It all equals out in the end…Not

Whenever there is a missed call by an official, some TV announcer will say something to the effect of…”they didn’t get that one, but it all evens out over the course of the season”.

Well I have news for everyone. It doesn’t even out.

Players make mistakes and cost their teams games. Officials make mistakes and cost teams games. That’s just the reality of basketball. If a player can make, or not make a play that impacts the final outcome of a game, we have to realize that so can officials.

Officials create turnovers. A traveling, 3 seconds, or palming call made or not made. A change of position opportunity. Given or taken away.

Officials create points. A goaltending call made, or free throws given.

A technical called vs an official just walking away.

If you just look at yesterday’s games, a player got ejected with 43 points and the lead. His team loses.

A coach gets ejected with 3 seconds left in a 2 point game, over a call he thought should have been made.

A team has no calls on what they thought should have been goaltending in the final seconds of two consecutive games.

And that’s just last night.

There are about60 to 70 “call opportunities” each and every game. You can assign your own percentage of calls that are made that are right or wrong, but no matter what percentage you pick, the number of incorrect calls across the course of a season adds up.

If that number, and I’m just using easy math to make a point, is 500 missed callsper team per season. What are the chances that 250 of the missed calls went in favor of that team, and 250 went against? What are the chances of it working out that way for 30 teams across the league?

Almost impossible.

In a given game, if there are 10 missed calls, and 5 happen to create turnovers for your team, and the 5 other missed calls happen to create foul shots for the other team, that’s 5 turnovers and at least 5 free throws they shouldn’t have had in a single game. Think that might impact the outcome of the game?

Bottom line is that games, playoff positions and jobs are critically impacted by players. They are impacted by coaches. They are also impacted by officials.

The purpose in writing this isn’t to criticize anyone. It’s purely to make two simple points…

1. Officiating is a critically important part of any game. Every official I know busts his or her ass to do their best job every night. The NBA works hard to put the officials in a position to succeed. The league knows how important their job is to the outcome of a game. Now hopefully the media will as well.

2. Missed calls don’t balance out for teams over the course of a season. There are going to be teams that are going to feel like they can’t get a break and are snakebit with bad calls…

…and they just may be right.

36 thoughts on “It all equals out in the end…Not

  1. Being competitive . Winning at all cost. Any team, any player, any fan, any owner that does not complain should question their own desire to try hard. To want to win. The reality of it all is that for every bad call against , there is a missed call that goes for. It is the nature of the beast to call out only the bad ones.

    Comment by runescape money -

  2. Guys like Artest, R. Wallace, etc get called for a tech or flagrant much quicker than a Tim Duncan, or other more mild temper players who might do the same thing. I’m not saying these players don’t deserve the call, but it makes a difference in the game if you have these types of players on your team. Saying that all these calls evens out is rediculous.

    Comment by wow powerleveling -

  3. NBA officiating is the worst anywhere in basketball…I here some say that these guys are professionals. If that is the case they should be held accountable just as the players are, by hitting them in there pocketbook..I’m not saying that fines are the answer but higher pay and choice of games might be. Maybe officials should have to go through a draft and all that goes with it. Officials should be able to be free agents and get paid well for good performance. When officials are being paid by how good they are and it starts turning into real money then the league/teams will hold them accountable as they do players!!!

    Comment by Tim Hutchings -

  4. NBA officiating is the worst anywhere in basketball…I here some say that these guys are professionals. If that is the case they should be held accountable just as the players are, by hitting them in there pocketbook..I’m not saying that fines are the answer but higher pay and choice of games might be. Maybe officials should have to go through a draft and all that goes with it. Officials should be able to be free agents and get paid well for good performance. When officials are being paid by how good they are and it starts turning into real money then the league/teams will hold them accountable as they do players!!!

