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Reaching the Objective

November 21, 2011 in by with 0 Comments

We’ve scoured the box score. We’ve generally figured out the best ways to manipulate game logs and lineup data. We’ve worked and re-worked the same numbers, and it’s become abundantly clear that the next analytic evolution will need to be drawn from a new well.

Rob Mahoney, Special to SI.com, “Time to take advanced defensive stats to next level in basketball”

If you haven’t read Rob Mahoney’s piece on SI today, I highly suggest you do so. Even for the non-stat-savvy among us, this piece is worth your time. Rob not only does a fantastic job of outlining how close we are to being able to analyze something as seemingly ambiguous as defensive prowess, but he also lays out how the field of statistical analysis needs to proceed to bring our understanding of defensive basketball statistics to the level of offensive basketball statistics and baseball statistics in general.

To me, though, the most important part of Rob’s piece is how it directly hits the crux of why basketball (and to an extent, sports in general) is so fascinating to many of us: How do you objectively value something that elicits a subjective emotional response within you? No one says “God I love Dirk so much because his PER is off the charts!” But we use metrics like PPG, clutchness, and PER to try to put into facts why we love what we love. That way, when individual passion morphs into competition between yourself and an opposing fan, you’ve got statistical ammunition to send his/her way. You’re right: Your player is awesome, and you’ve got the facts to back it up. Count the ringz? Please. Count the WARP, hijo! Just kidding, but you know what I mean. (Note: I’m only sort of kidding.)

This search for objectivity also puts fans in a unique place when judging player value on another plane: salary. I think most fans can agree that players should be able to earn what they are worth. This worth depends on many factors, three of the most important being how full the talent pool is with similar players (or market size), how much a team needs such a player (for whatever purpose they deem necessary), and how much an owner is willing to invest in such a player (or market value). Owners and GMs have been known to shoot themselves (and the future solvency of their franchises) in the foot with bad bets and arbitrary valuations of players. The fan is also tied up on this end: thanks to my dumb owner/GM, my team is handcuffed to mediocrity and luxury tax for the next 5 years. 

Eventually, I’d like to see these two types of objective valuations (ability and salary) merging. Obviously, salary is already based mostly on ability (among a host of other factors), but if owners and players can come to terms on a rigorously objective methodology to evaluate player talent, how could each side argue in good faith about the fairness of salary composition in either direction? If a player has an O score between 25 and 30 and a D score between 22 and 27, then they could be entitled to a salary in the range of 7-10 million, depending on market size, a team’s 5-year average winning percentage, and whether or not the bidding team is in an income-tax-free state. This completely fabricated scale makes total logical sense, doesn’t it?

Now, in a highly contentious atmosphere–where owners compete against players, owners compete against owners, players compete against players, and agents and lawyers take sides as needed–subjectivity will continue to outweigh objectivity for the foreseeable future. After all, it’s the subjective nature of salary structures and markets that allow all these parties to make their money on the margins: players make the salary, agents take a cut, owners make money on their investments in players, and lawyers step in to keep everyone on their toes. Introducing an objective salary scale might take away all the margins that these parties like. Less risk, less reward, even. But when we risk losing an entire season to something as subjective as ego, it may be worth drawing ideas from another well.

Boundary and Nexus: Maximizing Inefficiency

January 10, 2011 in by with 10 Comments

Image via Flickr

It’s a well known fact: the long 2 is the least efficient shot in basketball. 

The reasoning is quite simple, really. The further you are from the basket, the harder it is to make shots. And since by going further than the long 2 range you gain an extra point for every shot, long 2s are the furthest, low scoring attempts in basketball. 

This (correct) notion has become ingrained in our analytical DNA. Sure, the long jumper is impressive when it goes in, but no basketball fan in their right mind would rather see Lebron James settle for a foot-on-the-arc fadeaway when you know that he can take it to the rim at will. 

However, there is more to basketball than just “long 2s bad, close 2s and open 3s better” (yup, that was an Animal Farm reference. Because at HP we are dedicated to bringing you both snot-nosed, self righteous, social-critiquing literature, and zombie movies). Long 2s are shot, and often, whether it’s because the players that shoot them know they can make them, want to keep defenses honest, or are just plain lazy. But how damaging are they anyway? 

