Total:Under 52.5

NY Giants at Dallas

Outcome: Cowboys 28-21

Spread: Giants +7

Total: Under 52.5

Buffalo at Kansas City

Outcome: Chiefs 30-25

Spread: Chiefs -3

Total:Under 56.6

Indianapolis at Baltimore

Outcome: Ravens 27-20

Spread: Colts +7

Total: Over 46