After Felipe Reyes hit a pair of free throws with 1.11 left on the clock in the Copa del Rey final in Malaga yesterday evening it seemed like Real had the game sewn up with a 75-68 lead. But an 8-0 Barcelona run over the next minute put Real behind and set up Sergio Llull’s game winning long two  from the right corner.

Real’s defence had been superb over the weekend, but it was a number of key lapses in the final minute that almost cost them the game, with their normally air tight help defence being found wanting by Barcelona, before Barcelona’s own defensive mistakes allowed Llull to get open in the final seconds.

Play Number One: Llull gets Lost (Three Times), and Oleson Drains a Three

The logical first play to look at is Brad Oleson’s three, coming after Joey Dorsey pulled down a huge offensive rebound. On the play leading up to this we saw a Marcelinho Huertas layup knocked out of the rim by Rudy Fernandez. It seemed as if Barca were shaping to send Huertas left around a Dorsey screen, potentially setting up another of his floaters. But as Dorsey came to set the screen both Sergio Llull and Felipe Reyes were found out of position, allowing Huertas to drive right uncontested to the rim, only for Fernandez to knock the ball out. Real’s disorganisation on that play led to Dorsey’s offensive rebound, as Reyes had stuck close to Dorsey, anticipating having to hedge out to stop Huertas’ floater, he was recovering very late, as both Reyes and Llull turned towards Huertas heading to the rim the both crashed in on him. Leaving Dorsey unchecked to step into the paint and pull down the offensive rebound. With Reyes’ being the help defender, Llull, having already been beaten should have had the responsibility of putting a body on Dorsey.

It was Llull at fault for the Oleson three after the rebound too. With Huertas curling out to the left corner as Dorsey kicked the rebound out to Bostjan Nachbar, it was clearly Fernandez’s assigment to pick up Huertas in the corner, as he was the nearest man after the rebound. With Llull frantically recovering after losing Huertas on the previous play he floated in no man’s land, turning his head to an open Brad Oleson, before turning to an already guarded Huertas in the corner. When Nachbar fired a pass to Huertas in the corner, Llull rushed over, perhaps as an attempt to trap, or perhaps a mental lapse. As Llull closed down Huertas rips a pass off to the open Oleson who obliges by knocking down the open three.

This is what it looks like in images:

First we see Huertas taking a hand off from Nachbar, while Dorsey comes to screen. Then we see Huertas beginning his drive as Llull expects the Dorsey screen and Reyes overplays Dorsey also expecting a pick and roll. As Huertas had been knocked down multiple floaters in the game this not an unreasonable position, just very poor execution from Llull.

In these two pictures we see just how badly Madrid lost Dorsey, as all three Madrid players in the paint have their eye on the ball. Which allowed Dorsey to take his position in the second photo, on the edge of the no-charge semi-circle. It is also interesting to four of five Madrid rebounders  in the paint. This is partially the cause of the confusion after the offensive rebound. As Mirotic and Fernandez lost Nachbar and Oleson while pursuing the rebound.

Next we see the game still immediately after Dorsey has taken the rebound and kicked the ball out to Nachbar, who is just off screen to the left. With Huertas under the basket following his layup attempt we can see Llull (standing towards the left wing) has already turned his head and lost him, Oleson however is directly in his line of sight. Mirotic quickly closes out to Nachbar who dribbles towards the three point line, meanwhile Huertas cuts out to the left corner and Oleson drifts towards the weakside, while Llull steps up to the elbow and Rudy positions himself on the left of the paint.

As Nachbar passes to Huertas in the corner Llull and Fernandez both step to cover him, with Mirotic also shaping towards the ball as well, and with Reyes having to stick in the middle of the paint with Dorsey, Sergio Rodriguez was the only player left to cover the weakside, allowing Huertas to hit Oleson for the open three.

Four point game.

Real ball. 57.1 seconds left.