Lets start by taking it back a few steps, and numerically conforming the statistical inferiority of the long 2. With the help of the life-altering Hoopdata.com, here is a table of the league average eFG% for different shooting ranges as far as Hoopdata’s records go (the 2006-2007 season), and the averages over the entire stretch (since the current season is just midway, I weighted the results under the assumption that the average NBA team has played 34.7 games this season, as was true of January 7th). 

The results: 

 

The number that jumps off the page is that the percentages for the 10-15 foot “in-between” range were not only in the same area of the 16-23 foot range, but actually worse for 4 of the last 5 seasons and over the entire 5 year stretch. However, that figure becomes much less surprising when you look at the figure right next to it – the % of made shots that were assisted. This makes sense – although we very often see shots from that range taken in ISO situations, you see plenty of spot ups from just inside the arc, and very few spot ups from 10 to 15. And in general, it’s much easier to make shots when your body is all lined up and a passer hits you than when you have to create on your own. 

In addition, shots from in between are usually tougher makes. Many of them are either of the floater variety (hello Derrick Rose) or come off the mid-range post game (hello Kobe Bryant). But Roses and Kobes are few, and these shots tend to be harder to make, especially since they are taken closer to the shot-altering reaches of various big men. So while I didn’t expect the two ranges to be similar percentage-wise, it does seem to fit in with general convention – in a vacuum, you’d rather be open from 13 feet than from 18 feet, but how you get there and how you’re being guarded is a factor. 

Moving on from the percentages, we reach the amount of field goals attempted from each range. Interestingly enough, there has been a baffling drop in attempts at the rim in 2010-2011 – 4.5 less a game. However, the corresponding, nearly matching jump in shots from 10 feet in (up 4 shots a game) makes me think that shot locations may be counted differently this season in contrast to years past, thus creating the difference. I may be wrong with this assumption, but since it’s not our topic of focus, we’ll keep it at 2-bit conjuncture levels. 

In what is our topic of focus, though, the “shots attempted” numbers are quite odd as well. The average NBA team since 2006 attempts 20.9 long 2s a game, which accounts for 26% of all shots. This exceeds the amount of shots from every other range except at the rim. Remember, this is the widely acknowledged least efficient shot in basketball. Are teams just stupid? Or is there more to this? 

Allow me to toss out two theories as to why this is the case. First of all, the evolution of the sweet shooting big men – initially just known as Euros, then acquiring the ever descriptive name “stretch 4s”, has surely helped in this regard. While some of these gigantic sweet-strokers make their hay behind the three point line, a substantial amount of them score their points off the 20 foot range. Guys like Dirk Nowitzki, Kevin Garnett, Chris Bosh, The Artist Formerly Known As Rashard Lewis and David West have made multiple all-star teams behind the premise that their high point of release combined with their shooting prowess makes them efficient from the non-efficient range. Nowitzki, specifically, is probably the best long 2 shooter in recent history, making a ridiculous 53% from 16 to 23 feet this season (by far his best since in Hoopdata’s records and unlikely to sustain but still darn impressive) while taking 43% of his shots from that range. 

The list of big men shooters goes on and on. Amar’e Stoudemire has been more than just a dunker for years now. Al Horford seemingly can’t miss a long jumper. Pau Gasol, Lamarcus Aldridge, Luis Scola, Kevin Love. All good shooters. In today’s NBA, even if you’re big, you need to make that shot. With so many more players capable of making the shot, it makes sense that more players take them, even if it’s not as efficient as getting to the line or spotting up a bit further back for an extra point. 

Another reason could be the annoying-but-ever-present pick up mentality that a swished jumper is more impressive than banging into your defender for two freebies. What’s more memorable, those Kobe jumpers that don’t even touch the net as they account for 2 more on the scoreboard, or when he fools his defender into fouling him on a 3 point shot that was never intended to go near the rim? Players want to show they can make those shots, so they attempt a disproportionate amount of them, even if their strengths lie elsewhere. Just look at Allen Iverson’s career. 

