In Part 1, I introduced Bill James’ Pythagorean expectation for estimating the expected win percentages in Major League Baseball. Here in Part 2, I discuss how it can be improved [1].
As mentioned at the end of Part 1, Pythagorean expectation and Wins Above Replacement (WAR) use runs as the single measuring stick for calculating expected win percentage (for teams) and value (of players), respectively. Two teams that score the same average runs per game (RPG) should split games between them evenly. Two players with equal WAR have equal value. But is it possible that there are other factors at play?
Consider three teams, each of which scores an average of 5.0 RPG: Team A, which always scores 5 runs (5/5/5), Team B, which scores 4 runs two-thirds of the time and 7 runs one-third of the time (4/4/7), and Team C, which scores 6 runs two-thirds of the time and 3 runs one-third of the time (6/6/3). In none of these cases do the teams split their games evenly in head-to-head matchups, as predicted by the Pythagorean expectation. It is easy to show that Team A beats Team B 6 games out of 9, Team B beats Team C 5 games out of 9, and Team C beats Team A 6 games out of 9!
This rock/scissors/paper example shows that which is the better team is a non-transitive property. It immediately follows that no single numerical parameter, e.g., RPG, is sufficient to determine which team is better in a head-to-head matchup. Although simplistic, this example clearly shows that sometimes we must go beyond RPG to determine which team is better. The shape of the run distribution can also be an important factor: Team A is very consistent, Team B scores below their average more often (negative skew), while Team C scores above their average more often (positive skew).
In practice, baseball run distributions tend to have negative skew, i.e., like Team B above, with many games a little below average and fewer games above average but with larger deviations from the average. For example, a team that averages 5.0 RPG may have many games with 3 or 4 runs, but a few with 10 or more runs. Since Team B tends to lose more to Team A, it is a general rule that teams that are more consistent, and have a smaller negative skew in their run distribution, should win more games than just their RPG would otherwise indicate. A team with smaller skew also has a smaller standard deviation; standard deviation can be used as a second parameter, in addition to RPG, to help rank teams.
Teams A, B, and C above are very unrealistic. A more realistic (but still idealized) example is the following: Let team HR only hit home runs when they get a hit, Team 2B only hits doubles, Team 1B only hits singles with the runners advancing one base, and team 1B+ only hits singles with the runners always advancing from first to third on a single. Then Team HR scores once every hit, Team 2B scores on the second hit of an inning, Team 1B+ scores on the third hit of the inning, and team 1B scores on the fourth hit of an inning. Once any of these team has scored a run in an inning, they always score another run for each successive hit in that inning.
If we assume these teams all average 5.0 RPG, the HR team must have a batting average (AVG) of .156, the 2B team .284, the 1B+ team .373, and the 1B team .441. Pythagorean expectation would say that they all should split games against each other equally, but is that the case? The following table shows the winning percentage of these teams against each of the others, along with their standard deviation.
In each case, the team with the smaller standard deviation is favored to win more than 50% of the time, and the larger the difference in standard deviations, the more they are favored. Looking at the run distributions (below), we see that the HR team has the least skew, 2B team is next, followed by 1B+, and the 1B team has the most skew.
The difference in skew makes sense; the 1B team takes more hits in an inning to score, but once they get there, each successive hit scores a run, and with their higher batting average, that happens a lot. So they tend to have more bigger innings than the HR team.
Of course no team produces only one kind of hit. A more accurate model would allow a team to hit singles, doubles, triples, and home runs, take walks, and allow runners to sometimes advance extra bases on a hit (e.g., go from first to third on a single), or advance one base on an out (e.g., on a sacrifice or sacrifice fly). Using a Markov chain analysis, one can assume a team has a certain set of batting and base-running characteristics and then calculate their average RPG and the shape of their run distribution. Then playing different teams against one another, one can determine what modification is needed to the Pythagorean expectation to account for the shape of the run distribution.
It turns out that slugging percentage (SLG) provides the best additional parameter to use, even better than standard deviation. SLG is calculated by taking all the bases achieved on hits (one for a single, two for a double, etc.) and dividing it by the number of times at bat. For example, our HR team above has a SLG of .625, and the 2B team .567. A team with a higher SLG has a smaller standard deviation and will win more games, given the same RPG. The new, improved winning percentage formula for Team 1 playing Team 2 is
for the current run environment where an average team scores about 4.5 RPG; R stands for RPG and S for SLG. This can be compared to the (modified) Pythagorean expectation formula
The net effect of the new formula is that each additional .080 in team SLG (for the same RPG) adds about one win in a 162-game season. Thus “.080 SLG = 1 win” can be used as a supplement to the standard sabermetric valuation “10 runs = 1 win.” For reference, the current range of SLG in Major League Baseball is about .110. Thus the effect is small, but if you are looking for any small advantage, including SLG in your evaluation of players (above and beyond WAR itself) might be worth considering.