Play 2: Navarro Shows up on D, Reyes get his Comeuppance

Real inbounded the ball to Sergio Rodriguez who immediately set about wasting some time, running 16 seconds off before making any kind of move. He set up a high pick and roll, driving right around a Felipe Reyes screen, with Reyes before covered by Joey Dorsey in front, and some fantastic help side cover from Juan Carlos Navarro behind the pass wasn’t on. Chacho instead kicked to Nikola Mirotic in the right corner, who swung the ball immediately to Rudy Fernandez at the top, who swung on again to Sergio Llull to take an end of shot clock three. Navarro recovered and managed to get a key hand in the face off Llull, who missed the shot. On the ensuing rebound Felipe Reyes finally got his karmic retribution after he had been flopping and embellishing on every rebound in an attempt to draw fouls. As he wrestled with Joey Dorsey to try and get an offensive rebound the referees rightly blew the whistle on him, eliminating him from the game with his fifth foul.

This is the play in images:

In these images we see Sergio Rodriguez rounding the Reyes screen and kicking to Mirotic in the corner. The first image already show that Navarro has shaded off Llull in the corner to take a help position on the weakside of the paint, by the time the ball swings to the corner Navarro has come fully across the paint to take up a position that cuts off Reyes roll. Responding to this Llull comes out of the corner and increases the distance that Navarro will have to recover.

The next image cuts to Sergio Llull as he takes his shot after the ball rotated from Mirotic in the corner to Rudy at the top of the key to Llull on the left wing. As we can see Navarro has completely recovered to contest the shot. The second image shows Reyes wrestling Dorsey for his foul, after Reyes’ flopping all game, it was refreshing to see him on the receiving end.

Play Three: Bourousis…

After Dorsey missed both free throws Ioannis Bourousis inexplicably missed a box out on Brad Oleson, a man 9 inches shorter than him, and allowed the American to swat the ball out to Marcelinho Huertas. Huertas set up for a pick and roll with Joey Dorsey and Dorsey set perhaps the greatest screen of his career, forcing Rudy Fernandez to stumble. Bourousis played the Huertas pick and roll the same way he had all game floating in no man’s land in the middle of the key, which gave Huertas the choice of either a lob to Dorsey or a floater for himself. He chose the latter and knocked it down.

And now in pictures:

The first game still shows the effect of Dorsey’s screen, Rudy stumbles through it, freeing up Huertas to go against Bourousis, who doesn’t hedge out. As Huertas drives in Bourousis is backpeddling into the paint, afraid of Huertas’ ability to beat him. Huertas then takes the right decision to pull up and shoot the floater. The lob to Dorsey could also have been on, but with Nachbar cutting across the paint and bringing an extra help defender in Mirotic, it likely would have been a lot more heavily contested.

Two point game.

Real ball. 23.1 seconds left.

Play Four: Bourousis… (Again)

Real inbounded the ball to Sergio Rodriguez on the left wing, and he was immediately trapped by Brad Oleson and Bostjan Nachbar. As he attempted a pass out of the trap he found only Joey Dorsey, who quickly flipped the ball on to Victor Sada with 20 seconds left. With a defensive lineup on Barca were lacking the creativity of Juan Carlos Navarro and Marcelinho Huertas, they looked instead to Brad Oleson who set up a pick and roll with Joey Dorsey on the right wing, looking to head left around the screen. As Real again overplayed the screen (this time Rodriguez, not Llull), Oleson faked left and went right, and Rodriguez was caught by Dorsey swinging his screen around. Crossing over behind Dorsey’s screen Oleson left Rodriguez behind him and began driving left past the flat footed Bourousis, who ran to attempt to meet Oleson’s shot at the rim, clattering into him as Oleson left handed layup dropped in off the glass. The whistle sounds and Oleson sinks the free throw.

Here it is in image form:

First we see Dorsey come to set a screen for Dorsey, just like to set up the Huertas floater. But instead of taking the screen Oleson rips the ball over the hands of Sergio Rodriguez and starts his drive right, meanwhile Dorsey changes his course slightly to set a screen to tie up Rodriguez. With Rodriguez tied up on Dorsey, Oleson crosse from right to his favoured left and drives, which is what we see in the second image, though Oleson is obscured by Dorsey. It is also interesting to note that the normally aggressive help defence of Real isn’t present, Llull stays at home on Papanikolaou, Mirotic only shades slightly off Nachbar and most importantly Rudy stays with Sada in the corner, rather than coming to help on the Oleson drive. We’re Real that concerned about falling behind that they wouldn’t help off Sada on a layup?

