The Law of Competitive Balance Redux

April 20, 2022
                    The Law of Competitive Balance Redux
 
 

            If you will bear with me a little bit, this essay is written to thank you all, to thank my readers, for pushing me to think more carefully about this issue, and to advance the discussion just a little bit.   Before we get to that, however, I’m going to have to spend a page or two re-plowing ground that you may already be familiar with. 

            The first little shove which led me to The Law of Competitive Balance came from football, from the NFL in the late 1970s.  This is less true now than it was in the 1970s, but a standard defensive formation in football is or was 4-3 with four defensive backs, often two at the line (cornerbacks) and two deep.   However, in situations in which the offense was likely to throw deep, teams would use a "nickel defense", which was using a fifth defensive back, usually in place of a linebacker.  This is all ancient history; teams now sometimes use five, six, or, on rare occasions, even more defensive backs. They still call it a nickel defense, but five is no longer the limit.  I’d better stop writing about football now or limitations of my understanding will begin to shine through. 

            On talk shows in that era, it was common to hear people say "Why do they USE that defense?  The minute they go to that damned nickel defense, the offense starts scoring touchdowns."  Which was quite true in its own way; the number of points scored per minute when the nickel defense was used was obviously higher than when a regular four-defensive-backs defense was used.  But the increase in scoring did not result from the use of an extra defensive back; it resulted from the fact that the offense had gotten desperate.   You’re two touchdowns behind with five minutes to play; you take chances that you wouldn’t ordinarily take.  Because you are more willing to take chances, your chance of throwing an interception increases, but your chance of throwing a touchdown also increases.   The nickel defense does not cause the increase in scoring; rather, it is used in situations in which there is already an increased chance of a long touchdown being thrown. 

            But we rambled past a point there at which we should pause:  Why was there an increased chance of a touchdown being thrown? 

            Because the team was behind.

            Because the team was behind, they had an increased NEED to score.

            Because they had an increased need to score points, they scored more points. 

            That is one of three key drivers of The Law of Competitive Balance:  that success increases when there is an increased need for success.   This applies not merely in sports, but in every area of life.  But in the sports arena, it implies that the sports universe is asymmetrical.   Both the team which is ahead and the team which is behind "need" success, but the difference is this.   Let us say that one team has a 90% chance to win the game, the other team a 10% chance.   The team which has a 90% chance to win is 10 "marks" from victory.  The team which has a 10% chance to win is 90 "marks" from victory.  Their need is larger. 

            Because this is true, the team which has the larger need is more willing to take chances, thus more likely to score points.  The team which is ahead gets conservative, predictable, limited.  This moves the odds.   The team which, based on their position, would have a 90% chance to win doesn’t actually have a 90% chance to win.  They may have an 80% chance to win; they may have an 88% chance to win, they may have an 89.9% chance to win, but not 90. 

            Asymmetry creates imbalance.  There is an imbalance in the motivation of the two teams, an imbalance in their willingness to take risks, an imbalance in their strategic options. 

            From that insight, I realized that the same is true in other sports.  In a basketball game, a team which is behind as time is running out is more willing to jump the passing lanes and attempt to steal a pass, more likely to use a full-court press, more likely to shoot a somewhat guarded three-pointer, more likely to commit a foul to put an opponent at the free throw line. 

            In a sense, these gambles are unwise.  They are not 51% gambles.   They might be 35% gambles.  But when your chance of winning is 10%, 35% is a big step forward.  Ordinarily, you maximize your chance of getting ONE score.  But when you’re behind, you accept a diminished chance of getting one score to increase your chance of getting two or three scores in the same amount of time, or the same amount of outs.   You are trading an INCREASED number of not-as-good opportunities for a more limited number of better opportunities.  What you are actually doing when you put up a shot you wouldn’t ordinarily take is mixing a certain amount of 35% chance of winning with your pre-existing 10% chance, thus increasing the mix from 10% to 20%, or maybe 15%, or maybe 12%, but the point is that you are increasing the mix.  You’re improving your odds by doing things which, in a neutral situation, would damage your odds. 

            I said 35%, but many times the "bad shot" you are taking is not a 35% chance; it is just a 49% chance.  In a neutral situation, you try to stick to 51% or better options.  You try to secure the first down; you try to advance the runner; you try to get a good look at the basket.   When you’re not going to win by doing that, you try to hit the long bomb, you play for the big inning, you put up a three-point shot and you put it up quickly so you can put up another one. 