The idea that a more consistent scoring team wins more can be applied in a variety of ways. For example, if consistent offense is better, consistent pitching is worse (all other things being equal). A pitcher who is inconsistent, with many good games and a few very bad games, would be better for a team than a pitcher with the same allowed RPG who is more consistent; the inconsistent pitcher tends to lose in the bad games, but there are fewer of them.
[1] This article is a very condensed version of the paper I presented at the 2010 MIT Sports Analytics Conference, which was chosen as the best paper submitted by an academic.
None of this helps the White Sox look any better!!!
*sobs into Coke Zero*
At least you still have a team…
See ball
Hit ball
Run around the bases
Win game
Baseball is for napping.
*stops striking flint*
Wait, it’s not for knapping?
Does this mean I have to do math now?
Yes, but the stats can let you know how often ball gets hit, caught, etc. I will leave it to the whiz types to figure it out….as I am not particularly skilled in higher mathematics.
You throw the ball, you catch the ball, you hit the ball. Sometimes you win, sometimes you lose, sometimes it rains.
One question, whiz – with gambling getting so involved now, are baseball stat folks getting pulled in that direction, or are there simply more jerbs now?
I really am uncomfortable with all the gambling stuff out there now. I don’t have direct experience with it, and certainly, free people should be free to wreck themselves on any shoal, but gambling, to me, seems like one of the most destructive vices.
seems like one of the most destructive vices
State lotteries sneer at you.
Heroin raises an eyebrow.
State lotteries are to gambling as a .45 automatic is to russian roulette.
You have to admit, the odds are better with a 1911 vs most revolvers. 1/7 is better than 1/6 odds.
Well said, I’ll stop and get powerball.
Yup. State lotteries are effectively a tax on stupidity.
Stop knocking my retirement plan.
What if it’s the police shooting at you?
That apparently pays 3.25 Million if you hit the right number.
I am glad that gambling really has little to no appeal to me.
A city like Las Vegas wasn’t built from nothing in the desert to a huge spectacle because casinos and bookies hand out money like crazy…
Yep. I really don’t like to gamble at all. The most I’ll do is play poker for money–small stakes only. At least there’s some skill involved in that–not just making educated guesses and throwing my money to the winds of probability.
I generally agree, save that poker is absolutely a game of skill.
Yes, agreed. It’s why I enjoy poker, but can’t get into anything else. My boss’s boss is super into craps and blackjack and tries to get us to go to casinos on trips but I just don’t wanna.
You can win at blackjack if you count cards, as long as you aren’t too greedy and stay under the casino’s radar. It’s a slow slog and not lucrative that way, but you can come out ahead in the long run.
Surely you can win at it. I just have so little interest in the casino environment that I’d rather be sick in bed than at the tables.
Most casinos nowadays reshuffle the shoe whenever a new player joins the game, which makes counting cards pointless in blackjack. There are no-count systems that will pay a ~1.5% return long term, but that’s no fun unless you’re using it to launder money (or to sip comped Remy Martin at the high-rollers table.)
I make money consistently at Blackjack and can make money at craps. As whiz points out, BJ can be a grind, but you will come out ahead if you know what you are doing. Craps is very shooter dependent. If you get someone who is consistent in positioning/throwing the dice, you can get a reliable outcome. It takes practice and patience. My best streak is 46 rolls in a row. I was hitting the hard 10 so often the guy next to me started throwing a $25 chip at me everytime I hit it.
I used to be in the industry (finance side), so I’ve been in casinos all over the country. Probably haven’t spent $100. And most of that was in a sports book so I could watch a bunch of hockey games and get “free” beers.
Same here. Gambling could really fuck me up if I had any interest in it.
*reaches for Juul with shaky hand*
Did you hear about this?
FDA Bans Juul From Selling E-Cigarettes
Hope rhywun has a stash
Apparently Juul execs were being a little stingy when it came to giving out their campaign contributions. This should set an example for other companies thinking that they can go about their business without greasing a few palms.