The first image is just as Oleson starts his drive, we can see Rudy on the edge of the paint, and while it is pretty much a given that Oleson will beat Bourousis, Rudy still doesn’t alter his position even when Oleson is at the rim getting clattered by Bourousis on the foul.

1 point Barca lead.

Real ball. 8.8 seconds remaining

Play Five: Llull Redeems Himself

Facing and 8 point turnaround in the last minute Real had one chance to win the game. With no timeouts remaining Real had to inbound the ball immediately to Rodriguez after the free throw, with Victor Sada hounding Chacho as he drove down court. Rodriguez reached the three point line with 5 seconds left and drove left from the right 45 into the lane. Kostas Papanikolaou immediately came to help from Sergio Llull in the right corner. As it was impossible to cover both the Rodriguez shot and the passing lane to Llull both Sada and Papanikolaou jumped as Rodriguez shaped to pull up, looking like he was going to shoot Rodriguez fired a pass off to Llull open in the corner who sank the shot to win the game.

Papanikoalaou has been heavily criticised by the media (some of it rightly so) for his over exuberance in helping, especially when it looked like Victor Sada had Rodriguez covered. It is always easy to look back in hindsight and say what should have happened on a play, but nonetheless, the help on this play should not have been coming from Papanikolaou. Bostjan Nachbar had the opportunity to cover both Rodriguez and the pass to his man, Nikola Mirotic and stayed glued to the Montenegrin, and has drawn zero criticism. For every risky move like Papanikolaou’s there is someone taking a safe play that deserves equal criticism, in this case it is Nachbar.

And finally, Llull’s game winner in image form:

We pick up the final play after Rodriguez has already taken the ball over half court, he shapes right before crossing over to his left to drive in the second picture. In the first image we can see Papanikolaou in almost perfect help position, he can close out on Llull, and also come across and help late if Rodriguez drive. But, in the second picture we can see he has broken that to come to Rodriguez as he drives into the paint, even though Sada has played Rodriguez perfectly. The help should have been coming from Nachbar, stood near the left elbow, who could have stopped any drive by Rodriguez into the paint, and also covered the passing lane to his own man, Nikola Mirotic.

Now we see two stills a taken a split second apart, the first as Rodriguez shades to pull up, the second as the pass has already gone to Llull. Both Papanikolaou are aggressively contesting the Rodriguez fake pull up, and by the time both of them land in the second image it is too late to recover to Llull, and he gets the game winning shot off.

Back in 1985 Amos Tversky, an Israeli behavioural psychologist, published one of the earliest papers that could be categorised as ‘Advanced Analytics’, where he proved that shots should be categorised as individual events. This went against the assumed knowledge that players and teams should ride the ‘hot hand’ and that if a player had made a few shots in a row, he was more likely to make his next shot. Though widely accepted now at the time Tversky’s theory was rubbished with legendary Celtics coach and GM Red Auerbach commenting “Who is this guy? So he makes a study. I couldn’t care less” and Bob Knight saying “There are so many variables involved in shooting the basketball that a paper like this really doesn’t mean anything.” This led Tversky to assert “I’ve been in a thousand arguments over this topic. I’ve won them all and I’ve convinced no one.”

While writing the article published yesterday on shot allocation I thought a lot about just how teams can achieve an efficient shot allocation, having read long-time Tversky collaborator Daniel Kahnemann’s book “Thinking, Fast and Slow” (which is definitely well worth a read) shortly before I begun thinking about the “hot hand” fallacy. The issue at hand with the “hot hand” fallacy is that humans are intuitively bad statisticians, and we will instinctively ascribe some kind of causality when we see something that we believe is a statistical anomaly (like a player hitting three or four shots in a row), which is actually within a random distribution. As with this being an issue with instinct, shot allocations are too guided by instinct, players will take the shots that they believe are best for the team at the spur of the moment, it is the job of coaches to guide the instinct of players. But, given that the shot allocations are imperfect, how can we find a short cut to efficiency?

