How to defend Golden State Warriors in clutch time using Game Theory.

Jiacheng Xu

How to defend Golden State Warriors in clutch time using Game theory

Background Golden State Warriors is an NBA team who played surprisingly marvelous during 2015-16 season. At the beginning of this season, they won 24 games in a row , which set the new 1

NBA record and during that time, many experts were talking about how to defeat Warriors on TV shows and online articles. It is very difficult to beat Warriors not only because they have an astonishing strong ability to win even the most difficult game during clutch time, but also because they have probably the most successful 3-point on this planet nowadays—Stephen Curry . He can shoot from almost everywhere once he is over the half-court therefore he is 2

the most important player to defend during crunch time. Therefore this project will concentrate on how to defend Golden State Warriors and try to minimise the threat of Curry during clutch time using Game theory.

In this project, our modified definition of clutch time will be the last 5 minutes of the 4th quarter or OT within a game that ends with a final margin of +/- 5 . 3

Introduction to Warriors play style "Like Michael Jordan was a whole other thing, this guy is his own thing. It's beautiful for basketball.” ------ Kevin Garnett on Curry 4Undoubtedly, Stephen Curry has been a revolutionary player in basketball and the coach of Warriors also tailored a new playing style around Stephen Curry for the Warriors. Almost everyone in this team can shoot 3-point and they have a 3-pt field goal percentage of 41.6% 5

and they also have 2-point field goal percentage of 52.8%.

Shot Distance (5ft) FGM FGA FG% 3PM 3PG 3P% eFG% BLKA FGM %AST

Less Than 5 ft. 1,530 2,478 61.7 0 0 0.0 61.7 248 66.9

5-9 ft. 214 567 37.7 0 0 0.0 37.7 53 46.7

10-14 ft. 241 555 43.4 0 0 0.0 43.4 6 41.9

15-19 ft. 315 723 43.6 0 0 0.0 43.6 14 65.4

20-24 ft. 568 1,371 41.4 456 1,127 40.5 58.1 9 85.6

<http://www.nydailynews.com/sports/basketball/warriors-24-game-win-streak-ends-loss-bucks-article-1.2464246>1

<http://bleacherreport.com/articles/2482473-is-stephen-curry-the-best-shooter-ever-yes-say-many-of-nbas-all-time-marksmen>2

<http://nyloncalculus.com/2014/11/17/defense-actually-get-tighter-clutch/> 3

<http://www.foxsports.com/nba/story/michael-jordan-golden-state-warriors-stephen-curry-kevin-garnett-compares-to-his-own-4

thing-111215>

<http://stats.nba.com/team/#!/1610612744/stats/shooting/> 5

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We can acknowledge that Golden State Warriors made most of their shots in 20-24ft, 25-29ft and less than 5ft therefore we can also make an assumption that if the opponents defend 3points it will be very likely to lead to an easy 2-point shot for Warriors. Basically, if defenders are defending 3-points, Draymond Green, the power forward will then drive in and make an easy 2-points or pass the ball to his teammates on 3-point line and they will have the opportunity to make a wide open 3. If defenders are guarding 2-points, Warriors shooters can make 3-point jump shots with high shooting percentage. If defenders are too spread out and trying to guard 3-point shots desperately, Stephen Curry can choose to drive in and make an easy lay-up. Therefore we can divide their offense strategy into four categories in this project, which are:

(1) Stephen Curry shoots 3 points (2) Stephen Curry passes the ball (teammate shoots 3) (3) Stephen Curry shoots 2 points (4) Stephen Curry passes the ball (teammate shoots 2)

Game theory models (1) Battle of sexes Introduction In the battle of sexes, a couple argues what to do over the weekend. They want to spend time with each other but they cannot reach an agreement what to do. The man prefers to go to watch boxing whilst the woman wants to go shopping (go to the opera in some cases). Since they would like to spend time with each other, if they go separately, both of them will gain no utility. If they both go to watch boxing or shopping, both the man and the woman can receive some utility but only one of them will actually enjoy the activity. Therefore the payoff matrix is demonstrated as below.

25-29 ft. 595 1,392 42.7 595 1,392 42.7 64.1 5 75.6

30-34 ft. 18 38 47.4 18 38 47.4 71.1 0 27.8

35-39 ft. 2 6 33.3 2 6 33.3 50.0 0 0.0

Shot Distance (5ft) FGM FGA FG% 3PM 3PG 3P% eFG% BLKA FGM %AST

<http://stats.nba.com/team/#!/1610612744/stats/shooting/> 6

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In this scenario, there are two dominant strategies. (Dominant strategies are considered as better than other strategies, no matter what other players might do.) Therefore to help the player make a decision, we need to introduce a new concept—mixed strategies, which refers to strategies consisting of possible moves and a probability distribution which corresponds to how frequently each move is to be played. Thus we can look at the possibilities of the strategies.

Assuming that the possibility of the woman going to watch boxing is q, therefore the possibility that she goes shopping is (1-q).

Assuming that the possibility of the man going to watch boxing is r, therefore the possibility he goes shopping is (1-r).

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<http://www.policonomics.com/lp-game-theory2-battle-of-the-sexes/> 7

<http://www.policonomics.com/lp-game-theory2-mixed-strategy/> 8

Given the payoff matrix above, the expected utility of the woman going to watch boxing is q and that of going shopping is 2*(1-q). Similarly, the expected utility of the man watching boxing and going shopping are 2r and (1-r) respectively.

