Craigers!

The Counsell signing became official today, as Craig has passed his physical.

In strict tangible terms, I think there's a lot to like about this deal. While Craig Counsell isn't a very good hitter, he has some discipline at the plate, so he's not a complete lost cause (in fact, he had a .355 OBP in 248 ABs last year, which is nothing to sneer at), and he can play plus defense at three infield positions. $1 million for a guy who can field several positions competently and isn't completely lost at the plate is a solid deal, even for a 38-year-old.

If, however, I can move away from actual baseball performance and indulge in a bit of personal history here, I've felt for a while like Craig Counsell has a strange connection to my baseball watching life. I first got into baseball when I was 8-years-old, during the 1997 season. I was living in Milwaukee at the time, so I became a Brewers fan, and the first few games I went to were at old Milwaukee County Stadium. However, that year I found out my family was moving to Arizona. My first reaction was, "What? We can't move to Arizona. They don't have a baseball team!" My dad pointed out to me that, thankfully, Arizona was actually getting a baseball team the very next year, just in time for us. I was still apprehensive about moving, but knowing this did cushion the blow somewhat.

We moved to Arizona in late October. We headed out on October 22nd, and spent a little over a week driving down to Arizona. This, of course, was during the 1997 World Series, and I watched it every night. It was the one constant during the trip; we were sleeping in a different hotel in a different state pretty much every night, but there was always a World Series game to watch. This was the first World Series I ever watched, and it was, of course, between the Cleveland Indians and the Florida Marlins. I was rooting for the Marlins the whole way, not because I cared about Florida, but because I knew they were a young expansion team, and I felt like if they won the World Series, it would prove to me that a young expansion team could win the Series, and then I could hope that the Diamondbacks would win. Of course, that line of thinking doesn't really make any sense, but it's what I thought when there was a walkoff hit to end Game 7, and Craig Counsell rushed home to score the winning run for Florida.

And that line of thinking still doesn't really make any sense, but it was vindicated. Just 4 years later, in 2001, I was ecstatic to see that the Diamondbacks could, and did win the World Series, and of course, who better to be in the middle of it all but Craig Counsell, getting hit by a pitch to extend the inning just long enough for Luis Gonzalez to bring a championship to Arizona.

As I grew older, my baseball love began to ebb, but it came back when the Milwaukee Brewers, my original favorite team, from my original hometown, actually began to win some ballgames. And of course, admittedly serving in a reserve role, but nonetheless involved, with them was Craig Counsell.

So I'm glad they've brought him back; it just seems like it isn't right if he's not playing on the team I'm rooting for.

Follow-up on Michael Lewis piece post

Here's a great video from one of the Ted conferences about choice and horizontal segmentation and so forth.

There're a lot of directions I could go with this one, but for now I want to focus on something he mentions in the middle: that people don't know what they want, or at least can't accurately describe what they want. This, I think, backs up to some extent my assertion that people might misunderstand the utility of something to themselves, and thus break a pricing mechanism.

The thing about this point is it really cuts to the heart of most political debate: just how responsible are people for their actions? Libertarians believe in people having complete authority to make their own decisions; extremely statist liberals (for lack of a better term) believe in government superseding people's authority to make their own decisions. Ideologically, I fall more in line with the former belief, and, to a great extent, most Americans do as well, even the liberals, but reality does occasionally suggest that perhaps people shouldn't be trusted to make their own decisions as much. I suppose that's why it's debated over.

Again, I do hope to expand more on these thoughts, but that's what I have for now.

Let's talk about abortion!

When I started writing this blog, I wanted to try to avoid talking about politics. However, I find that is the sort of thing I'd talk to myself about often, so I decided there's not much point in keeping it away from the blog. While I'll make reference to my beliefs, I'm going to try to keep political posts focused less on beliefs themselves than on how they're perceived in the public sphere, which I think is an accurate description of this post. Besides, no one reads this blog anyway, so I don't really have anyone to offend.

