Core Statistics: Turnovers per Touch and the Shot Selection Index

In this post, we will define two more basketball analytics – Turnovers per Touch (TOT) and the Shot Selection Index (SSI) – which will complete a core glossary of statistics on the Basketball I.Q. website.  Though new analytic methods will be added in future posts, this post will provide Basketball I.Q. readers with an analytic foundation (along with Successful Possession Rate, Turnover-Adjusted Points-per-Shot, and Shot-to-Assist Ratio, see earlier posts) with which we can start the real fun – analyzing rumored trades, identifying league All-Stars, labeling our favorite goats, etc.

Turnovers per Touch (TOT)

In baseball, everybody knows that errors and fielding percentage are flawed statistics, and the Gold Glove is an award for defensive performance that seems to be based upon everything but defense.  The problem, of course, is range:  Derek Jeter, as he plays through his late 30’s, has little of it – and as a result, fields fewer balls and consequently makes fewer errors than many shortstops.  Because of this, and the fact that the balls he does not reach are the most difficult to field cleanly, his fielding percentage is always pretty good.  This may explain why he wins a Gold Glove over fellow shortstop Elvis Andrus, who appears to be able to play all nine positions by himself and, as a result, makes more errors.

Basketball has the same problem with turnovers (TOV).  The TOV is a statistic that measures a player’s error, and it is a pretty important error, as TOV absolutely ends a possession, with no chance for the player’s team to make up for it until they get the ball back.  The problem with measuring TOV as an absolute value is that the number is going to be higher for players who touch the ball a lot – and try to do a lot with the ball when they have it – than it will be for player’s who touch the ball infrequently and do not try to do a lot with it.  Consequently, the TOV statistic alone will unfairly punish players who take on a heavy scoring load for their teams, and those that try to create plays for teammates off the dribble – just like total errors will unfairly punish baseball players who are able to make a lot happen in the field.

Statisticians have tried to correct for this flaw in the TOV stat in a number of different ways.  One way is to look at TOV per minute – but this statistic still unfairly punishes those who touch the ball a lot, as opposed to players who spend their court time without the ball in their hands.  Another statistical correction has been the assist-to-turnover ratio, which seems reasonable since players who tend to create for their teammates (Primary Distributors, please see the January 8, 2011 post) make a lot of turnovers, too.  But the problem here is that players can do a lot of other things for their team with the ball, too – e.g., create a shot off the dribble – and an assist is just one of them.

The statistical measurement of turnovers that I propose is also a ratio, though a more comprehensive one – one that I refer to as the Turnovers per Touch (TOT).  This ratio attempts to measure an individual’s TOV in relation to how often he tries to do something with the ball.  As the statistic implies, the numerator of the TOT measurement is simple: TOV.  There is nothing more to measure.

But the denominator is an estimation of all touches a player may have on the floor, all of which have the opportunity of producing a turnover.  This estimate includes TOV (also present in the numerator, as stated), field goal attempts (FGA), free throw attempts (FTA), total rebounds (TRB), steals (STL) and assists (AST).  Because a FTA, in essence, represents half of an attempt to do something with the ball, it is weighted in the TOT statistic by half (FTA/2).  As a sum, the denominator of the TOT statistic is:

[TOV + FGA + (FTA/2) + TRB + STL + AST]

Taken together, the formula for TOT is:

TOT = TOV/[TOV + FGA + (FTA/2) + TRB + STL + AST]

As usual, my first step was to try it out on a bunch of different players, and just see what the numbers bore out.  Magic Johnson, Steve Nash and Isaiah Thomas, for example, have career TOTs of .095, .103, and .109, respectively (put another way, they commit a turnover on 9.5%, 10.3%, and 10.9% of their touches).  Shaquille O’Neal and Patrick Ewing (for their careers) and Dwight Howard (for 2009-10) have TOTs of .073, .085, and .097, respectively.  [Note: These statistics may have changed since last analyzed two weeks ago.] 

Again, just as the case was with analysis of Successful Possession Rate (SPR), it is unfair to compare players’ TOT if they do not assume similar roles on the floor.  As was previously discussed, the SPR (see the posting on December 26, 2010) gives disproportionate weight to players who accumulate a lot of assists.  In this instance, the TOT gives disproportionate weight to players who forgo an attempt at an assist – and run the risk of making a turnover – in favor of just shooting the ball, whether they make it or not.  As a result, “playmakers” will have high TOTs and “scorers” will have relatively low ones.  As with SPR, it became apparent to me that the comparison of player TOTs should only be made between players of the same quintile (i.e., players with a similar Shot-to-Assist Ratio, or SAR, see the posting on January 8, 2011), since that would be a more accurate comparison of players’ ability to protect the ball.

As examples, I would like to refer to players implicated in recent trade activity.  Let us take the comparative case of Carmelo Anthony of the Denver Nuggets and Danilo Gallinari of the New York Knicks – two players who are rumored to be part of a trade for one another, in a deal that seems unlikely to happen.  As of a couple weeks ago, Anthony has a career SAR of 7.49 (he shoots the ball about 7.5 times for every assist he registers), while Gallinari has a career SAR of 8.02 – rates that are very similar, and put each player in the quintile referred to as Primary Scorers.  In this manner, they are similar players. 

However, Gallinari’s TOT is a remarkably low .057 – he turns the ball over on less than 6% of his touches – while Anthony’s TOT is .083, which is a rate associated with players who accumulate many more assists than Anthony does.  By this measure Gallinari is far more protective of the ball than Anthony, his positional peer. 