            That is one of the three key drivers of the Law of Competitive Balance.  The others, of course, are adjustments and effort.  When you’re losing, it is easier to see what you are doing wrong.  Of course a good coach can recognize flaws in their plan of attack even when they are winning, but when you’re losing, they beat you over the head. 

            So, back to the nickel defense.  Observing this phenomenon at a low level, I thought about how it applied to other sports, and I realized that, in terms of in-game adjustments, it applies much less to baseball than to any other sport.  It applies, but not at the same level.  When your pitcher is pitching well, you let him work; when he is pitching badly, you switch to a different pitcher.  That fact favors the team which is behind—but not by very much.   The fact that you are three runs behind is a much, much larger factor than the fact that you’ve got a new pitcher on the mound.  It’s impact on baseball is muted by the randomness of sequences of action.   In football, you can CHOOSE to throw a long bomb.  In basketball, you can CHOOSE to go into a full-court press.  In baseball, you can’t really choose to hit home runs.  Baseball doesn’t work that way.  More on this later.

            So I put that on the back burner, but then I started to notice apparently different but actually related phenomena.  If a baseball team is 20 games over .500 one year, they tend to be 10 games over the next.   If a team is 20 games under .500 one year, they tend to be 10 games under the next year.  If a team improves by 20 games in one year (even from 61-101 to 81-81) they tend to fall back by 10 games the next season.   If they DECLINE by 10 games in a year, they tend to improve by 5 games the next season. 

            I began to notice similar patterns all over the map.   If a batter hits .250 one year and .300 the next, he tends to hit about .275 the third year.  Although I have not demonstrated that similar things happen in other sports, I have no doubt that they do.   I began to wonder if this was actually the same thing happening, but in a different guise.  You get behind, you make adjustments.  You lose 100 games, you make adjustments.  You get busy.  You work harder.  You take more chances.  You win 100 games, you relax.  You stand pat. 

            I did some small studies, which I won’t detail here, which confirmed to my satisfaction that this was what was happening.  I generalized these observations as the Plexiglass Principle and the Law of Competitive Balance.    I used those concepts for several years.

            But some time, I don’t know when, maybe early 1990s, I got a letter or an e-mail from somebody which caused me to put them on a shelf.  I do not remember exactly who it was from or exactly what was said, but it was an intelligent letter from a thoughtful person known to me. The essence of it was that I was merely lumping together unrelated phenomenon under a common name.  A batter falling back halfway toward his previous average has nothing to do with a team rallying from a halftime deficit.  

            By chance, I think, this missive reached me at a time when I was involved with something else—writing a book, no doubt—and I did not have time or energy to think through the issue.   I had received similar communications from other people.  Despite my stubbornness and contrarian nature, I just set aside the concepts related to the Law of Competitive Balance, and did not write about them, as I recall, for a couple of decades.   Probably somebody can find a place where I DID write about them, but. . .you know; good luck with that snipe hunt.

            But a few years ago I was thinking about this again, and I realized that whoever had written me that had just missed the boat.  What I SHOULD have done was to write back to explain to him that the fact that he did not SEE the common cause behind these phenomenon does not mean that it was not there.  It meant that he was not as smart as he thought he was.  It meant that he had not trained himself to see what was beneath of the surface.  Of course I would not have sent him that letter; I might have written it, but not sent it.   My point is that I should have stuck to my guns. 

            The Law of Competitive Balance re-surfaced here recently in a discussion of college basketball.  College basketball coaches almost universally sit a player down if he gets two fouls before halftime.  Analysts think this is a mistake.  You get more minutes out of the player, more points, more rebounds, if you let him play, rather than anticipating a foul call which more likely than not would not occur anyway.  Basketball coaches believe that, with the exception of one-sided games which you are going to win easily or lose badly anyway, games will come down to a few key plays at the end of the game.  Basketball games between competitive teams are 71-69 or 75-73; they’re not 84-70.

            In essence, college coaches are relying on the Law of Competitive Balance.  The Law of Competitive Balance predicts that, when evenly matched teams compete, the game will be decided in the last two minutes.  Therefore, a play made in the first half is not equal in importance to a play made in the last two minutes—not NEARLY equal to it.  A play made at the end of the game might be five times more important than a play made in the first half. 