So, abortion. I do consider myself pro-abortion, and I use that term rather than another one for reasons I'll get to. I do believe the government shouldn't step in to tell women they can't have abortions...but I'm not militant about that belief. That is to say (and if someone actually read this, they'd probably be offended), I'm not going to stand up and say, "How dare you take away the right to kill a fetus?!" It's really a judgment call on my part to be pro-abortion, and it's not something I can back up with rigorous documentation or appeal to facts; really, it's mostly a gut feeling. I'm wary about the intrusion of government power, and I feel banning abortion would go too far. Other people might feel it doesn't go too far, and I can respect that. I can't get all offended that someone feels that way.

But my views on abortion go beyond that. Not only can I not get militant about it, I don't even really care about it that much. I am far more interested in economic policy, foreign policy, hell, even gay marriage, than I am in abortion policy, because I feel that on the grand scale of things, it just isn't that important. (Perhaps that's why I feel the government shouldn't bother with it.)

This brings me to why I've decided to reject the labels "pro-choice" and "pro-life". First of all, needless to say both labels are just spin, and I don't like spin. I try to be a no-bullshit type of guy. People who are pro-abortion say they're "pro-choice" because being pro-abortion, well, first of all, just sounds sadistic, but second of all, "pro-choice" just sounds downright American. We should be able to choose for ourselves. And people who are pro-life could call themselves "anti-abortion", but you never want to identify yourself as "anti-" anything; you want to be for something! And what better to be for other than life? I mean, who's anti-life, other than serial killers?

But what I really don't like about the labels "pro-choice" and "pro-life" is that they try to be about more than they really are; they try to expand the issue. Being "pro-choice" means you're in favor of the choice to have (or not have) an abortion, but the implication is that you're in favor of choosing, in general, rather than being barred from making the choice. Well, that's all well and good, but does being in favor of the choice to have an abortion really say anything about how much you want to let people make their own choices? How many people think women should get to choose to have an abortion, but shouldn't get to choose whether they can smoke in a bar or restaurant? How many people believe in choice for abortion, but not for paying into Social Security? I submit there is no correlation between the two; being "pro-abortion" doesn't necessarily mean being "pro-choice".

And the same is true for "pro-life". People who are opposed to abortion regularly explain their opposition in terms of "protecting the sanctity of human life," and believing that "all life is sacred." Well, y'know, I think I'm a pretty "pro-life" guy, in a sense; I believe in respecting other people's lives, and enjoying my own life; I think life is worth living, and believe every day I wake up is a great one. In short, I don't think that being for abortion makes one any less "pro-life". Beliefs about abortion have a connection to beliefs about life, but it does not have to be a defining one; frankly, I think it's a rather tenuous one.

So I think we should abandon the terms "pro-choice" and "pro-life", and stop trying to pretend this whole thing is more than it is. It's really just about one thing, abortion, so let's say it's about abortion. You're either pro-abortion, or anti-abortion. Now, those who would call themselves "pro-choice" may object to the label pro-abortion because it implies being in favor of the act, when many pro-choice activists are opposed to the act, but think government shouldn't ban it. I understand this objection, and I would say "pro-allowing people to have abortions", but, sorry, it's just too damn long :-p. (I don't think the pro-life activists would really have a problem with the designation "anti-abortion".) At any rate, I'm trying to get away from the connotations of these words and just focus on the denotations. If someone says "pro-abortion", we all know what that means. It's not a good PR term, but frankly, I think we should all get away from the PR mentality; hell that's what I meant above, when I criticized "pro-choice" and "pro-life" as spin terms, and that I try to be no-bullshit. To me, no-bullshit pretty much means you're not going to try to sugarcoat what you think just to make it sound better to people. Let's call things what they are, and that's what I'm going to do: from now on, I'm done saying "pro-choice" and "pro-life", and I'm just going to stick to the accurate terms: "pro-abortion" and "anti-abortion".

Wall Street and calculating utility

Great article here by Michael Lewis (of Moneyball fame, as previously referenced on this blog) about the financial collapse.

The thing I find most interesting about it is how the heart of the matter is that assets were overvalued, and what that says about a market. Wall Street firms were selling assets that were ridiculously overvalued, and acting as though they had value. It is easy to try to blame the firms for inflating the value of their assets, except people were willing to buy these assets. It takes both a buyer and a seller to set a price, and buyers were just as irrationally overvaluing assets.