Therefore UBW=USW

1*q=2*(1-q) Therefore for the woman, q=2/3 Using the same method, r=1/3

Therefore from the woman’s perspective, she needs to think very carefully about the actual value of r. If r=1/3, the woman can go to either activity. If r<1/3, the woman needs to go to shopping because the man will receive less utility from watching boxing match(therefore the man will go shopping). However, if r>1/3, the woman should go to the boxing match because her partner will actually receive more utility from watching boxing match therefore he would do so. As a conclusion, she should carefully think about the probability of her husband going to either of these two events before she makes her decision.

How can this model be applied to the defense strategy against the Warriors? In a simplified case scenario, we assume the probability for the Warriors shooting a 3 in clutch time is p. There is 0.416*p*3=0.528*(1-p)*2 p=0.4583

Therefore if the probability of Golden State Warriors shooting a 3-point is greater than 45.8%, their opponents should always defend a 3-point. In fact, official statistics demonstrates that the probability of Warriors shooting a 3-point during clutch time is 46.7% 9

therefore their opponents should defend 3-point shots during clutch time.

However, if the two teams playing against each other in a playoff series, they would have no secrets to their opponent therefore the Warriors knows that their enemy will always defend a 3-point shot in clutch time therefore Warriors will have to make their strategy more complex to confuse their opponents. In this case, the defending team can only make the decision based on Warriors’ performance in that game to decide whether they should guard a 3-point shot or a 2-pointer. Otherwise, if they have a player who has long wingspan, the coach can also set up the intensity of defense according to the probability of Warriors shooting 3.

To conclude, if we do not take other conditions into consideration, the opponents of Golden State Warriors should always defend 3-point shots during clutch time.

<http://stats.nba.com/league/team/#!/clutch/scoring/>9

(2) Chicken game Introduction In chicken game, two men with something to prove drive at each other on a narrow road. The first to swerve loses faces against the other. If both of them swerve, they will both be ‘chicken’ so it is a draw for them. If neither swerves, however, a terminal fate plagues both . 10

In this game, there are four possible outcomes, which are both swerve, both go straight, one go straight and the other swerve.

The payoff matrix of a chicken game is shown as below:

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The game of chicken does not have a dominant strategy for either player. However, it has two equilibria using pure strategies, which are (Red, Blue) = (Swerve, Go straight) and (Red, Blue) = (Go straight, Swerve). Suppose that Red knows Blue is to go straight before the game, Red will definitely swerve because -1 is better than -5(which means being chicken is better than death). On the contrary, if Red knows that Blue will swerve, he should go straight because that will make him feel proud for being a winner and therefore he can show off to his friends. Obviously, Red will prefer the first equilibrium and Blue will prefer the latter.

In addition, a mixed-strategy Nash equilibrium also exists in the chicken game. Suppose the possibility of Blue going straight is p and the possibility of Red going straight is q, therefore the probability to swerve for Blue and Red are (1-p) and (1-q) respectively.

Therefore for Blue, (1-5)*p=-1*(1-p) p=1/5 1-p=4/5

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Therefore the possibility of Blue opting to go straight is 1/5, and the possibility of Blue opting to swerve is 4/5.

We apply the same method of calculation to Red, q=1/5, 1-q=4/5 Therefore both players are likely to choose to ‘chicken swerve’ at last.

How can this model be applied to the defense strategy against the Warriors? Recently, an online article called ‘Stephen Curry has become so good that the NBA might begin using one of the most radical strategies to stop him’ caught my attention. The article proposed a new method to defend Curry called ‘Hack A Curry’, which means ‘defenders could intentionally foul Curry, put him on the free-throw line, and get the possession back’ . 12

This strategy aims to ‘stopping the flow of the Warriors offense and taking Curry out of a rhythm’. In theory, this could work as the Warriors cannot find the flow in the game. We can also learn some lessons from Game 6 (Warriors against Cavaliers) in the NBA finals this year to find another way to make the Warriors feel uncomfortable. In that game, Curry was suffering from fouling problem (although some of these fouls are very controversial). He was fouled out in the 4th quarter and eventually Warriors lost the game 101-115 . Apparently, the 13

Warriors plays less aggressively without Stephen Curry therefore it gave me the inspiration: Why not just let players draw fouls on Stephen Curry? Or we can intentionally foul on Stephen Curry to break Warriors’ offense rhythm. Therefore to maintain the offense rhythm, Steve Kerr will have to put Curry on the bench.

If opponents want Curry to be ‘fouled out’, they have to constantly finish their offense by the player who is guarded by Stephen Curry. An implication of this strategy is that Stephen Curry either will be sent off by Steve Kerr or suffering from foul trouble, which obviously will weaken his performance. However, the opponents should also be aware that Curry is also an ingenious defender who can draw 4.5 fouls per game on opponents and the Warriors may 14

retaliate by doing the same, so that is the potential risk of drawing fouls on Curry, which could drag themselves into foul trouble simultaneously. In the other case, comparing with intentionally fouling on Stephen Curry, in fact opponents will be better off if they foul on Andrew Bogut, the main rim protector in Warriors from Australia with career free throw percentage of 55.8% . During the free throw, the technique will stop the clock so the 15

opponents will have an opportunity to get the possession back and break the rhythm of Warriors’ offense. Therefore they can have a chance to defeat Warriors.

<http://uk.businessinsider.com/stephen-curry-so-good-getting-intentionally-fouled-2015-11?r=US&IR=T> 12

<http://www.nba.com/2016/news/06/17/nba-finals-warriors-curry-ejected.ap/> 13

<http://stats.nba.com/player/#!/201939/stats/misc/>14

<http://stats.nba.com/player/#!/101106/career/> 15

Foul on Andrew Bogut: P=0.558*2=1.116 Foul on Stephen Curry: P=0.908*2=1.816 Therefore players would rather foul on Bogut as the payoff demonstrates.