            What happens in the first half is washed out by the ebb and flow of strategic adjustments.  You get ahead, the other team makes an adjustment, and they come back.  You get 10 points behind; you figure it out and have a run of your own.   What happens in that process matters, but it doesn’t matter as much.  It is mostly ground flat by the processes of the game.  You can’t win the game in the first half; it just doesn’t work that way.  If you can’t win the game in the first half, it doesn’t pay to put yourself in a weakened position trying to. 

            The key point here is, almost all basketball coaches either believe this to be true, or act as if they believed it to be true.   Which may be interpreted to mean that highly-paid professional people, whose income depends on making decisions in which this issue is involved, believe that the Law of Competitive Balance is a real thing, and an important thing.  Which means that I should not have backed away from it in the 1990s. 

            In recent weeks I have received several comments/questions in regard to this which have helped to sharpen my thinking about this issue, and for this I am writing to thank you.   Sorry; I don’t know who sent most of these; when I copy questions out of "Hey, Bill" the software doesn’t pick up the date of the question or who sent it. 

 

       Hey, Bill, about the Law of Competitive Balance. . . I like the label but it’s really an influence, not a law, right?  I remember in your original article that you wrapped it up by saying that it defined greatness.  The idea being that great organizations and great players and great managers aren’t blinded by success.  They make adjustments.

       That’s why PB’s observation that we’re ". . . dealing with human beings rather than coins" is so right on and applies to much of our calculations (sabermetric and in general).  As human beings we have the opportunity to adjust.  Coins don’t care if they are ‘winning’ or ‘losing’.  That’s why they are predictable.  Human beings in large groups are somewhat predictable, but many individuals are not, those are the ones who outperform (or underperform) normal expectations.

 

            Point 1, the term "Law" of Competitive Balance is used here in a manner consistent with many other usages throughout the language.  If you google "law of demand" the first result says that "The law of demand states that the quantity purchased varies inversely with price. In other words, the higher the price, the lower the quantity demanded." 

            The Law of Demand does not state that, in every single purchase decision, each purchaser must purchase less as the price increases.  Rather, it implies that, under certain conditions, an invisible hand (to use the Adam Smith term). . .an invisible hand will direct the sum of ALL the decisions to take a certain shape.

            Or take the Law of Survival of the Fittest.  The law of survival of the fittest does not dictate that every "weak" member of the species will die young and that every "strong" member of the species will survive and propagate; it merely states that, because the strong TEND to survive and the weak TEND to die out and not propagate, the species over time tends to evolve in the direction of those members of the species who are best adapted to survival.

            Or take the term "the Law of Diminishing Returns".   The Law of Diminishing Returns is "a principle stating that profits or benefits gained from something will represent a proportionally smaller gain as more money or energy is invested in it." 

            The Law of Diminishing Returns does not decree that whenever you sell something, you always sell the 100,000th copy of it for less money that you sold the 100th copy of it.  It merely states that there are forces operating which, in general and over time, tend to make the it less and less profitable to keep doing more of the same thing. 

            I think you have taken the word "Law" to imply compulsion, force or unaniminity, but that isn’t actually what it means.  The word "Law", used in the sense that I used it, means that there is a guiding principle operating which tends in the aggregate to direct outcomes in a certain direction.  The Law of Competitive Balance tends to direct the outcomes within a basketball game in such a manner that games between evenly matched teams will most often be decided in the last two minutes, even though there are periods within the game when one team pulls ahead of the other. 

 

            Point 2-- . . .the material about dealing with human beings, rather than coins.  The best I can do is to say that that’s true within the range where it is true, and false within the range where it is false.  With respect to the player who hits .250 one year and .300 the next, this would be mostly true; that is, the player who hits .250 one year and .300 the next is not fated beyond escape to drop back to .275 the third year.   How one player handles the situation is different than how another player handles the situation. 

            But when talking about what happens WITHIN a baseball game or within a season, this is almost 100% untrue—and it is an untruth which very profoundly prevents people from understanding what is happening on the field.  Sequences of events in a baseball game are not TRULY random, but they are FUNCTIONALLY random; that is, they have the functional characteristics of randomness.  Sequences of good games and bad games by hitters are indistinguishable from random sequences.   Sequences of at bats within a game are indistinguishable from random sequences. 