This is, in a sense, almost frightening, because it suggests a way in which the market system is flawed. It is essential to a properly functioning market that buyers and sellers understand the utility of what they're selling or purchasing; indeed, that's how the price is set. Buyers only pay a price that's equal to or lower than what the good (or asset) is worth to them, and sellers only take a price equal to or higher what it's worth to them, and an equilibrium is found.

However, what if buyers and sellers aren't able to know what a good is worth to them? It's not implausible. When we discuss the myriad calculations that must be done to determine a good's value, it is unreasonable to think that everyone performs those calculations; surely people value and undervalue goods.

That, however, is the key: error in valuing goods should be random. What happened in the run-up to the Wall Street crash is that error in valuing goods was systematic, and all in the overvaluing direction. This sort of systematic error subverts the market.

Hopefully I'll be able to clean up this post and expand upon it, but these are my thoughts for now.

Observation vs. Statistics

Nothing very relevant or topical about this, but I had some thoughts about sabermetrics and its critics. A common criticism goes something along the lines of, "You can cite all the numbers you want, but I saw so-and-so play, and you can't tell me they weren't great."

Now, leaving to one side the fact that you can very easily be deceived by what you see, I'm very intrigued by this concept that seeing a player tells you more than their stats do. I think this is a curious concept in a game like baseball, which is much less about what you do on any given day than about how much you do over a long period of time. Case in point: take a player like Chad Moeller. On April 27, 2004, Chad Moeller hit for the cycle. If you saw him on that day, you'd think he's a great player. But Chad Moeller has a lifetime OPS+ of 61. He's terrible. The only way you'd know that is by watching him over a large number of games, and seeing how he tends to do.

And what exactly happens when you watch someone over a large number of games? What exactly do you see that lets you know if they're a good player or not? You certainly don't see them get on base every time they step up to the plate; the odds are overwhelming you see a player make an out more than half the time. You do, however, see them get on base sometimes, drive in runs sometimes, get big hits sometimes, etc. More importantly, you see how often they do this. Even the worst player will hit a home run sometimes, and even the very best player will strikeout sometimes, but what separates the best from the worst is how often they do each thing. So if you rate a player well, you remember seeing them succeed often. Well, what's better? Saying, "Yeah, I saw this guy, he always came up with the big hit," or going back and counting...and seeing just how often the guy came through? I mean, any time you're trying to figure out how often something happens, which is better: trying to remember how often it felt like happening, or going back and counting how many times it actually did happen? Clearly, counting, that is, figuring out what the actual facts are, rather than just what they seemed like, is the way to go.

Of course, even the most vehement saber-critic recognizes this, which is why they still use numbers like batting average and RBI. More often than not the argument is not about whether to use numbers, but about which numbers to use. It is quite clear we need to use numbers, contra any "I saw him play" argument.

This brings to mind another thought which I've had on a few occasions. I feel like even many non-sabermetrically inclined people recognize that batting average and RBI and so forth don't tell you everything, and that's why they're so quick to say, "The stats don't tell you everything; you have to watch them play." They're used to stats that can be very misleading, and so they insist the same about all stats, even though sabermetric stats are designed to avoid the pitfalls of more conventional stats. It's almost like a Catch-22.

Did left-handedness keep Mark Grace out of the Hall of Fame?

Okay, completely out-there thought: Mark Grace appeared on the HoF ballot for the first time this year, and only garnered 4.1% of the vote, knocking himself off the ballot and guaranteeing that he'll never see the hall, unless the Veteran's Committee goes completely insane. His numbers don't really justify entry to the Hall of Fame...that is, at least considering that he was a first-baseman. However, Curt Schilling, in his blog, ran down the Hall of Fame ballot and said of Grace (in addition to him being the only teammate who talked more than Schilling), "Was literally a Gold Glove SS playing first base." Now, just because Curt Schilling referred to Mark Grace as a "Gold Glove SS" doesn't mean that he was one, but stay with me here for this thought experiment. Imagine a shortstop with a .303 average, .383 OBP, and a career 119 OPS+, with a peak OPS+ of 141. That's certainly not a lock for the Hall, but it's at least plausible. Suppose Grace really was athletic enough to play shortstop, but couldn't...because he's left-handed. Now, the easy rebuttal to this is that if he were that athletic, he should've played CF, which would give him extra positional value without requiring right-handedness. My rebuttal to that would be that probably the most important attribute for a centerfielder is speed, which Grace notably lacked, but shortstops can get away with less speed.