On the other hand, it seems irrational to foul on Bogut or Curry because according to the stats, the Warriors can only score 0.993 point per possession , which is lower than the points 16

lost by fouling on them. That also explains why teams do not intentionally foul on Bogut very often in NBA.

Additionally, the NBA changed the rules for ‘Hack-A-Shaq’ strategy after coaches frequently used it during clutch time because the league thinks it disobeys the sportsmanship and makes the games during clutch time less spectacular. The new rule states that the fouled team is awarded one free throw and retains possession of the ball, this rule will be extended to the last two minutes of each period . Therefore the constraint is, according to my definition, the 17

opponent can only use this strategy for 3 minutes in the last quarter, because it will not be beneficial for them in the last two minutes. Therefore this method will be effective, but only in a limited amount of time.

The disadvantage of using this strategy is that both team will lose their rhythm therefore in most of the games that this strategy was used, both team were worse off. As a conclusion, the attacking team can still finish their offense on Curry as defense is not his strength and that will cause him a lot of fouls. Therefore he should be constrained by being less aggressive to keep himself in the game.

(3) Game of Goldenballs Golden Balls is a British daytime game show presented by Jasper Carrott. It aired on the ITV network from 18 June 2007 to 18 December 2009 .There are four rounds in each 18

episode, in the final round two players will play a game ‘split or steal’. Basically, two contestants both have to choose one of the two goldenballs with ‘split’ written inside and the word ‘steal’ written inside.

If both contestants choose to split, the jackpot is split equally between them.

If one contestant chooses to split and the other chooses to steal, the Stealer gets all the money and the Splitter gets nothing.

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<https://en.wikipedia.org/wiki/Golden_Balls>18

If both contestants choose to steal, they both get nothing . 19

Thus the payoff matrix can be produced using the information above.

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This is very similar to the Prisoner’s Dilemma. Nonetheless, a key difference is that, in the standard Prisoner’s Dilemma, if one player chooses to defect (or steal), the other player is better off defecting instead of cooperating (splitting). However, in Golden Balls, as long as one player chooses to steal, neither player has a better strategy. That is to say, all three strategies that involve stealing are Nash equilibria and (Split, Split) is an unstable strategy . 21

In one episode, Nick and Ibrahim were playing split or steal for 13600 pounds. In the previous episodes, most games end up in one or both contestants defecting. However, in this episode, Nick used a very different strategy from other split-or-steal players. Instead of promising to choose split, he told Ibrahim directly that he was going to steal, and if he wins, he will split the money with Ibrahim after the show. Therefore a payoff matrix could be made using this information.

<http://blogs.cornell.edu/info2040/2012/09/21/split-or-steal-an-analysis-using-game-theory/> 19

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<http://blogs.cornell.edu/info2040/2012/09/21/split-or-steal-an-analysis-using-game-theory/ >21

!

By establishing a credible threat to steal, Nick puts all the pressure on Ibraham to decide only one of two things:

1. Does Ibraham trust that Nick will split the money with him after he has stolen the full jackpot, and

2. Would Ibraham rather both of them go home without any money at all than Nick win the jackpot and possibly not split it with him later on? 22

How can this model be applied to defense strategy against the Warriors?

The team playing against Golden State Warriors can try to pressure defense on four players but give up the other one. In the case of 2015-16 NBA finals, in the last three games against Cavaliers, Harrison Barnes (The starting Small Forward) only made 5 shots out of 32 attempts. Especially in Game 6, he missed all 8 shots, including some easy, open shots. Barnes missed a lot of chances in Game 6 and that resulted in the loss against the Cavaliers. In that game, Cavaliers players knew that he is an unstable shooter so they just gave him easy shots outside the 3-point line but Barnes let his teammates down. This match provides a very good example to beat the Warriors, which is to give up a player (who is the least likely to make the clutch shot) and press up on threats such as Stephen Curry and Klay Thompson to minimise the probability of the Warriors making the clutch shot. In other words, they would not give Warriors the chance to kill them with Curry and Thompson. This is similar to Nick and Ibrahim’s Goldenball game because these two scenarios both force the other player to make a choice. In this case, Cavaliers will put tight defense against Stephen Curry and Klay Thompson, which means they force Warriors to give the ball to the player who is not as reliable as other shooters.

Super defense strategy against the Warriors during clutch time:

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behavior/>

Therefore a strategy combining all the individual method above could be derived. Firstly, the defending team should defend a 3-point shot during clutch time. Otherwise, they could also put equally intensive defense on both 2-point shots and 3-point shots if they have a super defender on their team therefore this can lower Warriors’ shooting percentage significantly. Secondly, the defending team could use ‘Hack-A-Curry’ or ‘Hack-A-Bogut’ to force Steve Kerr to switch one of them off. The alternative of this strategy is that they can constantly finish their offense by the person guarded by Stephen Curry therefore they can cause Curry foul trouble. If he does fall in foul problems, he will have to be careful on every movement he makes in both offensive and defensive ends. Thirdly, the defending team can leave one player wide open. This strategy can be very effective when one of the Warriors is struggling to make shots. Therefore they can focus their defense on big threats on the court— especially Curry and Thompson.

What happens in real game examples?

In total, Golden State Warriors only had 9 losses out of 82 games in regular season (which broke the record set by Michael Jordan’s Chicago Bulls in 1996. However, from the game analysis, they are not unstoppable in fact. In 2015-16 season, they lost 5 games during clutch time against Denver Nuggets, San Antonio Spurs, Detroit Pistons, Boston Celtics, Minnesota Timberwolves respectively. In this section, I will review the games and reasons why they could defeat Golden State Warriors. And finally, I also will focus on how Thunders cornered Warriors in Western Conference Final and how Cavaliers defeat them in the finals in particular.