Heard it was coming and didn’t believe it. What a fucking scam – this reeks to high heaven of corruption on multiple levels.
Guess I’ll have to see what else is out there.
You have Hannity in your corner!
Hallelujah.
I won $500 playing some dice game in a dive bar once, not sure if it was liars dice or Chinese craps, but when the guy I was playing with offered to keep the game going after hours in that joint, I politely declined.
And that is a skill.
Sounds like someone was trying to set up a hussle and you walked away at the hook.
I kinda knew the guy, but I think that might have been a bit of an idea. He spent a bit of time in the hoosgow not long after that.
When I lived in Vegas, I hardly gambled at all. Sometimes would go to the Sahara with work friends, play a couple of football cards to get a free buffet.
When friends visited from out of town, we’d bring them to the strip and watch them toss away money. I might put $20 through slots while they lost at blackjack – sometimes walking out with some winnings.
I take it they weren’t counting cards…? Of course, in any given session you can lose at blackjack, but I’ve had some minor success overall. I’ve done much better at blackjack tournaments, where you just have to beat the other players.
Our over-educated friends who thought they could count cards, but couldn’t really.
I blew about ten bucks at the casino in downtown Cleveland once – my boss dragged me there.
You should have seen the crowd.
Let me guess: average BMI north of 40?
A mixture of that and what looked to me to be derelicts.
It’s all the sluts.
Casinos need to be spread around the country in poor neighborhoods. The poor can’t afford trips to Vegas.
#
foodgambling desertsIndian gaming is here to help!
Despite PA’s growing casino availability, I have no desire to pick such a bad habit.
Yep. It just seems so…dirty to have the State involved in that enterprise. Also so much opportunity for graft I’m looking straight at you, Ed Rendell.
I play online in PA, at Pokerstars (regulated by the Commonwealth). People are really, really bad at Omaha, in my experience, and you can seemingly turn a nice profit on that if you aren’t really, really bad.
I enjoy gambling, I gamble with money that’s already set aside for entertainment, and stick to the budget. As an example, poker is a lot less interesting if there’s no skin in the game.
I know people who do that too. They set aside a budgeted amount and do not go over. Certainly no problem with that. But from what I’ve seen, gambling addiction can be a real thing, and getting the states involved with promoting it is distasteful to me. I don’t care how many times they play the super-fast “Gambling problem? call 1-800-GAMBLER” disclaimer at the end of the radio ads.
I mean, nearly anything can be done to such excess as to cause serious problems in life. Gambling seems to be one of the slippier slopes.
Gambling is very addictive. My grandpa took his own life due to his addiction and people he owed…of the mob type
Oh, I don’t deny there are people with issues. Both on the scratch off/lottery side (queue Ohio lottery commercial “Did you know you can now play with a credit card?”) and the big money ones. Taking room and meal comps into consideration, I usually wind up just about even after a weekend in Vegas. It’ll be interesting once Ohio has legalized sports betting next year.
I like to imagine that number goes to a travel agency for casinos, or a bookie for sports betting.
“Got a gambling problem? You’re our kind of guy!”
I find it a bit ironic (and not in the erroneous Alanis Morissette sense) that my boss, a notorious tightwad, is quite the poker player, playing regularly in local groups and on his fairly frequent trips to Vegas. I’m sure he, too, sticks to a budget.
I read a book on the minor league poker circuit once, the kind of rounders stuff. It is all staying in your budget and knowing odds.
Most of these guys seemed pretty bored with it all, one of them talking about doing massive amounts of drugs to keep it interesting.
That is my wife and I. We set aside as entertainment…not to win. Typically a $200 seed and 6 hours of entertainment and making friends. If we go above the $200 it goes into pockets and we had a free night.
It take discipline though
That’s how I’ve done it in the past. However, it doesn’t have much allure to me. I remember sitting at the blackjack table in (the Venetian, I think?) with $80 in hand wondering why the hell I was burning $80 on this shit. I’d be happy to bring $20 to poker night or toss in $5 to a CTP pool for disc golf or spend $30 at the arcade playing chance games for tickets with my daughter than go do the casino thing.
Yep it’s all in how one looks at it. Once or twice a year is all we do, if at all. Especially if we have other entertainment wants.
I like poker. Our local home game went online during COVID; Pokerstars hosts private tables for free. I’ve been playing tournaments twice a week with them for two years, with a $20 entry fee each time. I’m currently up $2300.
In general, I like to gamble, but only if I’m winning. If a strategy or game doesn’t work out, I move on to something else.