    Comment by Tim Hutchings -

  5. To those who commented about my calculations (mine was the 2nd comment), you missed Mark’s original question. My goal was to answer Mark Cuban directly. Here is his original question:

    “What are the chances that 250 of the missed calls went in favor of that team, and 250 went against? What are the chances of it working out that way for 30 teams across the league?

    Almost impossible.” — M. Cuban

    So I calculated it out for an EXACT equaling out over one season. I just wanted to let Mark know he can remove the word “almost” from his answer of “almost impossible”.

    As far as standard deviations, yes, it is true that 66% will fall within one sigma. But that is the answer to another question! One I would like to discuss further perhaps elsewhere.

    Comment by greg -

  6. The earliest poster with the equations that show the minute probability that things even out *perfectly* in a single season used perhaps an incorrect definition of the word “end”. In the end, or at time infinity, things will even out. No, you won’t get 266 calls in either direction in your first season. Maybe you only get 45% of the calls in one given season. But you are just as likely to pick up 55% of the calls in the following season, all other things held constant. As you add more and more seasons, the number of calls for and against will approach 50%.

    Take free throw shooting. If you know that Shaq is going to make 60% from the line, what are the odds that he hits 6/10 on a given night? It’s not even money, that’s for sure. But let him shoot 10,000 free throws and he will come very close to 6,000 makes. Maybe 6,002, maybe 5,997 but percentage-wise, it’ll be darn close to 60%.

    Either way, these two or three games that are really decided by the officials (critical call in the last few minutes of a game, or one that causes foul trouble for a superstar) probably mean the difference of maybe four playoff situations. How many of these will translate into a different playoff outcome? Probably none. In March Madness, bowl games, and the NFL, these might make a difference. But in the NBA, over an 82 game schedule, then 7 game series in the playoffs? Unlikely. In the NBA, the team playing the best basketball in the playoffs almost always wins.

    Comment by Mike -

  7. I live in Australia and am a big fan of cricket. I am tired of players, commentators, and umpires telling us that bad decisions even out in the end.

    How can two wrongs make a right?

    Comment by Sunny -

  8. While an earlier poster calculated the exact odds of one team getting the exact number of close calls going for and against him and then carried that result out to say it is almost impossible for all teams to have this happen, I think he used the statistics pretty simplistic and misleading fashion.

    While simple statistics will tell you that almost no one gets exactly half the the close calls, slightly less simple statistics will tell you that a lot of teams get pretty close.

    He failed to consider standard deviation. Using his number for 532 close calls per team, I calculated one standard deviation, or sigma, to be 11.53 using the calculator found here: http://cnx.rice.edu/content/m11024/latest/#calc. Simple statistics say that 68% of the league or 22 teams will be within one sigma of the mean (in this case splitting the 532 close calls down the middle and getting 266 calls). This means that the majority of the league will get between 255 and 277 calls for them. 95% or 30 teams will be within two sigmas, getting from 243 to 289 calls. 99% or 31 teams will be within 3 sigmas and get between 232 and 300 of those calls. And the one remaining team will either be extremely lucky or exterely unlucky falling outside of three sigmas meaning they could get from any number from 1 to 231 or from 301 to 532 of the calls but nothing within 3 sigmas.

    So, while almost no team will have exactly 50% of the calls go their way over the course of the season, the statistics dictate that most of them will be close enough that it is a fair assessment that close calls balance out.