Admittedly, this ultimately comes down to a "If my aunt had balls, she'd be my uncle" argument, but it's something I've thought about a few times and found it interesting. Sometimes there's a lot of randomness involved in baseball.

Big Mac and the HoF

So, Mark McGwire got only 21.9% of the Hall of Fame vote this year, a decline from last year. He doesn't seem to be picking up support, and, frankly, I think that's a shame, for a few reasons:

1. We don't know for sure that he cheated. Granted, this is a fairly ridiculous point to make, because all the circumstantial evidence suggests that he did. However, I'm mentioning it anyway, because it informs my main and final point, which I'm getting to.

2. There are already plenty of cheaters in the Hall of Fame. This, I think, is a more germane point. The Hall of Fame is full of guys who cheated, and has been for a long time. Gaylord Perry is in the Hall even though he through spitballs. Whitey Ford is in the Hall even though he through scuffballs, and Yogi Berra is in the Hall even though he helped Whitey scuff the aforementioned balls. Furthermore, practically everyone who played in the 70s used Greenies (i.e., amphetamines) to keep themselves going. However, this isn't my main point, as you can argue that two wrongs don't make a right, or that steroid use is somehow a different form of cheating (although I think that's a hard point to argue WRT amphetamine use).

3. We don't know who did and didn't use steroids. This, really, is my key point. If the Mitchell Report has told us anything, it's that anyone who played baseball in the 90s could've been a steroid user. I mean, prior to the report coming out, no one thought Roger Clemens used PEDs, and now he's a symbol of the steroid era.

This, I think, is what really sells McGwire's candidacy for me. We keep him out of the Hall for using steroids. Well, Rickey Henderson got voted in today; what if he used steroids? It seems unlikely, and I have absolutely no evidence that he did, and don't even think he did, but it's possible. Or think about guys playing today who are considered locks for the hall, like Derek Jeter, Alex Rodriguez, Manny Ramirez, Randy Johnson, Ken Griffey, Jr., Mariano Rivera, et al. They all played during the height of the Steroid Era; do we really know for sure that none of them used? The notion of it may seem ridiculous, especially for some of them who are known for being "good guys", paragons of sportsmanship, but we don't actually know these people; we just know their images. The saga of Kirby Puckett should be instructive (see here). He was a revered figure, the ultimate good guy, and the next thing you know he's cheating on his mistress and pissing in parking lots.

I'm going to go out on a limb and predict that sometime in the next 10-20 years, the BBWAA will elect a steroid user to the Hall of Fame and have no idea that they did. It may have happened already. And when that happens, then it becomes apparent that Mark McGwire isn't being kept out because he used, but rather he's being kept out because he got caught. Furthermore, as I alluded to above, McGwire never actually got caught, per se; he's more being punished for a badly choreographed testimony before Congress. In other words, he's really being punished for having bad PR skills.

Furthermore, guys that no one suspects of having used steroids are really getting rewarded for good PR skills. Which would be more surprising, if we found out that Derek Jeter used steroids, or if we found out Alex Rodriguez did? Without a doubt, it would be more surprising to find out that Derek Jeter did, mainly because he's gotten revered by being so good at interacting with the press. Don't get me wrong, he's a great ballplayer, but not as great as the guy playing 40 feet to his right, who's hated, mainly because he comes off as a huge jerk. So we'd be more likely to believe A-Rod as a steroid user, because...he's not as nice as Jeter? That's the wrong way to make decisions, but I think that it ultimately comes down to that too often, and I think Mark McGwire's Hall of Fame candidacy has come down to that: he's not being punished for what he did, but for what he didn't do, and what he didn't do is handle the press effectively.