This is me. I love playing Hold’em and enjoy a lot of other card games. Craps can be fun as well.
Fuck the slots, and be very careful with some of the table games… too many bets going on, where the odds don’t really track well.
Holdem is fine, but Omaha Hi-Lo is the bomb.
People are going to gamble, whether it’s legal or not. Just like with any vice, prohibition usually makes things worse for the participants and everybody else, not better.
I’m not suggesting that prohibition is the way to go. I am suggesting that the state should not be involved in promoting it either.
I’m sure a number of them are using saberstuff to gamble.
I had a soccer betting system that worked for a while, but then went south. I quit while I was still ahead 🙂
That’s pretty cool.
Yeah!
I wonder who won “best paper submitted by a gutter hoodlum?”
That was Trashy, he’s since moved uptown into a can on the curb.
It technically wasn’t a paper, either. It was a BK whopper wrapper with applied statistics scrawled on the back using a hooker’s discarded lipstick.
” thats more white trash than a BK sack tossed in a Waffle House dumpster”
Was the lipstick discarded or did the hooker just not need it anymore because of a sudden lack of a pulse?
Let’s just say that her spleen was particularly tasty.
This is why I like this place. I don’t feel like a weirdo and outsider because of my penchant for hooker killing/eating. It feels good to belong somewhere.
There were two awards, one for an academic and another for, I think, student.
Lotsa math.
I sat next to Whitey Ford at a company dinner once. The game appears to have been much simpler then. He told me some pretty funny stories about the Yankees in those days.
Thanks for these, whiz. I don’t get it, but I still like the process!
I sat next to Whitey Ford at a company dinner once. The game appears to have been much simpler then. He told me some pretty funny stories about the Yankees in those days.
That sounds like a pretty interesting article.
Long ago. I also was his gopher (beers) at a trade show. He signed baseballs at our booth (he was a shareholder). Super nice guy.
Sports in general were more fun to watch back when they were just guys playing and the coach substituting for guys who looked tires. All the baseball analytics has cost us part of the game – young players are all being taught to hit exactly the same upswing for the fence now. Will there ever be another Rod Carew or Wade Boggs who flirts with .400 by slapping singles?
Analytics in basketball has made the sport unwatchable.
I’ll need that laminated.
Analytics in basketball has made the sport unwatchable
The NBA was unwatchable well before analytics took over.
It died with the Jordan rules.
So, you are saying it actually did die in the paint?
Not all fore-arm push-offs are equal.
Malice is absolutely savage.
I honestly don’t get either the original nor his response. Is there some context I’m missing?
The dude lost his daughter at Parkland and dedicated his life to making you a criminal. His post was a celebration of the red flag insanity.
Malice bitch slapped him.
This is good too:
Abort all gay guns?
https://mobile.twitter.com/michaelmalice/status/1540033989007884288/photo/1
https://twitter.com/Rothmus/status/1539752298473193473
I thought it was amusing.
Is there a theorem for how likely it is that the Avalanche will be hoisting a Stanley Cup above their heads come Friday? I’ll bet it’s damn near 100%.
#hockeyistheonlysportthatmatters
#baseballmakesmesleepy
QFT
Go AVS!
How do uncompetitive games impact the stats? Do they tend to even out across the dataset, or do they introduce problems when doing projections and comparisons?
Good question. I don’t know that that has been studied, even for the Pythagorean expectation. Of course, you have to define uncompetitive; some games looked to be so, but ended up being competitive.
I have a hockey analysis (using offense and defense and assuming Poisson distributions) taken from someone else, and they (and I) don’t account for uncompetitive games or things like open-net goals.
My guess is that those kind of things are a second-order effect at most. But then the slugging percentage aspect is also second order.
I do have a rating system where each additional point (or goal for goal-scoring sports) beyond what was needed for winning was weighted less. It has a variable parameter (0 to 100%), where 100% counted each point the same and for 0% you only counted whether it was a win or loss and the margin of victory was ignored. The 0% was much closer to an ELO-Chess type ranking, whereas the100% was similar to Sagarin’s Pure Points (and exactly the same as baseball-reference’s Simple Rating System).
Vishnu H. Koresh! Its past noon.
I need lunch.
Sorry, Swiss. Twitter, funny stuff.
https://mobile.twitter.com/KeithOlbermann/status/1539983585406484480
I think I see some misogyny, but hard to tell these days.
The right should seize on that and get him fired from whatever the hell he’s doing these days.
