| Proof By Contradiction Authored by Keith Berzanske - June 12, 2007 - 4:26 pm

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YET ANOTHER WAY TO APPLY MATH TO EVERYDAY LIFE
I teach night school, and every time I start a new class, I invariably get the questions "But when am I ever going to use this?" I always say "You use this knowledge more than you realize, sometimes without even thinking about it".
ALthough there is some truth in that answer, it's really just intended to shut people up so that I cna move on to the next point. But Sunday night, watching Game 2, trying to figure out why the Cavaliers looked so bad, I remembered some of my lessons and I realized that I could indeed apply them to this game.
In order to complete my Master's Degree in Statistics, I had to, as one of the requirements, complete a theory-focused exam. That's no numbers, no computations - all theory, focused on proofs. One of the best methods to use when proving something is called 'proof by contradiction', If you want to prove that something is true, you first assume it is not true, then go forward from there to reach a conclusion that can't happen, i.e contradicts something that is known to be true logically. Since all of the steps followed to reach the conclusion were valid, the only possible result is that the initial information supplied was actually incorrect.
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A common use of this is to prove that the square root of 2 is irrational. See:
http://en.wikipedia.org/wiki/Irrational_number#The_square_root_of_2
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In basketball, we would apply the technique in this way:
ASSERTION: Mike Brown is killing the Cavaliers with an array of coaching blunders never before seen in NBA history.
PROOF:
First we assume the opposite, which would be:
As a coach, Mike Brown is on the same level as Greg Popovich, and will do his best to take advantage of the strength of his personnel and the weakness of the opponent's personnel in order to give the Cavaleirs the best chance to win.
{WOW - sounds great, doesn't it?...}
OK so if that were true, the it would follow that Mike Brown is doing the following:
(1) Delegating the most minutes to the most productive players, and make substitutions accordingly
(2) Designing offensive sets that maximize the potential for scoring.
(3) Designing defensive sets that minimize the opponent's potential for scoring.
(4) Using timeouts wisely
(5) Instilling a winning attitude by showing his team that there is no tomorrow and he will do whatever it takes for the team to win today.
Let's look at these one at a time:
(1) Delegating the most minutes to the most productive players, and make substitutions accordingly.
Wait a minute here...
It should not have taken Mike Brown 2 full games to realize that Larry Hughes needs to sit and Daniel Gibson needs to be playing a LOT more. Even if Hughes were healthy, teh performance of the two players would indicate that a switch is needed. When you throw in the fact that Hughes could barely beat Jimmy Stewart's character from Rear Window in a foot race right now...I think the conclusion is obvious. I mean, has a team ever gotten less out of its starting point guard in two games of the NBA Finals? I'm not even talking about raw statistics - have you been watching the games? Hughes won't drive to the hole, he won't push on the break, he can't shoot very well, and he's getting toasted on defense. He's bringing absolutely nothing to the table, except guile and heart for toughing it out on a bad foot. And yes Coach Brown, it's true that the team has a good record with Hughes starting and they seem to have a good rythym. But this isn't about the last 3 months. This is about what is going on now, this week, and Larry Hughes should not be playing. When you add in how productive GIbson has been and how poised he looks under pressure, this is a no-brainer.
The other move that should be considered is to sub Anderson Varejao for Zydrunas Ilgauskas. Big Z is struggling, but his offense is important. If he were to come off the bench, it could help in a number of ways:
--if he is matched against front-line players, he will be rested while they will be fatigued. Also, some of them may have already picked up fouls and thus may be tentative.
--if he is matched against backup players, he should have a skill advantage (being a recent All-Star, after all) and should be able to score much easier.
--same on defense - his is either guarding someone more winded, or someone less talented, or who maybe isn't even a threat offensively.
--completely different style than Varejao, who annoys people. Z might pick up fouls after subbing in from annoyed overeager defenders, and his free throw shooting is top-notch.
Jones and Marshall should also play a bit more - the Cavs have proven that the small lineup is effective. Also, when you fall behind, go to the offensive lineup earlier - don't wait until it's too late. Snow is only useful on defense.
A Scot Pollard sighting might also prove valuable. Part of a coach's job is to use all of the guys on the team where appropriate.
Also, LeBron cannot sit for 9 minutes. I dont' care if he picks up 4 fouls in 3 minutes. The Cavs were lucky to whether the first 5 minutes last time and only be down 16-13. That's when LeBron should have come back in. The Spurs would have been thinking 'uh-oh, they just went on a run without LeBron and now here he comes in...'. Brown waited far too long. LeBron came back in cold and the game got away from them.
(2) Designing offensive sets that maximize the potential for scoring.
Uh-oh...
The Cavaliers offense has reverted, for the most part, to that annoying "LeBron dribbles for 16 seconds while everyone else forgets they are an NBA player and stands and watches - then someone takes a bad shot and no one is in position to rebound"
LeBron needs to be off the ball occasionally, and should also work in the post more. No one can guard him out there. But the most important thing is for him to attack right away. Catch the ball and go. Too often, he waits for the defense - be proactive, not reactive.
I thought LeBron's foul trouble would be a blessing in disguise because other guys would be forced to step up and remember that they are threats. But Brown's substitutions were erratic, and the team looked largely disorganized.
(3) Designing defensive sets that minimize the opponent's potential for scoring.
The Cavaliers defense is actually pretty good, but there are stretches when it seems the Spurs can do no wrong. However, I did notice some things
--someone needs to knock Parker down when he goes into the lane, and just take a hard foul. He is going in there wiuth impunity, it's ridiculous. He needs to fear for his life when he drives in there. I've taken harder fouls in church league rec games.