Of course, this still doesn’t excuse teams from focusing way too much on the least effective way to score points. While nobody would make the argument that good teams shouldn’t shoot long 2s at all – if you’re got a good shooter and you’re open, then by all means, knock it down – the stark contrast to conventional wisdom presented by these numbers makes one wonder. Do better teams try to lessen their long 2 attempts? Conversely, do they try to bump it up a few notches for their opponents? Does this even affect them? 

In order to answer these questions, I once again turned to last season’s shot location data per team (last season and not this season for the larger sample size). I plotted the percentage of shots each team took from from 16 to 23 feet (looking at the percentage of shots and not the total amount of shots from each range in order to adjust for pace) versus each team’s offensive efficiency, in order to measure just how damaging the “worst shot in basketball” is anyway. 

 

This graph clearly shows us that there is some kind of relationship between the relative amount of long 2s a team takes; however, this relationship is far from conclusive. As we can see, the scatter on this graph is fairly large, and the correlation between the two variables is only 0.0768 (running on a scale of 0 to 1, where 1 is a perfect relationship, and 0 being a Tony Allen-O.J. Mayo relationship), which means that many other variables have far stronger effects on offensive efficiency. However, some kind of effect is there, even if it’s minimal. 

Look at the two extremes on the chart, and you see exactly the teams you’d expect to find: Orlando took the least long 2s in the league by far, right on par with Stan Van Gundy’s “Dwight inside or everybody else from 3” strategy, taking it to second in the league in offensive efficiency; meanwhile, if you watched the Chicago Bulls last year, you know that Vinny Del Negro “coached” his team into an offense full of long jumpers and void of any offensive movement, resulting in the highest percentage of long 2s in the league and the 28thranked offense. Right on their heels were the Washington Wizards, who spent the season featuring notorious gunners; early on, Gilbert Arenas and Caron Butler were the ones taking your contested long shots, only for the likes of Andray Blatche, Nick Young and Al Thornton to take over the inefficiency load once the two former all-stars left the team via suspension or trade. 

As for some outliers, the iso-heavy yet offensively efficient Hawks and Blazers expectedly broke the trend, ranking 9th and 4th in percentage of long 2s, and 3rd and 7th in offensive efficiency, respectively. The Bosh-led Raptors also efficiently built around long jumpers, ranking 6thon both accounts. Underperformers were just as familiar, with a cluster of offensively terrible squads such as the Bobcats, Bucks, Pacers and Clippers appearing far below the trendline, with 09-10 laughingstocks New Jersey and Minnesota falling even further. All these 6 clubs were around the league average as far as taking long 2s, but were so atrocious elsewhere that it dragged them towards the lower regions of our graph. 

So good teams tend to take less long 2s, but it’s not a necessity for a good offense. How about good defenses? Do they corner opponents into long jumpers? We go for the same exercise, only with shots given up and defensive efficiency. 

The defensive graph seems to very easily break into three groups. The elite defensive teams of 2010-2011 – those in the 100 to 102 points per 100 possessions range – seem to have been all over the place as far as giving up long 2s. On one end we have the Magic, who seem to employ the same defensive strategy as they have on offense – have Dwight take care of the inside, everybody else close out strong on 3 point shooters, and thus force opponents to take plenty of 2 point shots from too far away. This plot ranked them 3rd as far as long 2s conceded. On the other side we have the Thunder, whose opponents were 3rd from the shallow end, presumably due to a lack of a true physical presence inside to deter opponents from stepping out for their 2 pointers. 

Looking past that elite group, we have an Atlanta-Portland-Dallas-Utah-Chicago clump, whose defensive efficiency ranges from 102.6 to 104 (ranked 10th to 14th), and whose opponents take long 2s 24.4% to 25.3% of the time. It’s hard to note any effect long 2s have on this particular group, since they are all very similar. 

The third group is the most interesting one as far as our research, and it shows the what pretty evenly breaks into the bottom half of the league defensively. In this region, there seems to be a pretty direct effect. In fact, the correlation for just this part of the chart was 0.381, by far stronger than that of the offensive graph. When we add the top 14 defensive squads, the correlation drops to 0.1019. In fact, if you take another glance at the trendline, it really does look as if it was tailor made for the top half of the graph before the evenly distributed bottom came and dragged it down in it’s original shape. 