I am not sure that would work. I can see women and girls marching around in handmaid hats while carrying paralegal pads.
I’m surprised he passed up the opportunity to blackshame Thomas.
He is such an unaware ass I am surprised he didn’t call Thomas’ wife a slur for marrying a black man.
I did not realize (or had forgotten) that I share a birthday with Justice Clarence Thomas.
*preens*
Happy Birthday
Thanks.
Happy birthday, Sheldon! Seems fitting to have a gun victory on your day.
Thanks!
I’m not sure whether the decision, or the dissents, are a better birthday gift.
Happy birthday!
And I must read the news/links tonight to see what is going on.
Happy Birthday!
Happy Birthday!
Any day now. https://i.pinimg.com/736x/9a/11/9d/9a119d060c1b4046d5b0cba4b5b06ac8.jpg
Relevant
Olby has been getting posted since the opinion dropped.
He is a bit deranged, ne?
Without the Supreme and other courts, most leftist victories never would have happened, or at least would have taken a lot longer. They throw a temper tantrum now not because they genuinely hate the court but because they hate the fact that their enemies have (if only temporarily) learned how to use it.
They throw a fit now because they think they have control of the government and they can’t stand the idea that there’s anyone telling them that it can’t do whatever they want it to at the moment they demand it. These people have no idea why checks and balances exist. They have no idea how our government is structured or why. The left actively looks to suppress the history of the last hundred years the clearly shows that their ideas lead to unaccountable tyranny and mass death. They pretend like the only things that happened were Nazis and a civil rights movement and completely ignore how the useful idiots that came before them that took down all the barriers to regimes with absolute power were also the first ones up against the wall. They are the worst imaginable combination of complete brain-dead stupidity and furious righteous anger.
They worship govt and feel betrayed by their god, when the enemy commands the heights.
They do not worship government so much as the image of themselves reflected in government.
Yep, and it’s an idealized image in the mirror.
Unless you’re reporting on the results of the sportsball game I don’t wanna hear it numbnuts. Dumbest bastard on Twitter except for the Twitterati who consider him a serious political analyst.
I think you’re a little to hasty giving out the dumbest bastard on Twitter award out so flippantly. That spot is more competitive than any of our professional sports by a country mile.
Hold on. Today is the NBA draft. Why is there an article on baseball instead of a mock draft and a few possible trades? UNSUBSCRIBED.
The draft is a mess this year, that is why.
nonsense. the 7 foot 120 pound white guy gonna be a star
The next Shawn Bradley?
Brad Sellers?
I was thinking the next Wilt Chamberlain
Wilt Chamberlain was big and strong – first time he ever did a deadlift, it was the #3 result in the world.
Chet just needs a burger or two is all
Wilt supposedly was in a bar where Gene “Big Daddy” Lipscomb was running down basketball players, and Wilt picked all 300 pounds of DT up and said – you don’t mess with me.
Wilt Chamberlain was big and strong – first time he ever did a deadlift, it was the #3 result in the world.
I did not know that. And he absolutely does not have the best body geometry to do deadlifts.
also there is the meme potential of Denver pairing Nikola Jokic with Nikola Jovic
Now that I approve of.
As long as their jerseys read Thing 1 and Thing 2.
It is bad enough I got something about an Arch in my bleacher report nba feed
Bleacher Report?!
*squints suspiciously*
yes I do read their nba feed. some of the worst articles you can imagine. sometimes it seems the authors don’t know the rules of nba trading
They are lucky they can manage to drool out an article on anything.
anyways an arch in texas has no business there
Do NBA execs understand the rules of NBA trading?
For a long time, the Bulls ones did not. They do now.
no, but they know guy
For as long as baseball season is (fucking 7 months long) the NBA and NHL somehow get away with being 8 months long.
For basketball, there is a Pythagorean expectation formula, but the exponent is more like 14, not 2 (or 1.83).
For football the best exponent is around 2.4.
Because nobody cares about the NBA?
I must admit that I have not cared about the NBA much since the 80’s.
Rob Deer and Adam Dunn rejoice! And replay with “Duh!”
reply not replay
@#$% Adam Dunn.
/White Sox
He was one of ours (Reds) like what….20 years ago?
Later than that. Votto basically pushed him out.
I saw Dunn play in Louisville. I thought he would eventually kill a kid on the carousel.
Dunn at first in Cincy led to Votto being played in left in Louisville. It was spectacularly unsuccessful.