    Comment by Jason -

  9. Some simplifying assumptions:
    500 missed calls per year from Cuban: approximately 100 games and 5 missed calls per game. Let us further assume that each results in 1 point. Missed calls are assumed to be errors and are split 50:50 between the teams. We further assume that the missed calls are independent of each other (no make up calls, etc.).
    Basic probability calculations tell us that the chances are 31.25% that the missed calls will give team A one extra point and 31.25% that team B gets one extra point. So if we buy into the above assumptions there will be a one point swing for or against a team 62.5% of the time. Swings of 3 points have probability of 15.625% in either direction. There is the chance that all 5 missed calls will go with one team and none in the favor of the other team. The probability is 3.125% for each team. To recap, in a game with 5 missed calls these will go against me with a
    3:2 split with probability 31% costing me 1 point
    4:1 split with probability 16% costing me 3 points
    5:0 split with probability 3% costing me 5 points
    We can all remember games where an extra 5 points would have changed the outcome. Some of the time our team got the break and the missed calls. I tend to remember are the ones where the other team got the unearned points. So luck plays a role and it not just talent. But this not just in missed calls. The drop of sweat on the floor that makes the ball bounce just a little less than expected that contributes to a turn over could also be though of as being due to chance. What are the factors that make one jump shot go in and another not get that ‘lucky bounce’? Some are skill and some might be called chance. The missed call is more painful because it is more preventable – better training, more officials, technology, …
    Alan

    Comment by Alan Forsythe -

  10. Some simplifying assumptions:
    500 missed calls per year from Cuban: approximately 100 games and 5 missed calls per game. Let us further assume that each results in 1 point. Missed calls are assumed to be errors and are split 50:50 between the teams. We further assume that the missed calls are independent of each other (no make up calls, etc.).
    Basic probability calculations tell us that the chances are 31.25% that the missed calls will give team A one extra point and 31.25% that team B gets one extra point. So if we buy into the above assumptions there will be a one point swing for or against a team 62.5% of the time. Swings of 3 points have probability of 15.625% in either direction. There is the chance that all 5 missed calls will go with one team and none in the favor of the other team. The probability is 3.125% for each team. To recap, in a game with 5 missed calls these will go against me with a
    3:2 split with probability 31% costing me 1 point
    4:1 split with probability 16% costing me 3 points
    5:0 split with probability 3% costing me 5 points
    We can all remember games where an extra 5 points would have changed the outcome. Some of the time our team got the break and the missed calls. I tend to remember are the ones where the other team got the unearned points. So luck plays a role and it not just talent. But this not just in missed calls. The drop of sweat on the floor that makes the ball bounce just a little less than expected that contributes to a turn over could also be though of as being due to chance. What are the factors that make one jump shot go in and another not get that ‘lucky bounce’? Some are skill and some might be called chance. The missed call is more painful because it is more preventable – better training, more officials, technology, …
    Alan

    Comment by Alan Forsythe -

  11. First, to use mathmatics equations, one must have a constant that never changes. A referee’s interpretation and judgement on an specific play is not a constantm and therefore not subject to the laws of mathmatics. The arguement that it will all eqaul out over time is also false as there are far too many variables that do not constitue an equal opportnity reaction (ie…Heads vs Tails).

    The comments from some that a team should have played better prior to a terrible call (ie…”Had Webber made 2 prior FT’s the non-Goaltending call would’nt have mattered”) are somewhat true, but flawed. IN basketball (as in most things), there is a reaction to every action. Execpt at the end of a game, when there is little or no time for the “recation”. So a missed goaltending call in the first period or in a 25 point blow-out is NOT EQUAL to a missed goaltending call that likely cost a team a victory.

    My issue is that officials, being the human beings they are….are not a constant, and while its understood they are human…as a whole they seem to understand that a touch foul on the Bobcat’s 3rd team PF is exactly the same as a touch foul on Tim Duncan. And until the league announces mistakes (the non-GT the other night was laughable and left ZERO doubt as to whether a mistake was made), publicly applauds AND discipline their officals…they are setting themselves up for such negative feedback from fans, coaches, and players.

    BTW, am I the only one who found the humor in Mark’s comment above:
    “A team has no calls on what they thought should have been goaltending in the final seconds of two consecutive games”?
    He convienantly combined the questionable no call in the Sac-Phx game with the obvious mistake that went for his Mavs. What they (the Kings) thought should have been? Ummm Mark, what EVERYONE KNOWS should have been called. Had that play been reverse (Sac beating Dallas on a bad no-call)….Cuban would have been all over the news promoting we got robbed.