            For the "human adjustments" to work, the batter or the pitcher has to have control of a specific outcome.  He doesn’t.  The game is too difficult for that.  In basketball or football, a player or coach can direct the action such that he has some control of the outcomes.  In baseball, he can’t.  There are individual skills, yes, and there are human decisions and human adjustments, but there are a long, long series of "random screens" between the person and the outcome which prevent the athlete from having control of when a specific outcome occurs. 

            Before sabermetrics, there were literally hundreds and hundreds of things which people expected to be true and which people assumed WERE true, but which turned to be not true when we studied them.   People thought that some hitters would consistently hit better in the clutch.  They don’t.  To give you one smaller example, we always believed, growing up, that when a pitcher had to run the bases, it would effect his performance in the following inning.   But David Smith of Retrosheet studied it, and. . .no such effect.  It doesn’t happen. 

            WHY doesn’t it happen?  Random screens.  In order for there to be an observable effect in that case, the pitcher has to have a certain degree of control of the outcomes.  The outcome, though, depends on the batters who happen to be coming up, the pitches that are called, whether the batter happens to read the pitch or doesn’t read it, whether he happens to get his bat in exactly the right place or 1/10th of an inch too low, whether the umpire calls the borderline pitch a strike or whether he calls the same pitch a ball, whether he happens to get his bat across the plate at exactly the right instant or 1/100th of a second too late, and whether the fielder happens to be standing where he can get to the ball or whether he is six inches away from being in the right place.  Nobody controls those things.   So the sequences of action—while of course Bryce Harper’s sequences are different from Victor Robles’s sequences—are indistinguishable from random sequences, and are NOT measurably impacted by things like whether or not it is a clutch situation and whether or not the pitcher has just been forced to run the bases.

            In 1982 Hal McRae turned 37 years old in July, and drove in 133 runs, which was a career high by 41 runs.  The next spring I asked him whether he thought he could have as good a season again.  "It all depends on the pitches they throw me," he said.  "If they throw me the same pitches they threw me last year, I’ll have a good year."  Not quite, actually, but that’s the general idea.   The issue is not MERELY whether you face exactly the same pitchers and whether they throw you the same pitches, which of course they will not; it is also whether the umpires make the same calls, whether the wind is blowing in the same direction, and whether they have the same fielders behind them who make the same plays.  But that’s the general idea. 

 

            Let me try this again. . . .when we simulate baseball in an APBA game, or Strat-o-Matic or Ballpark, we simulate it as if the outcome was determined by the pitcher or the batter or (occasionally) the fielder, plus one random indicator—a random number or a dice throw.  But in reality, there are many more levels of randomness than just those.  There is also a catcher making randomized decisions about what pitch to call for, and an umpire making randomized decisions about marginal ball and strike calls, and a sun that is in the batter’s face one at bat and behind a cloud the next one, and a batter’s hand that is sore one day but feels fine two days later, and a pitcher who is fresh in one at bat and fatigued in the next one, or sometimes fresh at the start of the at bat and worn out by the end of it.  We don’t simulate all the factors that are actually there.

            What people SAY is that simulated outcomes are just random, but in real life they result from decisions made by the hitter and batter.   But that’s not true.  The simulation model doesn’t overstate the randomness; it understates it.  It tends to simplify the randomness, because you have to.  You can’t play a game in which you have to roll the dice 20 times to determine what happens.  You have to simplify the randomness to make the game work. 

           

            Here’s another letter:

 

       Hey Bill, parenting helps me understand the law of competitive balance. I have an eight year old who is, uh, not the easiest, and who responds very poorly to battles of the wills. To parent him effectively, you really can’t be on autopilot; you have to consciously make a hundred correct decisions in a day, or maybe in an hour. When we do that for awhile, my wife and I "take the lead," so to speak: he behaves better, things are easier, the mood lightens, and in our carefree state we gradually dismantle our parenting systems and instead rely on our instincts, which is just so much easier. At which time, of course, our lead collapses and the cycle repeats. What’s interesting is that I’m fully aware that this is how it works, but I haven’t yet learned to prevent it. For one thing, hard work is just HARD. But also the hard work you did while "down" feels inappropriate to/bizarre in the new circumstances. Probably we have to figure out a different form of hard work in the good times.