This is where the riding the hot hand comes in, while it provides no benefit in terms of boosting FG%, it can provide us with a nifty little heuristic short cut to a better shot allocation. As players with higher field goal percentages will be more likely to have a chain of made field goals than a low field goal percentage riding the hot hand will mean that shots are allocated towards those who make them. Riding the hot hand has an undeserved reputation, I feel this is because it is typically confused with a “heat check” shot where we see a player hoist up a normally ill advised pull up jump shot early in the shot clock. Riding the hot hand needn’t mean ill advised shots, it should just mean that offences look to find players that have been making their shots, whether it be a big man finishing a pick and roll at the rim, finding a shooter in the corner or even in some rare occasions a pull up jump shot early in the shot clock.

Allocating shots in this way is essentially advocating a meritocracy, which would also lead to a change in attitude for players, if the most efficient players are given the most shots then the least efficient players will be forced to reconsider their shot selection if they wish to maintain a place in the rotation.

A further benefit to this is that it solves the issue of how to deal with turnovers that was presented at the end of yesterdays article, if players begin to instinctively look for the player that has made the longest chain of shots then they will also take into account turnovers that occur in an attempt to get the ball to that player, and will look elsewhere if it is turnovers begin to occur if the ball is forced into that player. It will also automatically adjust to the situations in the game, if a player has a favourable or unfavourable match up then they will either be more successful or less successful and will be get more or less looks, or if a player is playing through injury or illness it will automatically adjust downwards too.

While it would not provide a perfect allocation, that can only come through players have complete perfect knowledge of the percentages from each spot on the floor relative to the defence, which is impossible. Riding the hot hand can provide a very quick short cut as it will necessarily favour the most efficient shots and the players that take those shots. For a long time the term ‘hot hand’ has been a bogey term used by those who don’t fully understand statistics, it’s time for this to change and for it to be considered as a legitimate strategy to boost efficiency.

We all have our own gripes while watching basketball, mainly about players taking bad shots (my own personal gripes on this topic are typically aimed at Pero Antic), but how can we qualify whether a player is taking a poor shot in the context of his team? Furthermore, how can we quantify whether an entire team is being effective in its allocation of shots between the available players?

As a former Economics student when the word ‘allocate’ appears my mind automatically makes a jump to allocative efficiency, which is a condition that leads to maximisation of economic welfare in a market, as the value put on a good or service by the consumer is equal to the cost of production, that is to put it in economical terms, where Marginal Benefit is equal to Marginal Cost. To put this in laymans terms it means that any dead weight is lost and that any resources are allocated to their best use.

So, how can this be applied to basketball? If we consider the ‘resources’ at hand to be possessions, and the allocation to be how these possessions are distributed amongst the players on the team, then we should be able to assess the effectiveness of each team in their allocation of possessions. As the ultimate goal of a basketball team is to score points (radical theory, I know) then the definition of a successful possession is one that ends up with the maximum scored amount of points possible. In order to be successful allocating possessions then the amount of points scored per possession is of little significance, as due to the vast differences in the budgets of some teams we can only expect a 30 Million Euro team to have a higher PPP than a 5 Million Euro team. What matters in this case is the variance amongst the points per possession of each player on the team, as that will show which players are underused and overused by their team, and the extent to which this happens.

To relate this back to our economic theory we can consider the marginal cost to be the teams average PPP, because if a player is to take a shot the cost is forgoing a shot for someone else which will be weighted at the average PPP of the team*, and the marginal benefit will be the PPP of the player taking the shot. So, according to this in order to be operating at allocative efficiency the PPP of any given player must equal the PPP of the team*.

*(NB: In this case in order to normalise the PPP of the player and the PPP of the team, we will count a possession in both cases as that which ends with a turnover, missed shot or made shot, with an offensive rebound starting a new possession. As we are looking at shot allocation we should minimise the effect that offensive rebounding has on our calculations, as despite offensive rebounding being positive thing, every team would rather the initial shot was successful rather than relying on the offensive rebound.)