    Comment by Mark Harrison -

  12. Imagine you’re the coach of an NBA facing Shaq and the Heat. In the 4th quarter, you begin “Hack a Shaq,” realizing that Shaq is having the worst free throwing percentage of his career. But wonders of wonders, Shaq ends up hitting 100% of his free throws and you lose! You think, “That is so unfair…that shouldn’t happen! I employed the right strategy….”

    Imagine now that you’re the coach of the Lakers. You’re down by 1 point with 1 second left in the game, and have possession of the ball. Kobe is being defended by Earl Boykins. You call a play that gives the ball to Kobe. He shoots a jumper and misses and you lose. You think, “That’s ridiculous. Kobe hits those game winners all the time. There is not a better go-to man in the game.”

    In both cases above, the coach employed the right strategy, but the end result was not the one that should have happened. But over the course of a season, it WILL balance out and how good a team really is will show. Bad calls are similar. Most calls are good, but sometimes they are bad, but usually over the course of a season, the cumulative effect of the good calls overwhelm the effect of the few bad ones–meaning, e.g., the best teams usually end up in the playoffs.

    Even in the context of a single game, I think it’s ridiculous when people blame a player for missing a game-ending shot that results in a loss; or they credit a win to a game-ending field goal. They ignore all the shots (good and bad) that led up to that situation. If a team had built up a nice lead, then missing the last shot of the game would have been meaningless. Blaming a loss on one or two supposedly “bad” calls is just as ridiculous, imho.

    Comment by Eric Tsuchida -

  13. Your hypothesis is that things might not even out. If things are uneven, is it trackable?

    Are there some players that have more calls go against them, because of their attitude or the way they conduct themselves?

    Are there some coaches that have more calls go against them, because of their attitude or the way they conduct themselves?

    Comment by Tom Cunningham -

  14. Why not create a market around referee errors? Alleged referee errors can be posted on a post game web site. An independent commission can investigate the alleged errors. If an error was made that cost the team points, each point can be assessed a financial penalty, payable to the offended team. The league would pay the penalty to the team. Eventually, the league will know which referees are costing them money and will correct the situation. Fans can be rewarded and be even more involved with their teams. Referees would finally be subject to oversight.

    Comment by El Guapo -

  15. IF a game can come down to the last fraction of a second and ONE throw by a player then one single bad call the wrong way could definately determine a game, or 100 games over time.

    Comment by Rob Thrasher -

  16. I surely hope that what’s happened to football never happens to basketball, even though it appears that many wish it would. I’m talking about the plague of instant-replay. Football has made it possible to allow everything that’s measurable (is a player in the endzone or not, were both feet down, was a player down before a fumble, etc.) to be reviewed by using the thousand cameras trained on the field of play. This works fairly well (with limits) because of the nature of the game where there are natural delays between each play.

    Basketball, on the other hand, is much more of a judgement sport that features continuous action. In the Kings/Phoenix game, Miller should (frankly) have attempted to dunk that ball instead of that weak shot. In light of the Motown Throwdown, Carter should have been tossed. (And Bowen should be fined for dirty play too.) And the lack of a goaltend cost the Kings the Mav’s game – in my opinion the clearest example I’ve seen yet of a call (or lack) costing a team a game. (The league has probably fined the officials and sent an appology letter to the Kings, but that doesn’t help them.)

    Can the shortcomings in officiating be “repaired?” I have yet to hear a reasonable proposal. The NBA found a way to add instant-reply without ruining the pace of the game by allowing a review of game-clock violations at the end of quarters by taking advantage of a natural break in the action. Let’s pray that they don’t fall into the trap of going for replay in the middle of the action.