(1) Denver Nuggets On 13th January, the Nuggets played against Warriors in their home court. There are some obvious reasons why they can defeat Warriors over clutch time. Firstly, they can answer the shots made by Warriors therefore they can keep the leading and secure it to the end of the game. The second reason is the attitude of the Warriors, ‘I thought we gave a tremendous effort in the fourth quarter -- well, in the last half of the fourth quarter.’ said Luke Walton, the coach of Warriors, ‘But for a championship team and what we're trying to accomplish, in my opinion we didn't play hard enough and we didn't play smart enough for a majority of that game.’ The fourth reason could be the scheduled rest of their Power Forward—23

Draymond Green, therefore Warriors lost a strong rim protector and threatening basket attacker. In addition, Curry was off for almost the whole game, and he admitted he was a bit distracted during critical plays. Nonetheless, he still scored 20 points in the 4th quarter even though the Nuggets was trying their best to defend him.

However, as a conclusion, there is some kind of pattern in Warriors’ clutch plays. Although they have a lot of excellent shooters, the key plays are usually finished by either Stephen Curry or Klay Thompson. Therefore it suggests that a team is more likely to win over

<http://www.dailymail.co.uk/wires/afp/article-3398786/Nuggets-hand-Warriors-defeat-NBA-season.html>23

clutch time if they can defend Curry and Thompson successfully. And this was exactly what the Nuggets did during the clutch time. For this particular game, even though Nuggets is not as competitive as Warriors, they understood how to use their physical strength to force Warriors to make difficult shots as well as to consume Stephen Curry and Klay Thompson when they are moving without ball.

(2) San Antonio Spurs On 19th March, the Spurs defeated Warriors 87-79. It is worth mentioning that 79 is the lowest score for Warriors throughout the regular season. How did Spurs defeat them? First of all, Curry was continually harassed by Green, who blocked two shots while holding the MVP front-runner to 4-for-18 shooting. The Spurs held Curry 14 points with 1-12 in 3 points . They knew that Warriors are very good at fast-speed transition therefore Spurs’ 24

coach replaced Tim Duncan with Boris Diaw as the starting centre in order to slow them down. Secondly, giving pressure to Curry is necessary. The Spurs kept intense defense in clutch time and Warriors did not score in the last two minutes, which directly led to the defeat. Thirdly, the Spurs have the characteristics to counter Warriors. For instance, Leonard is the consecutive Best Defensive Player of the year and he can easily defend almost every position, Danny Green is energetic and aggressive, so he can defend either Curry or Thompson, Tim Duncan is a strong rim protector near the basket. All their players and team defense can make Warriors very uncomfortable therefore it is very difficult for Warriors to implement their classic playing strategy.

(3) Detroit Pistons In this game, although the score was not close during clutch time, it is very impressive that Pistons, a middle-range team can defeat the top team in the league by 113-95. Stephen Curry dropped 38 points on them and Klay Thompson also had 24 points, which should have been a win for Warriors with that amazing performance. So what was wrong with Warriors in that game? Firstly, the Warriors grabbed 10 rebounds less than Pistons, which means more field goal attempts for the Pistons; and it is obviously true: during that game, the Pistons had 101 field goal attempts while the Warriors had merely 94 attempt . 25

Moreover, greater control over rebounds also means less chance for the Warriors to play their favourite transition attack. However, only controlling the rebound is not enough. The key of winning is the Pistons’ attitude on defense on Stephen Curry. Essentially most of the teams treat Stephen Curry outside the 3-point line as if any open shot will be the end of the world. But Pistons decided to treat him just as a normal player, allow him to have more open looks than he usually does, but keeping their defensive integrity everywhere else. In other words, they focus on defending other players and give more free shots to Stephen Curry and Klay Thompson. And this strategy turned out to be successful. Although Steph and Klay scored 62 points altogether, other players contributed only 33 points to the game (Green only dropped 5 points in the game). 26

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This method seems easy and feasible. So why would not everyone else do it? The reason is that the Pistons has unique characteristics. The first is the shooting guard, Pope. He is fast and long therefore Curry can only have a little space to shoot therefore Pope is the perfect person to guard Curry. In addition, the Pistons also has Andre Drummond playing as the centre to give support in rebound to reduce Warriors’ chance of transition.

(4) Boston Celtics On 1st April, Boston Celtics visited Golden State and ended Warriors’ historical 54 home winning streak. Nobody expected Celtics to win the game as they lost their small forward—Jae Crowder. In NBA, Celtics is famous for their indomitable defense. However, their strategy is totally opposite from what Pistons did. The Celtics threw a lot of different looks at league MVP Stephen Curry — including moments with Evan Turner on him, double teams, and, at one memorable moment, having the entire team defend him. Celtics was able to stay 27

in the game because Avery Bradley (the guard in Celtics) is a great defender and harried Curry for much of the first half. Another reason is that, although the Warriors’ offense is one of the most beautiful things in sports, but there is a way to disrupt it — you turn the game ugly. The Celtics did that. They hung guys up on screens, dove after loose balls, banged bodies in the post. The Celtics teaches other teams a crucial lesson—pressure the Warriors on defense!!

(5) Minnesota Timberwolves On the way of chasing record for Golden State Warriors, nobody expected that they received the ninth loss of the season playing against Minnesota Timberwolves. Although Timberwolves won the game with the help of their sharp offence, a very clever strategy could be derived from that game. To counter Warriors’ small lineup, the best thing their opponent can do is to play in a faster, more defensive small lineup. That lineup outscored the Warriors by 12 points in the heat of the fourth quarter and in overtime, utilizing quickness and an attacking mentality. They also provided a good case for Thunders to learn, who almost defeated Warriors in the Western Conference Final.