      

 

            Right; similar problem.  There are forces within the relationship, within the nature of your eight-year-old, which are pushing the family in a certain direction.  In a basketball game, you can take out the player with two fouls; you can let him play—but either way, you’re still going to wind up tied with two minutes to go most of the time.  In a family, you can be patient, you can be impatient; you can go to family therapy, you can refuse to go.   Many times, you’re going to wind up in the same place a year from now either way.  The tide comes in; the tide goes out.  You bear down and work hard; you relax.  There are smart decisions and there are stupid decisions, but there are also forces outside your control which are not going to permanently stand aside. 

 

            And here’s the final letter:

       Hey, Bill:  interesting missive on Competitive Balance.  T-Boone Picked used to say that the cure for high oil prices is high oil prices.  Oil prices get high enough and there will be more drilling, exploration, and more oil brought to the market, and thus prices are the same—raise prices and farmers will grow more corn, wheat, hogs, whatever and then the prices should fall.  In any competition (sports, war, etc.) I think the loser often looks to make adjustments whereas the winner thinks he has a pat hand and does not change.  Given the above and what you said, my question is "How in the heck did the Yankees stay so good for so long?  Maybe the winners share was so much more relative to salaries back then is part of the answer.  Scouting?  Opponents didn’t care/bother to adjust?

 

            I gave a different answer to this question when I posted it, but the question forced me think about what he was saying.  Why EXACTLY do teams stay strong over time? 

            The Law of Competitive Balance actually doesn’t have anything to do with the strength of an organization.  It has to do with the strength of your position relative to the strength of your team.  This is a new realization for me.  

            In the NCAA basketball championship game, Kansas trailed at halftime by 15 points.  But Kansas was not a weaker team than Carolina; they were an equally good team which happened to be in a weaker position.   In the AFC Championship game last January, Kansas City led Cincinnati 21-10 at halftime.  But Kansas City was not a stronger team than Cincinnati; they were an equally good team which happened to be in a stronger position.  Luck doesn’t even out over the course of a game, and certainly doesn’t even out over the first half. 

            Or to take the player who hits .300 one year and .250 the next; he is not (in most cases). . .he is not actually a worse player one year than he is the other.  He is the same player who happens to be in a weaker position.  He had some injuries; he lost playing time and couldn’t get going.  As Hal McRae said, circumstances don’t even out over the course of a season. 

            In the case of the Yankees versus the Browns, the Orioles, the Kansas City A’s, whoever. . .that’s an entirely different thing.  The Yankees had ACTUAL strength, based on playing in a larger city with more fans and wealthier owners.  The Law of Competitive Balance doesn’t flatten out actual strength; far from it.  Success breeds success.  

            When you push on an issue, when you confront the questions which are hiding WITHIN your initial assertion, you wind up understanding what you are trying to say better than you did when you first said it.  I appreciate you all leading me through the process of discovery in relation to this assertion.   Will open this up for comments tomorrow morning. 

 

 
 

COMMENTS (12 Comments, most recent shown first)

DefenseHawk
Great article, Bill.

Of course, decades ago in your Abstracts you were warning us about how teams generally regressed (or improved) closer to .500 in the following year. Which helped explained why so-and-so didn't keeping improving when they jumped from .475 to .550. Yes, randomness changes things (i.e. a big free agent signing), but by and large we see it over and over.

"one of three key drivers of The Law of Competitive Balance: that success increases when there is an increased need for success."

That is why there's a saying, "Three to nothing is the most dangerous lead in hockey."

The team with the lead tends to sit on it and the trailing team starts taking more chances (thus improving the likelihood they will score the next goal). The main reason is because the team that is ahead is in such a defensive posture they are not able to take advantage of the trailing teams's mistakes as easily as they would if they weren't in a defensive shell. And before you know it, it's 3-3.

Oh, and FrankD? Thanks for once againing confirming Godwin's Law. ; )

1:09 PM Apr 26th
 
ForeverRoyal
Great article and I appreciate you revisiting it. The “Plexiglass Principle” is something I’ve enjoyed referencing to my colleagues throughout my career. I’ve always found it so elegant.
1:05 PM Apr 23rd
 
3for3
It works in hockey as well. Teams with a lead in the third period will play more defensively. The trailing team will eventually pull its goalie. Same idea.

