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.