The difference between top and bottom is very odd, and I find no explanation for it, seeing how there is no reason why something should only affect bad defenses and immediately stop mattering once you creep up to number 14. As such, we can probably dismiss it as a fluke, leaving a message very similar to that of the offensive graph: channeling your opponent to the inefficient long 2 gives you a better chance of being a good defensive team, but you can just as easily be a great one without it. There are many ways to skin a cat, this just happens to be an effective one. 

To get a good look at the complete effect of long 2s, I combined the two graphs by plotting differentials – offensive minus defensive. Since this is basically combining the two previous graphs, we shouldn’t be surprised that the results are pretty similar. The Magic again were stalwarts, with the absolute best differential in both categories, proving both that they strategically avoid the inefficient shooting range while funneling their opponents towards it, and that they are extremely successful in doing so. 

 

The conclusions here may seem trivial. However, they have analytical value. We know that long 2s are bad shots, but this gives us two seemingly conflicted truths: that it is generally smart to reduce those shots for yourself while encouraging your opponent to take them; and that is more than possible to fail while doing so, or succeed without it. While the long 2 is often considered to be inefficiency incarnate, it is not a death knell. It can be manipulated and molded into a prosperous ordeal.

NBA HD: How To Get Your Free Agents Half-Off

August 26, 2010 in by with 6 Comments

Lost in the whole Free Agentpalooza of 2010 was the fact that the party could have been bigger. Outrageously bigger.

With the cap-slashing climate over the past few years, the writing was on the wall well before the calendar reached July 1, 2010: this class of free agents were due for an enormous payday.  Seeing the formation of the storm on the horizon, organizations wisely arranged meetings with their imminent 2010 free agents and their representation in effort to prevent their prized players from hitting the market at all.  The plan? Sign them to a contract extension.

Contract extensions can be mutually beneficial; the player receives job security  from the team and the team gets the player at a discount.  The latter part of the deal isn’t guaranteed by any means but the team doesn’t have to compete with other bidders to sign their player long-term.  And that exclusivity is a huge advantage for teams.  But how can we quantify that advantage?

Let’s compare some contracts.  Of course, every free agent’s situation is different but to responsibly compare apples to apples, let’s examine the 2006 draft class whose rookie scale contracts were generally due to expire after the 2009-10 season, allowing them to become free agents this past summer.

First, the guys who cashed in early.  Can you imagine if Brandon Roy, Rajon Rondo, and LaMarcus Aldridge joined the free agent sweepstakes? Believe it or not, each of these players could have waited to test the free agent waters but elected to sign long-term with their respective clubs in the fall of 2009.  But they weren’t alone; Andrea Bargnani and Thabo Sefolosha also agreed to contract extensions before hitting free agency.  How much did they sign for? Let’s take a look.

For each player, the first two columns after their name tell us the contract length and dollar amount, with the third column calculating the average salary over that contract. For example Rajon Rondo inked a contract extension with the Boston Celtics in early September 2009 for 5-years, $55 million for an AAV (average annual value) of $11 million.

Then, for each player, I included their 2008-09 Wins Above Replacement Player (WARP09) with the “09″ signifying the year.  I chose 2008-09 to reflect their output before they signed their contract extension.  The WARP numbers are courtesy of BasketballProspectus.com and the brilliant work of BBP author and Indiana Pacers consultant Kevin Pelton.  To be clear, this version of WARP is not his newest version, WARP2, which incorporates an added bonus for players who space the floor with 3-point shooting.  Why? The Basketball Prospectus site has not updated their databases with WARP2 yet so for continuity purposes I opted for the older version.

So, this chart tells us that Rajon Rondo received a $11M AAV contract extension after a 13.2-win season in Boston, meaning he was being paid $0.8 million for each win that he accrued that season.  To be sure, teams pay for future projected performance not past performance, but this provides a quick dollar-value conversion that I’ve outlined in previous articles.

Through some research, I found that teams roughly paid $2.25 million for each win in this past free agency period.  Using that standard, the contracts handed to Rondo, Roy, and Aldridge were incredible bargains for their respective organizations.  Sefolosha received a contract fairly in-line with the going rate and Bargnani’s salary hasn’t quite reflected his production in the eyes of the WARP model (although WARP’s opinion is not unique in the statistical nor the scouting world).