When we observe the graphs below, which use data from the 2012-13 Euroleague season it’s obvious that Anadolu Efes had the lowest spread with their variance at just 0.004 as opposed to the team with the highest spread, CSKA Moscow, who had a variance 8.5 times higher at 0.034. It is important to note here that variance is not the perfect measure of the spread here, as it takes no account of the usage, so those players with a low usage will be overweighted whereas high usage players will be underweighted. So when looking at the graphs it is important to bare in mind that while a perfect allocation will be a horizontal line, a triangular shaped distribution will also be desirable, with the base being to the left and the vertex to the right, as there are likely to be higher variations in PPP when players are at lower usages.

FC Barcelona Regal

• Team PPP (counting offensive rebounds as separate plays): 0.976; Variance: 0.013
• Tomic, Jawai, Navarro, Abrines, Mickeal, Ingles and Lorbek should all be used on more possessions. Rabaseda, Huertas, Wallace, Jasikevicius and Sada should be used on fewer possessions.
• This graph illustrated how big of a loss Pete Mickeal was after his illness, having to replace 11 plays per game at over 1 PPP is a huge ask.
• Barcelona have a solid distribution, with their top three players in terms of usage (Tomic, Navarro and Mickeal) also ranking in the top 5 in terms of PPP.

Caja Laboral

• Team PPP (counting offensive rebounds as separate plays): 0.9832; Variance: 0.021
• Cabezas, Pleiss, N. Bjelica, Lampe and Oleson all should have been used on more possessions. Causeur, Nocioni, M. Bjelica, Heurtel, San Emeterio and Cook should have been used on fewer possessions.
• If Cabezas and Oleson are both removed (both of whom left mid way through the season) then the Caja Laboral allocation is a lot more efficient, with Pleiss and Cook being the only true outliers.
• This shows the impact of Maciej Lampe, who still averaged almost 1 PPP despite a poor three point shooting year (31.8%) on over 14 possessions per game.

CSKA Moscow

• Team PPP (counting offensive rebounds as separate plays): 0.996; Variance: 0.034
• Kaun, Krstic, Erceg, Vorontsevich and Christmas should have been used on more possessions. Weems, Khryapa, Teodosic, Micov, Jackson, Ponkrashov and Papaloukas should have been used on fewer possessions.
• The obvious stand out point for CSKA is that they have 5 highly efficient players (Kaun, Krstic, Erceg, Vorontsevich and Christmas) 5 slightly below average efficiency players (Weems, Teodosic, Khryapa, Jackson and Micov) and two players with very poor efficiency (Ponkrashov and Papaloukas). This is probably the best example and argument for the efficiency of finishers and shooters being necessitated by the inefficiency of shot creators, even when they are creating for themselves.
• As pointed out by many writers around the final four, perhaps the release of Christmas was a mistake for CSKA, as his efficiency from behind the three point line was greatly missed in the Final Four.

Anadolu Efes

• Team PPP (counting offensive rebounds as separate plays): 0.893; Variance: 0.004
• Vujacic, Erden, Farmar, Savanovic and Gonlum should have been used on more possessions. Tunceri, Barac, Guler, Lucas and Shipp should have been used on fewer possessions.
• Efes are by far the worst offensive team here, having a PPP (without offensive rebounds) below 0.9, but they are unique in the fact that four of their five highest usage players (Vujacic, Erden, Farmar and Savanovic) average a PPP higher than the team PPP, meaning they should have been used more. While their role players were relatively inefficient.
• Despite being the worst offensive team of the eight playoff teams they were the most allocatively efficient, having the lowest variance.