Regarding options increased volatility increases value for all options, whether they are in the money or out. Here’s an obvious example. Stock is 101, the day before expiration. If I tell you the stock won’t move, the 100 line call is worth $1. If I tell you the stock will be either up or down 10% the next day (think earnings are due) the option is worth $5.50.
1:26 AM Apr 22nd
 
raincheck
The comments so nice we made them twice.
7:37 PM Apr 21st
 
FrankD
Bill: thank you for the further explanation. And I'll throw in an historical example: Its fall '44, Hitler's armies are being driven back everywhere and he's losing everywhere. So, Hitler goes for the football long bomb. He launches a full fledged offense in the Ardennes (The Battle of the Bulge). His generals think this is crazy, but could never explain any other course but delaying the inevitable. Ike was in a 'nickel' defense in that he kept a broad front instead of in one sector having a massive drive. The Americans, although surprised and pushed back, stop the 'long bomb'. I think this 'crazy' attack by Hitler slightly improved the German's very low odds of winning .... and fits the above article ......
7:16 PM Apr 21st
 
FrankD
Bill: thank you for the further explanation. And I'll throw in an historical example: Its fall '44, Hitler's armies are being driven back everywhere and he's losing everywhere. So, Hitler goes for the football long bomb. He launches a full fledged offense in the Ardennes (The Battle of the Bulge). His generals think this is crazy, but could never explain any other course but delaying the inevitable. Ike was in a 'nickel' defense in that he kept a broad front instead of in one sector having a massive drive. The Americans, although surprised and pushed back, stop the 'long bomb'. I think this 'crazy' attack by Hitler slightly improved the German's very low odds of winning .... and fits the above article ......
7:16 PM Apr 21st
 
Gfletch
Bill, that guy who was going on and on about coins not being people sounds like a real moron.
5:00 PM Apr 21st
 
maordorica
I decided to look at this using win shares. I picked every player who had 500 or more PA in ages 25, 26, and 27 from 1900-2008. I wanted to control for normal aging patterns, and serious injury. It is absolutely shocking that the data shows EXACTLY what is presented here. On average, a player than changed 2.5 or fewer WS from age 25 to 26 stayed the same from 26 to 27. A player that changed more than that, on average, changed halfway back the next year. For example if a player improved by 8 win shares, on average they would lose 4 win shares the next year. If they got 12 win shares worse, on average the next year they would get 6 win shares better. If a player changed by more than a couple win shares either way, they were 75 percent likely to regress the next year.
3:14 PM Apr 21st
 
evanecurb
Well said, Bill. I was going to add a million examples from sports and business and politics that agree with what you said, but that really wouldn't move the discussion forward. I've heard coaches and team leaders say all my life that it's tougher to repeat as champions than it is to win the first time. I still don't know if this is true, but I certainly understand what they mean.
2:57 PM Apr 21st
 
evanecurb
Well said, Bill. I was going to add a million examples from sports and business and politics that agree with what you said, but that really wouldn't move the discussion forward. I've heard coaches and team leaders say all my life that it's tougher to repeat as champions than it is to win the first time. I still don't know if this is true, but I certainly understand what they mean.
2:57 PM Apr 21st
 
raincheck
This is the sports version of the option theory I learned at business school. The Black-Scholes option pricing model is based on the premise that, when your options are underwater (the stock is trading below the price that you have an option to buy at), increased volatility in the stock price increases the value of the option.

Intuition tells us, no, it should only be things that will increase the value of the stock. But, in fact, Black and Scholes make the case that pure volatility, up and down, adds value to the option. Downward price swings have no impact on value if you are already under water, so all volatility is good.

It is a principle that can be applied to a surprising number of things in our daily lives. Including how a basketball team behaves when it is down 10 points with 3 minutes left.
2:22 PM Apr 21st
 
raincheck
This is the sports version of the option theory I learned at business school. The Black-Scholes option pricing model is based on the premise that, when your options are underwater (the stock is trading below the price that you have an option to buy at), increased volatility in the stock price increases the value of the option.

Intuition tells us, no, it should only be things that will increase the value of the stock. But, in fact, Black and Scholes make the case that pure volatility, up and down, adds value to the option. Downward price swings have no impact on value if you are already under water, so all volatility is good.

It is a principle that can be applied to a surprising number of things in our daily lives. Including how a basketball team behaves when it is down 10 points with 3 minutes left.
2:18 PM Apr 21st
 
 
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