If you would like to defend Anthony’s TOT, relative to Gallinari’s, because of his scoring prowess, it could be countered that Gallinari’s Turnover-Adjusted Points-per-Shot (TAPPS) is a remarkably high 1.05 (because of good three-point shooting and excellent free throw shooting, combined with low turnovers), while Anthony’s is a pretty good (but not quite as good) 0.94. 

If you would like to further defend Anthony, as Nate Silver did in the New York Times this weekend, by saying that he does more for his teammates, this might be countered with two further statistics:  Gallinari’s SPR (which combines scoring with assists to teammates) is .572, while Anthony’s is only .525 (please see the December 26, 2010 post for further explanation, but to put it roughly, if they were baseball players, Gallinari would have an on-base percentage that is almost 50 points higher).

The other statistic that might be invoked in the Anthony vs. Gallinari debate is the Shot Selection Index, which is described in the second half of this post.

Shot Selection Index (SSI)

How do you know if a player is taking good shots?  I suppose one of the ways in which you might estimate this is to look at total points scored – if you score a lot of points, you must be taking good shots – but the flaw in this measure is easy to detect: A player can score a lot of points simply by taking a lot of shots (Brandon Jennings), whereas another player can score only a modest amount of points by taking nothing but good shots (the 2011 version of Shaquille O’Neal).

Another way to look at this would be shooting percentage, or the vogue statistic, true shooting percentage, which weights three-point shots by 50%.  By these metrics, players with high shooting percentages – “raw” or “true” – are clearly taking good shots.  There are two problems with this measure, in my opinion:  First, this statistic eliminates the absolute best shot a player can take – an absolutely open one, with no defender allowed in front of you, directly in front of the basket with full use of the backboard, otherwise known as a free throw. 

The second problem is that shooting percentages do not necessarily take into account your opponents’ opinion of the shots you are taking.  By my reasoning, if your opponent would rather give you the opportunity to shoot two uncontested one-point shots (in other words, he fouls you), rather than let you take the shot you are about to attempt, then you must be taking pretty good shots. 

In other words, if you are a 75% free throw shooter and your defender fouls you in the act of shooting, he must think the shot you are taking has greater than a 75% chance of going in – probably even greater, since he is willing to push himself 16.7% closer to being disqualified from the game by doing so.  Even if you are a 50% free throw shooter (like Shaq), a foul in the act of shooting means that your opponent thinks your shot has a better than 50% chance of going in, which is still pretty good – especially when you consider, again, that your defender is willing to push himself toward disqualification (“fouling out”) in his attempt to send you to the line.

And so what I devised is the Shot Selection Index (SSI), which is a very simple statistic:

SSI = FTA/FGA

It is free throw attempts divided by field goal attempts, and it estimates your opponents’ opinion of the likelihood that your shots will go in, which I hypothesize is the best gauge of your shot quality (taken in conjunction with someone’s shooting percentage, “raw” or “true”).

As a reference, the team median for SSI in 2009-10 was .296, while the team mean was about .301.  Players, on average, shoot free throws a little less than a third as often as they attempt field goals.

As individual examples, Shaq has an SSI this year of .698 – the quality of his shot selection is more than twice as good as the league average (though no doubt this is impacted by his poor free throw shooting).  Lebron James, who is a good free throw shooter, has an excellent SSI of .482, while Kobe Bryant (also good from the foul line) is well above the league average at .388.  Meanwhile, Brandon Jennings has an absolutely average shot selection (.303) and Wilson Chandler of the Knicks, who makes 80% of his free throws, has a remarkably low SSI of .193 – which, to me, means that his coach might be asking him to shoot too many three’s, and is not designing enough “clear-outs” to get this very athletic player driving to the basket.

Let’s re-visit the Anthony vs. Gallinari debate, using SSI as a platform.  By a few measures, Gallinari appears to be getting more done when he has the ball.  As mentioned, however, Nate Silver of the New York Times suspects that Anthony’s court presence alone creates a lot of easier opportunities for his teammates.

Even by SSI, Gallinari puts up the better number: .534 (excellent) vs. Anthony’s .425 (still very good).  However, let’s argue Silver’s point that Anthony does a lot for his teammates.   Looking at Gallinari’s point guard (Raymond Felton), swingman (Wilson Chandler) and big man (Amar’e Stoudemire), they have respective SSIs of .253, .193 and .436 – with the exception of Stoudemire, all below average, and all below Gallinari’s SSI.  Meanwhile, the same position players who play with Anthony – Chauncey Billups, J.R. Smith, and Nene – have SSIs of .633, .305, and .655, which is absolutely fantastic, and two of these three SSIs are better than Anthony’s own SSI.  By this measure, Carmelo really might be creating more opportunity for his teammates, just by being there.

The next step in the analysis would be to look at what the players’ respective teammates actually do with these opportunities.  What you could look at is the TAPPS of the players’ teammates.  Felton, Chandler and Stoudemire come in at 0.89, 1.04, and 0.96 – all of which are pretty good, but none of which are as high as Gallinari’s career TAPPS.  Meanwhile, Billups, Smith and Nene come in at 0.99, 0.94 and 1.16 – which not only is significantly better than their Knick counterparts, but all of which are as high or higher than Anthony’s career TAPPS – suggesting that Anthony might be making his teammates better than himself.

I must concede at least one point to Nate Silver: Carmelo Anthony may very well make his teammates better, just by lacing up his sneakers.

Next post: The comparative trade value of Carmelo Anthony, done in greater detail.