    Comment by Dave Spencer -

  17. If something is “riggable”, it almost always rigged. There is way too much $$ wagered on NBA games. A ref does not need to be paid to award the game to the other team, but one or two early foul calls on a players like Shaq, Garnett, Lebron, or Dirk will greatly increases the odds of the other team winning. A 1% move in probabilities equates to millions of $$’s.

    Comment by IK -

  18. Something my father told me a long time ago… If you don’t like the situation you are in think about how to avoid it next time. The reality is that Vince Carter’s actions put him into a position to be yanked. Teams/players put themselves into those positions. See Rasheed Wallace, the Indiana Pacers, and Shawn Bradley. Of my examples, Shawn is the king of reaction. He’s always a step late getting to the baseline and an elbow from being ejected. Dennis Rodman… reaction yes, but his rebounding skills were so much about anticipation.

    Some teams/players have way too much reaction and not enough anticipation. It’s not about right and wrong (everyone is wronged at some point), it’s about how can I stay in the game and help my team… yelling at an official or arguing with a call typically doesn’t offer that help.

    Comment by Jason -

  19. “2. Missed calls dont balance out for teams over the course of a season. There are going to be teams that are going to feel like they cant get a break and are snakebit with bad calls”

    Welcome to Major League Soccer since day 1.

    Comment by Amy -

  20. When the call is against your team it isn’t fair, when it is against the other it is justice🙂

    Derrick

    Comment by Derrick Pizur -

  21. Does anyone really have a problem accepting human error? Problem I have is when an official’s ego clouds his/her judgment and consequently upsets the flow of the game. Commentators seem to just dismiss this by stating that a player should or shouldn’t know how to behave with a certain official. Don’t think I’ve bought an NBA ticket yet in hopes of seeing how Joey Crawford might impose his authority.

    Comment by JD -

  22. If you flip a coin a million times, you probably ARE NOT going to get heads 9,999,999 times and tails once. But that’s assuming there’s an even chance of heads vs. tails. Over the years there have been millions of calls made in the NBA, and we all know that the primary purpose of officiating is not to ensure that teams play by the rules but rather to keep the Mavs from winning.

    Comment by ert -

  23. greg your calculations are a bit slanted, of course there is a slim chance for there to be EXACTLY the same number of calls for and against, but annoucers say it averages it out, which means you can have similar numbers say 260 to 272 or different variations, 265 to 267 etc.., and factor in for critical calls etc.. and im pretty sure it would be a much higher percentage

    Comment by dave -

  24. There is no way for it all to balance out perfectly, but there is little that can be done to change that. The statement that “it balances out in the end” is not so disconnected from reality. It is really just an acknowledgement that bad calls will happen, and it inevitably is going to go the other direction as well. There is nothing wrong with putting things in perspective; but there is something wrong with dwelling on something negative that cannot be changed.

    Comment by Theodore -

  25. Mark, you forgot to add one more point about calls and how they “even” out. You are exacatly right, but you forgot to note, some players/teams get the benefit of a doubt on a questionable call. On the flip side of that, some players who have issues with officals are more likely to get calls against them quicker. Guys like Artest, R. Wallace, etc get called for a tech or flagrant much quicker than a Tim Duncan, or other more mild temper players who might do the same thing. I’m not saying these players don’t deserve the call, but it makes a difference in the game if you have these types of players on your team. Saying that all these calls evens out is rediculous. I don’t know if you watched the Pacers/Pistons game on Christmas, but in the first five minutes of that game the officals decided they would become part of the outcome of the game. They were much quicker to call fouls and even Reggie got a quick tech when he can usually complain for much of the game before he would normally get one. These are just a few examples I have noticed on how officals can have on a game.

    Comment by BJ Ruble -

  26. Greg, I think about fifty stat companies are lining up to call you after that one. Good work — if you don’t work at 82games.com, I’d be shocked.

    The refs seemed to be overtired and in a serious rut at this point in the season. It’s just like school at this point in the year — this is about the time that two fat kids start fighting in the hall because one dropped a cupcake and they feel the need to dive after it for its rightful ownership. It’s sheer frustration.