PS3s at New Yankee Stadium?

Yankees strike deal with Sony

So, according the article linked above, the Yankees have struck a sponsorship deal with Sony which includes, in addition to all the usual signage and so forth, flat panel TVs set up around the stadium, including on the concourse, to broadcast the game for when you step away to take a leak or buy more nachos or whatever. Okay, so far, so good. I've always been in favor of sponsorship deals, because as far as I'm concerned, if a sponsor is paying money to someone producing a good I'm enjoying, that's less money I have to pay them. Furthermore, having TVs set up around a baseball park is actually pretty nice; when I went to see the Brewers in the playoffs at Citizens Bank Park in Philly they had TVs set up broadcasting the game, and it was cool.

What caught my eye, however, is this passage: "In addition, Sony PlayStation 3 entertainment systems and VAIO notebook computers will be available to fans in select locations throughout the Stadium."

Seriously? I mean, I know most people think baseball is boring, but seriously? People are going to spend hundreds of dollars to go to a baseball game...so they can go play GTA 4 between innings? (In fact, it's even worse than that, 'cause it's not like they'd ever put GTA 4 on one of those things, so you'll have to play, I dunno, Sonic or something like that). I dunno, I'm not at all an opponent of new sponsorships, and I'm not even much of an opponent of fancy new features at ballparks, but this one just seems a little ridiculous to me.

BTW, when I was typing out "New Yankee Stadium", I realized I felt like there should be a nickname for the new park. I mean, "New Yankee Stadium" is a nickname to begin with, because it's officially just "Yankee Stadium", just like the old one, but we all know it's not the old one. I'm not a huge fan of David Chalk, Devil Rays blogger at Bugs and Cranks, but I do think his nickname for old Yankee Stadium was pretty apt: "That Old Dump in the Bronx". With this in mind, I think it'd be appropriate to nickname the new stadium "That New Dump in the Bronx". If that's too long, another one that occurs to me is "Yankee Stadium III", in recognition of the fact that the old stadium was really "Yankee Stadium II" ever since the mid-70s remodel.

Trevor Hoffman, and this year's Gabe Kapler

The Brewers signed Trevor Hoffman to a 1 year, $6 million deal, with incentives that could raise it to $7.5 million

Not a huge surprise, as the rumors have been picking up steam the past few days. I'm of two minds about this. On the one hand, it's picking up a solid relief pitcher for not too much money, so it's hard to get terribly upset about it, but on the other hand, the Crew needs another starting pitcher way more than a closer. The bullpen really wasn't a problem last year, and frankly I don't think it'd have been a problem this year, even before the signing of Hoffman. Doug Melvin has done an excellent job of picking up cheap pieces to pitch in, and last year showed us that the cheap pieces can be just as valuable. I mean, who would've thought Salomon Torres would be our closer? And yet, he performed brilliantly.

With that in mind, I'm more interested in guessing who'll be this year's Gabe Kapler signing for the Crew. In other words, who'll be the under the radar pick-up that's ignored at the time but ends up being an essential piece? I've got my money on R.J. Swindle. The Brewers picked him up back in November for the league minimum salary. He only has 4.2 major league innings to his credit, all for the Phillies, and was shellacked in them, but that's a small sample size, and his minor league numbers are quite honestly incredible. Against lefties in 51 Triple-A innings, he's got 1.41 BB/9 and 15.53 K/9, for a K:BB ratio of 11. (Yes. Eleven.) Furthermore, he's no slouch against righties, either, striking them out at a nearly 8 K/9 clip and walking them about as much as he walks lefties. All told, in 146 minor league innings he has an 8.19 K:BB ratio and has given up 0.03 HR/9. Clearly these numbers won't be as good in the majors, but they should still be stellar (the major league equivalency on minorleaguesplits.com suggests a 5.57 K:BB and 0.04 HR/9), so in other words he's fantastic at the three things that pitchers actually have control over (striking guys out, not walking them, and keeping the ball in the ballpark). If he gets opportunities to play and can keep up what he's been doing in the minors, he could be a breakout star.