--next time Ginobili does his 'drive left, push off with right arm, then flail back to the left so it looks like I was pushed' move, the Cavs defender shuld grab the arm he is pushing off with. Then whne Ginobili flops he might dislocate his arm. Not to wish injury on anyone, but there needs to be a stop to all this 'let me flail around and see if I get a call'. Like when LeBron elbowed Ginobili in the face, that is a correct no-call because Ginobili is PLAYING DEFENSE WITH HIS FACE. They always teach you that even in little league - you stick your face in too close, you can get it whacked, so be careful. HELLO!
{speaking of flopping, Varejao looks a lot worse than he is because of his hair. He actually takes several hard hits per game, mostly because he is active and gets under people's skin}
--never guard Jacque Vaughn. Ever. Vaughn hasn't made a jump shot outside 13 feet in like 6 years. His man should sag off. If the Cavs were really smart, they would design the defense so every Spurs possession results in a shot for either Vaughn or Bruce Bowen
--double team Duncan with a guy who is not guarding Parker, Ginobili, or Horry
(4) Using timeouts wisely
I keep seeing the SPurs go on these huge runs and the Cavaliers never call timeout. Now, I don't believe in automatically calling time evey time the opponent scores 2-3 baskets. But c'mon! What are yuo saving those things for? Maybe if oyu call timeout, someone can remind you that Larry Hughes has one foot and that, hey, LeBron hasn't played in over 6 minutes...
(5) Instilling a winning attitude by showing his team that there is no tomorrow and he will do whatever it takes for the team to win today.
I haven't heard anyone talk about this yet, which astonished me, especially given ESPN'S penchant for overanalyzing - um, Mike, the game is not over with 50 seconds to play. Quit taking LeBron out of the game! QUIT CONCEDING! Foul. Extend the game. The Spurs are not a great free throw shooting team. Stranger things have happened. IT'S THE FREAKING FINALS. THERE ARE NO DO-OVERS!!! This infuriated me. You cut a 29 point lead to 8 in 6 minutes, but you don't think you can shave those last 6-8 points off?!!!
You don't want to get away from what got you here totally, but you have to adapt a lot quicker in the Finals. If something isn't working, you have to try something different. Sometimes the game is about matchups. Sometimes it is about tempo.
Speaking of tempo - speed it up! The Cav have better athletes and younger legs. The SPurs are awesome in the halfcourt set on defense. So run the ball. What have you got to lose?
So none of our five onclusions has any truth to it whatsoever. UH OH - A LOGICAL PARADOX!
This means that our original assertion has to be incorrect, thus proving that Mike Brown has been overmatched and genrally inept in this series, and is costing the Cavaliers a chance at winning the series.
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Speakign of which, I'm glad that you guys are reading my column, but did I really need over 100 "Monday Morning quarterback" emails, telling what a meathead I am for picking the Cavaliers? Where were you all after the Pistons series?
Granted, maybe I was a bit optimistic - I mean, I did overlook the "Mike Brown factor", i.e. the huge disadvantage the Cavaliers have in any kind of game plan. I based my prediction on the way the Cavaliers had been playing and the direction they were going, and on hw well they matched up with the Spurs ( much better than Phoenix, althogh Cleveland is not as good a team as Phoenix). I thought that the Cavaliers could steal one of the first two games, and that the momentum and confidence, thier stellar defense, and the presence of their superstar, would propel them to victory.
I also have made the mistake of taking Tim Duncan for granted. He is the best player on the court. I said earlier that the team with the best player usually wins, but I mistakenly gave the honor to LeBron. LeBron, you are wonderful, but Dincan is the greatest power forward of all time, and really deserves to carry that mantel until it is taken away.
But it's still there to be taken away. With 4 transcendent games, LeBron could establish himself as the best player, will his team to victory, and carve his place in history. Yes, this seems unlikely now - it's hard to imagine the Cavaleirs winning three straight, even at home, and if they win 2 of 3, then they need to win both games 6 and 7 in San Antonio. I just can't see that happening. But history has shown that stranger things have happened.
Just look at two years ago:
Game 1 (2005-06-09 at SAS) SAS 84, DET 69
Game 2 (2005-06-12 at SAS) SAS 97, DET 76
Game 3 (2005-06-14 at DET) DET 96, SAS 79
Game 4 (2005-06-16 at DET) DET 102, SAS 71
Game 5 (2005-06-19 at DET) SAS 96, DET 95
Game 6 (2005-06-21 at SAS) DET 95, SAS 86
Game 7 (2005-06-23 at SAS) SAS 81, DET 74
Note that the Spurs destroyed the Pistons in Games 1 and 2 even worse than they beat the Cavaliers, and then barely survived to win a 7 game series. Game 5 was an OT game that could have gone either way.
And we all remember what happened to Dallas last year - not only did they win Games 1 and 2 handily, but they were ahead by 13 halfway thru the 4th quarter of Game 3. And then Dwyane Wade went nuts.
So let's end the talk of the Cavaliers being the worst team in NBA Finals history. Let's end the talk that the series is over. The Cavaliers are still in it. They need to win Game 3, though. To do that, they'll need Mike Brown to make some adjustments, try some new things - really push the envelope. Leave no stone unturned in the quest for a championship Coach Brown. And remember, the game isn't over until the horn sounds, and until that happen we expect our team to be fighting and clawing, with LeBron James on the floor. This team has shown its heart in this postseason, notably coming back in the 4th quarter of the last two games after being badly outplayed for most of the time. Give them a chance to step it up another notch, Coach Brown. Show them that you believe that they can win, and they might now just surprise you, but everyone else as well.
It's time for you to start proving us wrong.
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