Dunn was a Red from 2001-8.
– Big Donkey
He had one decent year as a WS.
Hey now! He was one of the original Dayton Dragons! Don’t be dissin’! 😠⚾🐲
He is the God of the Three True Outcomes (and Rob Deer was his prophet).
Strike out swinging, strike out looking, get lucky?
HR, Walk, Strike out.
Adam Dunn had weirdest career in MLB history:
https://www.youtube.com/watch?v=jiZfc0b2t3Q
“HR, Walk, Strike out.”
Not when Dunn was a White Sox player…
I remember when Marge Schott called Eric Davis her “million dollar nigger”.
Not baseball, but here’s a weird out in cricket: https://www.youtube.com/shorts/Uc9HPD9f_0A
So is the batter the only one out, is the other end guy out too?
No, the guy at the other end is not out, just the guy who hit the ball. I remember watching an international game on TV when I was a kid and the batsman hit the ball onto a close-in fielder’s leg, from where it bounced up in the air and was caught.
This is, obviously, a weird situation, but it is also not possible for more than one person to be out on the same delivery.
when I hear cricket I realize I don’t understand it and it reminds me of Sports Night
Dana: You don’t know anything about cricket?
Jeremy: That’s what I’m saying.
Dana: Really?
Jeremy: Yeah.
Dana: Nothing?
Jeremy: No.
Dana: And there’s no information you can give me about my shoes? (they enter the conference room)
Jeremy: Dana, a very big sports story is happening.
Dana: Jeremy, if a very big sports story was happening, we’d know it.
Jeremy: We do know it, we just don’t understand it.
Dana: You don’t understand it.
Jeremy: You understand cricket?
Dana: I know a little something.
Jeremy: What?
Dana: I know they drink tea.
Jeremy: I think they do more than that.
Dana: I didn’t claim to be a student of the game. (Others enter the conference room) Natalie, do you know anything about cricket?
Natalie: I know they drink tea.
Dana: Elliot?
Elliot: No.
Dana: Kim, do you know anything about cricket?
Kim: What’s goin’ on?
Dana: A guy in New Delhi just did something.
Kim: What?
Dana: Jeremy won’t tell us.
Jeremy: I honestly don’t know. And I wouldn’t have even brought it up except that whatever this guy did it was huge.
Natalie: What did he do?
Jeremy: He took all ten wickets in an inning.
Natalie: What does that mean?
Jeremy: I don’t know.
I’m gussing this isn’t available in Romania?
it is
Also I still have my pirated dvds from back in the day of Sports Night
Was that one of the dialogues he copied word for word into West Wing?
Could not say never watched the west wing. Just sports night and studio 60
https://twitchy.com/samj-3930/2022/06/23/lol-not-enough-popcorn-check-out-this-thread-of-some-of-the-worst-blue-check-meltdowns-on-twitter-over-scotus-gun-ruling/
Never change Preet
And they’re just getting warmed up for the abortion decision.
Assuming, of course, none of the Justices cracked and switched their votes. I wonder if that’s why its taking so long to drop?
Probably want to hold off the riots, sorry, “mostly peaceful” demonstrations until after the term has ended.
I would guess they wanted to be far from the madding crowd.
“Bharara was born in 1968 in Firozpur, Punjab, India”
Return to a gun-free paradise is only a plane ticket away…
I’d donate to a gofundme ticket campaign.
Submitted w/o comment.
Cupcake Cannon
Alito’s concurrence
Ouch!
“And while the dissent seemingly thinks that the ubiquity of guns and our country’s high level of gun violence provide reasons for sustaining the New York law, the dissent appears not to understand that it is these very facts that cause law-abiding citizens to feel the need to carry a gun for self-defense.”
Ouch again.
HAHAHA, Breyer’s dissent is 52 pages long. Cry more, asshole.
That motherfucker really likes to smell his own farts.
Burn.
Alito has grown on me over the years. Definitely could have worse.
Alito’s entire concurrence is basically “STFU Breyer you whiny bitch.”
an academic
Go Cyclones.
Physics and Astronomy
That explains a lot.
*Doffs cap*
A little afternoon pick-me-up.
Cheers!
This article is a very condensed version of the paper I presented at the 2010 MIT Sports Analytics Conference, which was chosen as the best paper submitted by an academic.
Best paper? Nicely done!
Thanks. That was 12 years ago and I don’t think it would have won since about 2013 or so — there are lot of people doing a lot of sophisticated things recently.