How did Thunders corner Warriors in the Western Conference Final?

First of all, it is necessary to introduce the rules of NBA playoff games. The NBA playoffs are a best-of-seven elimination tournament among 16 teams in the Eastern Conference and Western Conference, ultimately deciding the winner of the NBA Finals. In 2016 Western Final, Thunders was leading Warriors 3-1, then Warriors made a huge comeback in the last three games and defeated Thunders 4-3, defended Western Champion.

The point is: how did Thunders corner Warriors in the series? Clearly Thunders needed the right personnel to win when they go small, actually, Thunders went with a very similar lineup to the Timberwolves’. The Thunder’s rout of the Warriors in Game 3 could be attributed to the Thunder using a five-man group that featured Serge Ibaka as the only power forward/

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center on the floor. The effect of the smaller lineup gave Golden State matchup problems. Warriors big man Andrew Bogut only played 11 minutes in Game 3 and had the same total in Game 4 Tuesday — when again the Thunder used a small lineup to dismantle Golden State. Even though Thunder went with small, they crushed Warriors on rebound. In their three wins over Warriors, they controlled rebound successfully with 62-55, 62-48 and 68-49. On pure defense 28

strategy, Thunders need to let Westbrook guard Curry. One of the Warriors favourite plays is Curry/Draymond Green pick-and-roll. The bulk of the scoring though comes from situations in which Westbrook switches off of Curry on the pick. When Westbrook switches to Green, the Warriors are scoring 1.2 points per chance . The switch is setting up a mismatch on 29

Curry that makes it easier for him to get either a high quality shot, or find his open teammate. When Westbrook goes over the pick, however, and stays with Curry, the situation changes significantly. Now the Warriors are scoring only 0.4 points per chance. Another is to make sure that Adams and Serge Ibaka are in the game. When the two of them are on the floor, the Thunder defense is the best in the league at protecting the paint, with a qSI in the paint of minus-4.1. To give that some context, the Warriors would be second in the league with a qSI of minus-2.8. Without those two on the floor, however, the Thunder struggle to defend the paint, allowing shooters a qSI of plus-1.2 -- which would be the worst in the league. Last but not least, the Thunders maximised their advantage, which is their physical 30

strength. "We've got a physical team, an athletic team and we tried to use that to the best of our ability ," Westbrook said. "Our guys do a great job of putting in the work every day. My 31

job is to put the ball in their hands." The Thunders used their great physical strength to play a fierce defense against Warriors, which caused the Warriors a lot of trouble in the first four games.

How did Cavaliers defeat Warriors in the Finals?

In the 2016 NBA Finals, the Cavaliers defeated Warriors. They had 1-3 deficit from the first four games and yet they still managed to came back to win the last three games. They defeated the Warriors 4-3. The Cavaliers also became the first team in franchise history to come back from a 1-3 deficit.

Some commentators pointed out that if Cavaliers wanted to defeat Warriors, they would have to win on the boards (this means rebounding well). The Cavs do have some advantages when it comes to matching up on the boards, as Tristan Thompson possesses the mobility to stay with Green, while also having a considerable height advantage over him. While most centers can't hang with Green, Thompson has the mobility and length to allow the Cavs to play small without being small at times. In addition, especially when the Warriors go small, the Cavaliers will have more advantage on rebounds and defense in the paint. Moreover, the Cavs has some excellent defenders. Apart from LeBron James, who can defend almost every position on the

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warriors>

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warriors>

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court, they also have Shumpert and Dellavedova to defend Curry and Klay Thompson. It is worth mentioning that Dellavedova was shadowing Curry everywhere he went on the court, which made Curry extremely uncomfortable on the court.

Despite that players have advantage guarding in the matchup, their team defense strategy also worked, which was giving Harris Barnes wide open 3-point shots because he was a relatively unstable shooter in the Warriors.

In addition, one important factor determined their win against the Warriors is their defense attitude. We can see that they tried their best to not to give Stephen Curry open shots. He averaged 22.6 points in the final, and he only had two 30+ games . The average point was 32

his lowest in the entire 2016 playoff.

Common themes of defending Warriors in real games: In summary, teams that defeated the Golden State Warriors in the 2015/16 season either had strong team defense tradition or ‘super’ individual defenders who could defend a large area on the court. In addition, those teams had strong control over the rebound area of the game which prevented the Warriors from playing their fast break. In addition, the teams also had to be incredibly disciplined in order to able to able to play a suffocating defensive game for the entire length of the game.

Comparison to super defense strategy At this stage, it is useful to consider whether teams employed a defensive strategy against the Warriors that in any way represented the ‘super defense strategy’ proposed earlier in the project.

Firstly, there is plenty of evidence that several coaches (across teams in the NBA) attempted to defend the Warriors by prioritizing the defense of 3-point shots in clutch time. For example, the Detroit Pistons and the San Antonio Spurs both used this strategy combined with and strong rim protectors (i.e. good rebounders). This led to the Warriors missing a higher percentage of 3-point shots than normal and did not allow them to follow-up a score a rebound. In one particular game against the Spurs, the Warriors only had 79 points (season low) and Curry only made one 3-point shot out of 11 attempts.

Secondly, in the 2015/16 final, the Cavaliers gave Harris Barnes a lot of open shots. In the last three games in that series, however, Harris Barnes only managed to make 5 shots out of a possible 32 attempts. This shows that my strategy works!!