    If there was any way to give these refs more downtime and less opportunities to take advantage of the tiredness excuse (maybe by working in half-year shifts?), it may help out. Otherwise, let the yelling commence and continue loudly.

    Comment by ben collins -

  27. I personally feel that NBA officials are the worst in professional sports. Many of them seem angry, biased and have a chip on their shoulder for whatever reason. Lets face it, calls are part of the game. They are part of any game. Professional athletes that cry like babies over a call or two should just be quiet. They can’t. We can’t. Fans can’t. Owners can’t. Thats the beauty of Sport in general. Being competitive . Winning at all cost. Any team, any player, any fan, any owner that does not complain should question their own desire to try hard. To want to win. The reality of it all is that for every bad call against , there is a missed call that goes for. It is the nature of the beast to call out only the bad ones. Thats human nature. If the Kings would have made a shot here, and would have dunked there, they would have won the game regardless of the bad call. Bad calls happen, overcoming them is how championships are won. I was at the Kings game on Friday. Vote for Pedro, a few feet from Mark. My seats baseline 5 rows from the court. I watched the goal tend and watched Mark cover his head waiting for the goal tending call. It never came. I started to boo along with the 17,000 in the crowd and watched Mark raise his hands and shake his head with a huge grin on his face. How many times has Mark been on the other side of such calls. So, will Mark remember this call later in the season or only the ones that went against his team? It may all depend on if his team wins the championship or not.

    Comment by Matt Flynn -

  28. Tim, I don’t know who you’re watching when you say the team is whining to the officials, the Mavericks really don’t do it that often. As for you saying Mark doesn’t talk about the calls that benefit his team you’re wrong. Mark mentions goaltending because he knew Dampier should’ve been called for that against the Kings, he realizes on any given night some teams get the calls and some don’t, what he’s saying is over the course of the season it’s not equal.

    Comment by AJ -

  29. Saying that officiating doesn’t even out over the course of the season just because there are not an exact number of calls for and against a team is silly. I’m waiting for Mark Cuban to come out and talk about all the bad calls that help the Mavericks. I’ve never once heard him mention a single instance of a bad call helping his team, they’re always the victim. And, unfortunately, that attitude seems to have rubbed off on the players, as they seem to scream at the officials for a foul after every missed shot. Just play the game. Calls are missed, officials are human, but it is rare enough and random enough that it does not, over the long term, affect the ultimate outcome. What probably does have an affect is the constant berating by Cuban of the officials. He can say all he wants that he supports the officials, he knows they’re doing the best job they can, etc, etc, but that’s just a politically correct way of criticizing them. It just comes off as whining. Let the teams play the game, let the officials do their job, and the best team(San Antonio, in this case) will continue to win in the end, just like they always do.

    Comment by Tim -

  30. In the case of Vince Carter the official is guilty of letting his personal feelings get in the way. He directly impacted the outcome of that game. If Allen Iverson had been ejected for arguing too much tonight the Magic would have won. They walked away. They should have separated Carter then allowed play to continue. But officials are human. Who is to say that the fit the Kings threw on the court against Phoenix when the officials did get it right didn’t impact the subconscious of the officials in the non-call against Dallas. It may or may not have. But it is interesting to think that maybe officials try to even things out on their own without even trying to.

    Comment by Steve -

  31. Mark’s post is silly. Each call goes for one team and against another, just as each game goes for one team and against another, so things certainly do balance out. Although not every team has a 0.500 record at any given point in time, the total number of wins league-wide is equal to the total number of losses. It is the same thing with missed calls. At any given point in time, the league-wide number of missed calls for is equal to the number of missed calls against.