The Pat Burrell signing

I'm a couple of days late on this one, but I was thinking earlier today that the Rays' signing of Pat Burrell for 2 years and $16 million makes the Phillies look even worse for the Raúl Ibáñez signing. The Phillies signed Ibáñez for 3 years and $30 million to replace Burrell, essentially, even though Ibáñez is 4 years older, isn't as good offensively, is even worse defensively (which is saying something), and, apparently, is more expensive than Pat the Bat. It's absolutely incredible how that worked out. The Phillies ended up paying more money and committing to more years for a player that's straight-up inferior. It suggests a few things:

-We've been seeing the effects of the depressed economy on free agent signings, but this seems to suggest that it's worse than people thought it would be even a few months ago when everyone knew it was bad. (Supporting this notion is the fact that the players' union encouraged free agents to turn down arbitration, even though this has come back to hurt several players [Jason Varitek, for one].)

-The Rays got a tremendous deal. I've heard it suggested that Burrell gave them a discount for some reason. I suppose this is possible, and it would somewhat excuse the Phillies for signing Ibáñez, but it's looking more and more like the market for all-hit no-glove guys just isn't there. I mean, even Manny bloody Ramirez can't get signed, let alone guys like Adam Dunn and Bobby Abreu. I wouldn't be terribly surprised if they (Dunn and Abreu) get deals in the same ballpark.

-Perhaps the Phillies' front office has a real problem with Pat Burrell. I haven't really looked into that, but if there is a problem, it's certainly not a widely known one, because it's not the sort of thing that comes up every time he's mentioned. Furthermore, I also haven't heard any suggestions that he's a problem in the clubhouse. Clearly I don't work in the front office of an MLB team, and if I did, maybe I'd think differently, but I think if I were GM and I had a personality problem with a player, if he went out and performed well and didn't cause trouble in the clubhouse I'd keep paying him and try to re-sign him. But maybe there were bigger problems afoot in Philly.

"The Germans make great stuff, y'know"

So über-blogger Joe Posnanski had a piece mentioning infomercials, and of course ended up talking about the Shamwow. One of the things he highlighted is the fact that the Shamwow ad stresses the fact that it's made in Germany, and he wondered why. To wit:

"If it said: 'Made in USA,' OK, I’d get it, we’re trying to play the patriotic card. But what possible good could come out of people knowing that the ShamWow is made in Germany? Are there people out there thinking: 'Well, Germany is known for their shammy-type products. Who could forget the ShamCow, which was only a four inch square but could suck up an entire half-gallon carton of milk. And the ShamPlow. Those Germans are Shammerrific.'"


I think the idea is that it’s not made in China, Taiwan, Korea, Pakistan, etc. People have an idea that stuff made there is somehow inferior, because they don’t understand how exploiting comparative advantage reduces cost, and figure if it’s that much cheaper, there must be something wrong with it. The recent well-known problems with goods coming from China only reinforces this view. Products from Germany don’t have this same stigma because, if anything, they tend to be more expensive (just think about cars: Mercedes, Porsche, etc.).

This, of course, lends some credence to ideas of upward-sloping demand curves: people assume that if something is more expensive, it must be better. Clearly this phenomenon does not often dominate, but I wonder how pervasive it is.

NFL Overtime

The Colts-Chargers game yesterday went into overtime, which in the NFL is still sudden death. Sudden death, of course, gives a huge advantage to the team that wins the coin toss, and sure enough, the Chargers won the toss and scored on the first possession to win the game.

This led me to wondering, of course, just how much of an advantage winning the toss gives you. I did some research and found out that since regular season overtime was implemented in 1974, teams winning the toss had won approximately 52% of the games and teams losing won approximately 44%, with the rest ending in ties (if there is no score during the 15 minute overtime period, the game ends in a tie). However, the percentage of OT games won by the team winning the toss has grown closer to 60% since 1994, when the kickoff was moved back from the 35-yard line to the 30-yard line. This change has increased the chances of scoring on a possession.