Finally, there was no evidence that (across the 82 games) any teams tried to foul out Steph Curry of the Warriors.

In conclusion, the super defense strategy was indeed used by coaches in real games to some extent, therefore it is applicable and feasible.

<http://www.espn.com/nba/player/gamelog/_/id/3975/year/2016/stephen-curry>32

Update and prospect of 2016/17 season

This summer, Kevin Durant signed a two- year contract with Golden State Warriors. This just made it more difficult for other teams to defend the Warriors as they now have one more elite shooter in the NBA therefore opponent teams will have stretch their defense wider and thus Warriors also have more chance to score in the paint. During clutch time, opponents will now struggle even more to decide who to guard because Warriors now have a number of threatening shooters. Therefore it will be less realistic to win over Warriors by merely strong defense. Their opponents will have to be strong offensively as well as defensively in order to defeat the Warriors.

The Warriors also traded Harris Barnes and Andrew Bogut in order to chase Durant. This is unsurprising, given that both Barnes and Bogut were identified as the weak links in the teams – and were targeted as such by opposition teams. The only disadvantage, however, is that the Warriors now lack a strong rim protector, which is something that can be taken advantage of by other teams to attack them. 33

How to defeat Golden State Warriors in the next season?

According to the super defense strategy, it is possible to win over Warriors during clutch time. The addition of Durant, however, makes it that much harder. Although teams can beat them on the basis of defense, they should improve their offense performance to counter Warriors in both ends. Basketball is a team sport and it needs a proper balance between offense and defense. Therefore technically strong offense and good defense are necessary to win Warriors. The most successful example last year was the Cleveland Cavaliers. They had suffocating defense, the best offensive basketball player in the world in LeBron James and a never-give-up attitude, which all made them worth the NBA champion title . Therefore a 34

team should improve their performance on both defense and offense to be ready to defeat the Golden State Warriors.

Reference: [1] Warriors lose first time this season in 108-95 defeat to Bucks, record now stands at 24-1, NY Daily News, <http://www.nydailynews.com/sports/basketball/warriors-24-game-win-streak-ends-loss-bucks-article-1.2464246> [2] Ric Bucher, ‘Is Stephen Curry the Best Shooter Ever? Yes, Say Many of NBA's All-Time Marksmen’, Bleacher Report, <http://bleacherreport.com/articles/2482473-is-stephen-curry-the-best-shooter-ever-yes-say-many-of-nbas-

<http://bleacherreport.com/articles/2676925-kevin-durant-has-been-everything-the-golden-state-warriors-hoped-for>33

<http://www.sbnation.com/nba/2016/6/6/11866130/nba-finals-warriors-vs-cavaliers-not-over-yet>34

all-time-marksmen> [3] Krishna Narsu, ‘Does Defense Actually Get Tighter in the Clutch? <http://nyloncalculus.com/2014/11/17/defense-actually-get-tighter-clutch/> [4] ‘Kevin Garnett compares Stephen Curry to Michael Jordan’, Fox Sport <http://www.foxsports.com/nba/story/michael-jordan-golden-state-warriors-stephen-curry-kevin-garnett-compares-to-his-own-thing-111215> [5] NBA stats, <http://stats.nba.com/team/#!/1610612744/stats/shooting/> [6] NBA stats, <http://stats.nba.com/team/#!/1610612744/stats/shooting/> [7] Game Theory II: Battle of sexes, Policonomics <http://www.policonomics.com/lp-game-theory2-battle-of-the-sexes/> [8] Game theory II: Mixed strategies, Policonomics <http://www.policonomics.com/lp-game-theory2-mixed-strategy/> [9] NBA stats, <http://stats.nba.com/league/team/#!/clutch/scoring/> [10] Game Theory.net, <http://www.gametheory.net/dictionary/Games/GameofChicken.html> [11] Politics and “chicken”, Boundless Rationality <https://boundlessrationality.wordpress.com/2011/05/24/politics-and-chicken/> [12] Scott Davis, ‘Stephen Curry has become so good that the NBA might begin using one of the most radical strategies to stop him’, Business Insider, <http://uk.businessinsider.com/stephen-curry-so-good-getting-intentionally-fouled-2015-11?r=US&IR=T> [13] Tim Reynolds, ‘Curry gets ejected late in Warriors' Game 6 loss’, NBA.com <http://www.nba.com/2016/news/06/17/nba-finals-warriors-curry-ejected.ap/> [14] NBA stats, <http://stats.nba.com/player/#!/201939/stats/misc/> [15] NBA stats, <http://stats.nba.com/player/#!/101106/career/> [16] NBA stats, <http://stats.nba.com/teams/traditional/#!?sort=PTS&dir=-1&Season=2015-16&SeasonType=Regular%20Season&PerMode=PerPlay&Period=4&TeamID=1610612744> [17] Todd Dybas, ‘NBA institutes ‘Hack-a-Shaq’ intentional foul rule changes’, Washington Times <http://www.washingtontimes.com/news/2016/jul/13/nba-institutes-hack-a-shaq-intentional-foul-rule-c/> [18] Golden Balls, Wikipedia <https://en.wikipedia.org/wiki/Golden_Balls> [19] Shane, ‘Split or Steal: An Analysis Using Game Theory’, Cornell University <http://blogs.cornell.edu/info2040/2012/09/21/split-or-steal-an-analysis-using-game-theory/> [20] The Society Pages, <https://thesocietypages.org/socimages/files/2012/04/114.jpg> [21] Shane, ‘Split or Steal: An Analysis Using Game Theory’, Cornell University < http://blogs.cornell.edu/info2040/2012/09/21/split-or-steal-an-analysis-using-game-theory/> [22] Jason Welker, ‘UPDATE: Golden Balls, Game Theory, the Prisoner’s Dilemma, and the cold rationality of human behavior!’, Welker’s Wikinomics, <http://welkerswikinomics.com/blog/2012/04/20/golden-balls-game-theory-the-prisoners-dilemma-and-the-cold-rationality-of-human-behavior/> [23] AFP, ‘Nuggets hand Warriors third defeat of NBA season’, Daily mail, <http://www.dailymail.co.uk/wires/afp/article-3398786/Nuggets-hand-Warriors-defeat-NBA-season.html>