    Over a increasing span of time, any given team’s ratio of missed calls for to missed calls against will certainly approach 1:1. If the figure is 500 calls per year for a team, over the course of a century, the team will experience a total of 50,000 missed calls. Although the number of missed calls for will not necessarily be exactly 25,000, the difference between the actual number and 25,000 will be insignificant.

    Comment by M N -

  32. The past few days I’ve been thinking of how a computerized officiating system will work with a network of sensors to officiate basketball games. It is extremely complex but it can be done.. and someone should give it a try.

    Comment by Sherwin -

  33. Well, can we please remove the 65 calls in a game that’s decided by more than a handful of points. b/c they clearly don’t have an impact on a team.

    and how about teams that don’t make the playoffs. do you think “my” knicks are really affected by calls? At best, a non playoff team might get an extra pingpong ball as a result of bad luck with calls.

    and for playoff teams, how many are in a situation where they’ve had enough bad calls go against them so as to actually affect their seeding? a handful? Less?

    and how many of those playoff teams, b/c of this incorrect seeding, actually play a game 7 where the HCA is actually applied?

    Looking at those things, instead of just trying to create a really small number makes more sense. And for the record, why would anyone care to have it EXACTLY equal? why not look at 2 standard deviations to get a more realistic picture?

    just because something doesn’t exactly balance out to perfectly 50% doesn’t mean that the law of averages is faulty.

    By your logic, since any one point on a dart board has an infinitely small chance of being hit by the dart, then it’s impossible to hit the dart board.

    Comment by kronicfatigue -

  34. It may not even out over a season but it should be the goal of any team to be in a position where the game is not close enough to give the possibility of a referee deciding the game.

    Comment by Edgar -

  35. I couldn’t resist:

    The question you propose can be mathematically answered using statistics, more specifically, a binomial probability distribution.

    Quick refresher from college stats:
    Binomial experiment is one that
    1) experiment consists of N identical trials (we assume the refs are completely unbiased..ugh..this may be a reach. But for now, lets do it)
    2) Each trial results in 1 of 2 outcomes, either a Success or a Failure. (Call “for” your team “S” and call “against” your team “F”)
    3) Trials are independent (another blanket assumption that the refs do not “carry over” any emotional ties to a previous call or the fact that Don Nelson and Mark Cuban are yelling horrible things at them. For now, refs are robots)
    4) The random variable of interest is what we call “Y”, the number of successes observed during N trials.

    In Mark’s example, N = 500. He states that there are “60 to 70 call opportunites” in a given game. Let’s actually calculate N out to be 65 (midpoint of Mark’s assumption) times 82 (games in a season) = 533. I’ll round down to 532 (even number) because the real question is this: “What are the odds of a team getting exactly 266 calls for them and calls against for an entire year”.

    N = 533
    Probaility for a Success = 0.5
    Probaility for a Failure = 0.5
    Y = 266

    Probability = 533!/(266!(533-266)!)*(0.5)^(266)*(0.5)^266

    Probabilty = 0.034576…

    Or, 3.46% of the teams on a given year will end up with the exact same calls “for” and “against”. The odds of two teams having exactly 266 calls “for” and “against” is 0.034576 times 0.034576 = 0.001195 or one-tenth of 1 percent.

    You see where this is going: There are 30 teams in the league, so (0.034576)^30 (this decimal times itself 30 times!) is something like 0.00000000000000000000000000000000000000001 percent. Or, in other terms, it will take 10^43 seasons for all 30 teams to have identical calls each way.

    Or, scientifically speaking, “it ain’t gonna hapen”. you can quote me.

    Just my $0.02

    Comment by greg -

  36. If there’s nothing that can be done to improve call accuracy then

    there’s no harm in saying it all balances out.

    If there is something that can be done then

    how much will it cost? When can it be put into place?

    And since we’re talking about this – how much would it cost to put an intern behind a set of replay machines and announce every day every missed call for or against the Mavericks or some other team?

    How much would it cost to get 30 interns and produce statistics for the entire league?

    Comment by joe blow -

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