Olympiacos Piraeus

• Team PPP (counting offensive rebounds as separate plays): 0.942; Variance: 0.008
• Powell, Printezis, Mantzaris, Shermadini, Sloukas, Hines and Papanikolaou should have been used on more possessions, Antic, Spanoulis, Perperoglu and Law should have been used on fewer possessions.
• The sheer importance of Vassilis Spanoulis is illustrated here, while he is not particularly efficient (just 0.82 PPP) he is used on approximately 7 more possessions per game than Olympiacos’ next highest usage player, Georgios Printezis.
• This is perhaps the graph that I find most interesting, with a rash of highly efficient role players (who in all likelihood have the majority of their shots created for them by Spanoulis) making up for the relative inefficiency of Spanoulis. Especially when we consider the effect Spanoulis can have.

Panathinaikos

• Team PPP (counting offensive rebounds as separate plays): 0.912; Variance: 0.01
• Gist, Banks, Lasme, Maciulis and Bramos should have been used on more possessions, Tsartsaris, Diamantidis, Ukic, Panko and Schortsanitis should have been used on fewer.
• Another intriguing distribution, with shots being very evenly distributed among the players but with a relatively large variation in the efficiency.
• This is probably the biggest demonstration of the decline of Dimitris Diamantidis, with his PPP at 0.77 and usage over 10 possessions per game he is becoming a very inefficient scorer.

Real Madrid

• Team PPP (counting offensive rebounds as separate plays): 0.948; Variance: 0.021
• Begic, Fernandez, Mirotic, Slaughter and Carroll should have been used on more possessions, Draper, Rodriguez, Suarez, Reyes and Llull should have been used on fewer possessions.
• Notable here is the efficiency of Jaycee Carroll, who along with Marko Popovic, is the only guard to be used on more than 10 possessions per game while still shooting with a PPP over 1.1.
• The relatively large variance can be explained by the inefficiency of Dontaye Draper, who is 0.2 PPP worse than Real’s next worst scorer (Sergio Rodriguez at 0.8 PPP), if he is removed then Real have a far more even distribution.

Maccabi Tel Aviv

• Team PPP (counting offensive rebounds as separate plays): 0.973; Variance: 0.012
• Smith, Hickman, Logan, James and Landesburg should have been used on more possessions, Thomas, Ohayon, Caner-Medley, Eliyahu, Planinic and Pnini should have been used on fewer possessions.
• Maccabi had four high usage, high efficiency players, with Shawn James, David Logan, Ricky Hickman and Devin Smith all scoring around 1-1.1 PPP on 10 possessions per game or more.
• This was countered by some inefficient secondary players and role players, with Lior Eliyahu, Yogev Ohayon, Malcolm Thomas, Nik Caner-Medley and Darko Planinic all scoring under 0.9 PPP.

It is important to note that the only impact that this study looks at is in scoring, and obviously this is only a very small aspect of the game, as shown in the link under the Olympiacos graph, it is obvious that despite Vassilis Spanoulis’ inefficiencies as a scorer, his impact on his team mates more than makes up for this.

Furthermore it is important to note that turnovers are included in the possession total, which will skew results slightly, especially against shot creators and towards catch and finish/shoot players. Just to illustrate this, if a player turns the ball over trying to create his own shot, then this type of turnover would fit in well with what I am trying to demonstrate, as the player is being ‘used’ on that possession, and a certain amount of turnovers are to be expected from a player attempting to create a shot for himself. The issue comes when we consider when the ball is turned over in an attempt to create a shot for another player, as the turnover will be attributed to the passer, rather than the intended shooter, this will obviously increase usage per game, as well as decreasing PPP, when the player that was intended to be ‘used’ on the play doesn’t have a possession attributed. As there is no way to distinguish between these turnovers without logging each game, then we have to deal with slightly inaccurate data, and take the findings with a pinch of salt.

Finally, efficiency in the sense spoken about here does necessarily breed success (Efes for instance were the worst offensive team, despite having the most efficient shot allocation), there have been arguments (notably, here) that having a high usage low efficiency player can lead to efficiency amongst the rest of the players on a team. This would certainly explain the success of Olympiacos, with the low efficiency of Vassilis Spanoulis necessitating the efficiency of the other Olympiacos players. The most likely reason for this is the natural bias of defences towards superstar players (who are also more likely to make ‘highlight’ plays), perhaps acting more on instinct and in reaction to the ‘highlight’ plays rather than considering the information at hand.