[24] ‘Spurs beat Warriors in showdown, stay perfect at home’, Sports Illustrated, <http://www.si.com/nba/game/1570894> [25] NBA stats, <http:/ /stats.nba.com/team/#!/1610612744/stats/?Season=2015-16&SeasonType=Regular%20Season&OpponentTeamID=1610612765> [26] Joetruck229, How the Pistons demolished Warriors <https://www.reddit.com/r/nba/comments/41qzro/oc_how_the_pistons_demolished_the_warriors/> [27] Nate Scott, ‘9 reasons the Celtics snapped Golden State’s 54-game home win streak’, For the win, USA today sports, <http://ftw.usatoday.com/2016/04/celtics-warriors-highlights-keys-boston-golden-state> [28] Michael Rand, ‘Did the Timberwolves give Thunder the blueprint to beat Golden State?’, Startribune <http://www.startribune.com/did-the-timberwolves-give-thunder-the-blueprint-to-beat-warriors/380835491/?refresh=true> [29] ‘Small group big win for the Oklahoma city thunder’, ESPN <http://www.espn.co.uk/nba/playoffs/2016/story/_/id/15546959/nba-playoffs-2016-how-oklahoma-city-thunder-beat-golden-state-warriors> [30] ‘Small group big win for the Oklahoma city thunder’, ESPN <http://www.espn.co.uk/nba/playoffs/2016/story/_/id/15546959/nba-playoffs-2016-how-oklahoma-city-thunder-beat-golden-state-warriors> [31] Agence France-Presse,‘Golden State face uphill task as Oklahoma City take 2-1 Western Conference finals lead’, The National Sport,

<http://www.thenational.ae/sport/nba/golden-state-face-uphill-task-as-oklahoma-city-take-2-1-western-conference-finals-lead> [32] ESPN, <http://www.espn.com/nba/player/gamelog/_/id/3975/year/2016/stephen-curry> [33] Michael Pina, ‘Kevin Durant Has Been Everything the Golden State Warriors Hoped For’, Bleacher Report, <http://bleacherreport.com/articles/2676925-kevin-durant-has-been-everything-the-golden-state-warriors-hoped-for> [34] Tom Ziller, ‘5 reasons the NBA Finals aren't over yet’, SBNation <http://www.sbnation.com/nba/2016/6/6/11866130/nba-finals-warriors-vs-cavaliers-not-over-yet>

Bibliography: [1]Warriors lose first time this season in 108-95 defeat to Bucks, record now stands at 24-1, NY Daily News, 1st December <http://www.nydailynews.com/sports/basketball/warriors-24-game-win-streak-ends-loss-bucks-article-1.2464246 [2] Ric Bucher, ‘Is Stephen Curry the Best Shooter Ever? Yes, Say Many of NBA's All-Time Marksmen’, Bleacher Report, 2nd December, <http://bleacherreport.com/articles/2482473-is-stephen-curry-the-best-shooter-ever-yes-say-many-of-nbas-all-time-marksmen> [3] Krishna Narsu, ‘Does Defense Actually Get Tighter in the Clutch?’, 10th September, <http://nyloncalculus.com/2014/11/17/defense-actually-get-tighter-clutch/> [4] ‘Kevin Garnett compares Stephen Curry to Michael Jordan’, Fox Sport, 7th July, <http://www.foxsports.com/nba/story/michael-jordan-golden-state-warriors-stephen-curry-kevin-garnett-compares-to-his-own-thing-111215> [5] NBA stats, <http://stats.nba.com/team/#!/1610612744/stats/shooting/> [6]Game Theory II: Battle of sexes, Policonomics <http://www.policonomics.com/lp-game-theory2-battle-of-the-sexes/> [7] Game theory II: Mixed strategies, Policonomics <http://www.policonomics.com/lp-game-theory2-mixed-strategy/> [8] William Spaniel, ‘Game Theory 101: Battle of the Sexes’, YouTube, 12th August <https://www.youtube.com/watch?v=VjkShMpDzLc> [9]William Spaniel, ‘Game Theory 101: Calculating Payoffs in Mixed Strategy Nash Equilibria’ , YouTube, 12th August, <https://www.youtube.com/watch?v=08JlYCgckDQ> [10]NBA stats, <http://stats.nba.com/league/team/#!/clutch/scoring/> [11]Game Theory.net, <http://www.gametheory.net/dictionary/Games/GameofChicken.html> [12] Politics and “chicken”, Boundless Rarionality <https://boundlessrationality.wordpress.com/2011/05/24/politics-and-chicken/> [13]Scott Davis, ‘Stephen Curry has become so good that the NBA might begin using one of the most radical strategies to stop him’, Business Insider, <http://uk.businessinsider.com/stephen-curry-so-good-getting-intentionally-fouled-2015-11?r=US&IR=T> [14]Tim Reynolds, ‘Curry gets ejected late in Warriors' Game 6 loss’, NBA.com <http://www.nba.com/2016/news/06/17/nba-finals-warriors-curry-ejected.ap/> [15] NBA stats, <http://stats.nba.com/player/#!/201939/stats/misc/> [16]NBA stats, < http://stats.nba.com/player/#!/101106/career/> [17] Todd Dybas, ‘NBA institutes ‘Hack-a-Shaq’ intentional foul rule changes’, Washington Times <http://www.washingtontimes.com/news/2016/jul/13/nba-institutes-hack-a-shaq-intentional-foul-rule-c/ [18] Golden Balls, Wikipedia <https://en.wikipedia.org/wiki/Golden_Balls> [19] Shane, ‘Split or Steal: An Analysis Using Game Theory’, Cornell University <http://blogs.cornell.edu/info2040/2012/09/21/split-or-steal-an-analysis-using-game-theory/> [20] The Society Pages, <https://thesocietypages.org/socimages/files/2012/04/114.jpg> [21] Shane, ‘Split or Steal: An Analysis Using Game Theory’, Cornell University < http://blogs.cornell.edu/info2040/2012/09/21/split-or-steal-an-analysis-using-game-theory/> [22] Jason Welker, ‘UPDATE: Golden Balls, Game Theory, the Prisoner’s Dilemma, and the cold rationality of human behavior!’, Welker’s Wikinomics, <http://welkerswikinomics.com/blog/2012/04/20/golden-balls-game-theory-the-prisoners-dilemma-and-the-cold-rationality-of-human-behavior/>