One suggestion for improving NFL overtime is to move the kickoff back to the 35-yard line for overtime. I decided to model overtime games to see how much this would help.

It is fairly easy to construct a model based around the probability of scoring on a possession. Assume for now that the teams are evenly matched and have an equal chance of scoring on any given possession, and call their chance of scoring a probability P. Scoring on a possession wins the game, so their probability of winning the game is the sum of the probability they'll score on any of their possessions. The probability they'll score on a given possession is P times the probability that no one has scored and ended the game yet, which is (1-P)^2n, where n is the number of possessions the team has had. This creates an easily solvable geometric sum, which can be seen in this chart:



As you can see, reducing the probability that the team will score on a given possession (which is what moving the kickoff line back up would accomplish) does reduce the advantage of winning the toss, but no matter how low you reduce it, the team that wins the toss is still favored.

Proponents of the sudden death overtime say that losing the toss is no problem because your defense should be able to stop the drive. This should be obviously fallacious, but as a different way of looking at it, I modeled the case where the team that wins the loss is worse than the other team, and by this I mean, is less likely to score in a given possession. Here's a chart for the odds of winning, given their probability of scoring in a given possession, for a team 20% less likely to score on a possession (NB. When I say 20% less likely, I mean 20 percent, not 20 percentage points, i.e. if the team that won the toss has a 35% chance of scoring on a possession, the other team has a 42% chance, not a 55% chance.)



As you can see, even if the team winning the toss is significantly worse than the other team, their odds of scoring on a possession need to be brought down to 15% or less for them not to be favored to win!

Another overtime method suggested is the "two possession rule"; that would involve each team getting at least one possession in overtime, and then it would revert to sudden death. While this still favors the team winning the toss, it is not nearly as much as an advantage. Here's the chart for evenly matched teams (NB. that I was unable to account for the differences in scoring field goals and touchdowns, so I just modeled the case where both teams have to score a touchdown--which has been suggested as a variant of the two possession rule):



The blue line represents sudden death, and the red line represents the two possession rule. As you can see, the team winning the coin toss has a fairly low advantage for a wide range of scoring probabilities. What's particularly interesting is that for cases where the team losing the toss is better, there's a range where the probability of the team winning the toss winning the game goes down even as their probability of scoring on a possession goes up. To make it really obvious, take the case for a team that is 50% better losing the toss:



As you can see, the red line has a clear dip in it. This is because as the probability of scoring on a given possession goes up, it produces two countervailing forces. On one hand, it increases the chances of winning, for obvious reasons. But because of the way I've set the model up, it also increases the chances of the other team scoring even more, which reduces the first team's chance of winning. In the sudden death case, the first force dominates over the entire range. However, in the second case, the latter force dominates for much of the range. Again, a lot of this is wrapped up in the arcana of how I set up the model, but it makes one point clear: under the two possession rule, how good the team that loses the toss is becomes a lot more relevant.

Here's a link to the spreadsheet I made: NFL Overtime

"If it saves just one life, it's worth it."

A few years ago, the town I live in built a stoplight at an intersection where a high school girl had died in a car accident. While they were building it, I drove past there with a friend of mine and his mother. When he commented that there was really no need to build a street light there, his mother said, "If it saves just one life, it's worth it."

Now, it's possible that his mother knew how much it cost to build and maintain a streetlight there, and decided one life would be worth it, but it's far more likely that she meant that any expense is justified if it saves "just one life"; i.e., lives have an infinite value. This, of course, is absurd, because it would imply we should devote all of our resources towards saving lives. This, in turn, becomes even more absurd, because there are various places towards which resources must be directed to save lives (food, shelter, healthcare, etc.), but if lives have an infinite value, it becomes impossible to efficiently determine just how these resources should be allocated towards saving lives. Infinite values do not work well in a market.

In short, it's clear that lives do not have an infinite value, and there must be some finite value we could place on a life. There must be some dollar value that it's not worth spending, even "if it saves just one life". However, as a society we're extremely uncomfortable placing a finite value on a life, and try to treat all lives as having infinite value, even though this is an untenable position. It is, I think, not difficult to see how many political disagreements can and do stem from this dilemma.