[23] AFP, ‘Nuggets hand Warriors third defeat of NBA season’, Daily mail, <http://www.dailymail.co.uk/wires/afp/article-3398786/Nuggets-hand-Warriors-defeat-NBA-season.html>

[24] ‘Spurs beat Warriors in showdown, stay perfect at home’, Sports Illustrated, 20th November, <http://www.si.com/nba/game/1570894> [25] NBA stats, <http:/ /stats.nba.com/team/#!/1610612744/stats/?Season=2015-16&SeasonType=Regular%20Season&OpponentTeamID=1610612765> [26] Joetruck229, How the Pistons demolished Warriors <https://www.reddit.com/r/nba/comments/41qzro/oc_how_the_pistons_demolished_the_warriors/> [27] ‘Harrison Barnes is ruining the Warriors’ best lineup’, SBNation, <http://www.sbnation.com/2016/6/18/11965612/harrison-barnes-statistics-bad-warriors-nba-finals-2016 [28] Nate Scott, ‘9 reasons the Celtics snapped Golden State’s 54-game home win streak’, For the win, USA today sports, <http://ftw.usatoday.com/2016/04/celtics-warriors-highlights-keys-boston-golden-state> [29] Michael Rand, ‘Did the Timberwolves give Thunder the blueprint to beat Golden State?’, Startribune <http://www.startribune.com/did-the-timberwolves-give-thunder-the-blueprint-to-beat-warriors/380835491/?refresh=true> [30] ‘Small group big win for the Oklahoma city thunder’, ESPN <http://www.espn.com/blog/statsinfo/post/_/id/118801/small-group-big-win-for-the-oklahoma-city-thunder> [31]ESPN, <http://www.espn.co.uk> [32] Sharon Katz and Ben Alamar, ‘Thunder have pieces to exploit Warriors' few weaknesses’, ESPN <http://www.espn.co.uk/nba/playoffs/2016/story/_/id/15546959/nba-playoffs-2016-how-oklahoma-city-thunder-beat-golden-state-warriors> [33] Justin Rowan, ‘NBA Finals: a guide for how the Cavaliers can beat the Warriors’, SBNation <http://www.fearthesword.com/2016/5/31/11818838/nba-finals-a-guide-for-how-the-cavaliers-can-beat-the-warriors> [34] ESPN, <http://www.espn.com/nba/player/gamelog/_/id/3975/year/2016/stephen-curry> [35] Michael Pina, ‘Kevin Durant Has Been Everything the Golden State Warriors Hoped For’, Bleacher Report, 15th December, <http://bleacherreport.com/articles/2676925-kevin-durant-has-been-everything-the-golden-state-warriors-hoped-for> [36] Tom Ziller, ‘5 reasons the NBA Finals aren't over yet’, SBNation, 11th December <http://www.sbnation.com/nba/2016/6/6/11866130/nba-finals-warriors-vs-cavaliers-not-over-yet>

[37] Robert O’Connel, ‘Why the NBA Loves—and Fears—Stephen Curry’, The Atlantic <http://www.theatlantic.com/entertainment/archive/2016/02/stephen-curry-nba/461901/> (accessed 12 December 2016)

[38] Satchel Price, ‘NBA scores 2016: Nuggets hand Warriors their third loss of the season’, SBNation, <http://www.sbnation.com/nba/2016/1/14/10765016/2016-nba-scores-nuggets-warriors-stephen-curry-salah-mejri> (accessed 8 December 2016)

[39] Scott Rafferty, ‘The 6 steps to defending and maybe stopping Stephen Curry and the Warriors’, Sporting News, <http://www.sportingnews.com/nba/news/stephen-curry-warriors-klay-thompson-defense-draymond-green-pick-and-roll/myn7ny0fn1e71sis8b7l0guqd> (accessed 5 April 2016)

[40] Simon Cherin-Gordon, ‘Golden State Warriors’ Winning Style Is Completely Unique’, Bleacher Report, <http://bleacherreport.com/articles/1872370-golden-state-warriors-winning-style-is-completely-unique> (accessed 12 January 2016) the [41] Benjamin Morris, ‘Stephen Curry Is the Revolution’, FiveThirtyEight, <http://fivethirtyeight.com/features/stephen-curry-is-the-revolution/> (accessed 23 February 2016 )