All in all, the players who received contract extensions were paid about $1.4 million per win which is far below the free agent price observed this season.  Rondo undoubtedly would have received a max contract had he tested free agency and a case can be made that Aldridge would have pulled one down as well, given his age and productivity.  They left money on the table for job security, ensuring that they’d be set long-term should a career-altering injury occur in 2009-10 (which happened to Roy to some extent).

But how much money did they leave on the table? To find out, I looked at the going rate for their fellow 2006 draftees who received at least three-year deals in free agency: Rudy Gay, Tyrus Thomas, J.J. Redick, Jordan Farmar, Ronnie Brewer and Kyle Lowry. (The three-year qualifier captures players in the same stratosphere as those worthy of an extension and excludes players like Shannon Brown.)

While these free agent deals aren’t all completely egregious, the free agent premium bears out in this small group with the average price for a win costing $3 million compared to the previous group’s $1.4.  In fact, according to this method, inking an extension gave the parent organization about a 50% discount on the commodity of wins.

The biggest difference? In free agency, it’s nearly impossible to sign a talent like Rondo at a clearance markdown price.  Rondo has nearly four times as much impact on the standings as Rudy Gay but the latter will earn about $25 million more over the next half-decade.

So how are teams able to convince players to sign extensions that are probably below their market value?  Well, it’s not easy.  It’s paramount for an organization to produce a winning attitude from the top on down.  That means not just winning in practice but also in style (right, Dan Gilbert?).  It’s the responsibility of the owner, front office staff, and the coaching staff to make the players feel like there’s no sense to risk losing the professionalism, commitment, and comforts they can enjoy at home.  In other words, make your lawn as green as green gets.

NBA HD: Market Update II

July 30, 2010 in by with 2 Comments

Richard Jefferson signed a few days ago which mean’s it’s time for another market update on the free agency price.  To recap, I’m comparing every newly-signed player’s salary to their WARP2 from last season. It’s a quick and handy measure of how much teams are willing to pay for talent this summer.  Last year, the going rate for free agents was $1.49M for each win.  This year? It’s risen to $2.2M.

Here’s the full run down:

To reiterate from last week, the last row on this table subtracts players who likely signed for lower than the free market rate (LeBron James, Dwyane Wade, Chris Bosh, and Dirk Nowitzki).  This takes a more accurate view of what teams pay free of cap spending restrictions.

$2.2 million per win is an increase since the last count because the newest additions have been sold at the rate of $3.3 million.  WARP2 didn’t think much of last year’s production of Ronnie Brewer, Joel Anthony, Richard Jefferson, and Marquis Daniels but teams were willing to pay more than the minimum and in some cases, much more than the minimum for these near replacement-level efforts.

Newly minted Matt Barnes looks like one of the best deals of the summer and should help bolster the Lakers’ chances of bringing home another championship.  It’s hard to imagine Ridnour posting another 5.3-win season but this objective method makes David Kahn look like a genius.

Next week, look for a team by team and position by position break down.  We’ll see if the summer’s $700,000 premium sticks.

Much thanks to Kevin Pelton of Basketball Prospectus.

NBA HD: Market Rate Update

July 15, 2010 in by with 8 Comments

In last week’s post, I calculated the going rate for free agents this summer by applying the dollars-per-win method that others have used in the past.  If wins were a known commodity (which they aren’t), then this would represent the price.  To be sure, not all teams value wins at the same rate.  Some teams have an easier time swallowing risk or ignoring risks altogether.  But aggregating the talent and dollars gives us a good window into the pricing climate.

I found that teams were paying about $2.23 million per win according to Kevin Pelton’s WARP system.  Since then, Kevin has kindly pointed out that he made an updated version of WARP (referred to as WARP2) and they haven’t been published yet on the Basketball Prospectus player cards just yet.  Being the helpful gent that he is, I was sent the WARP2 numbers for last season (denoted 10WARP2) and those numbers are reflected below.

You’ll notice I have cited two prices here.  The $1.69 million pricetag reflects the entire free agency lot with the max guys included.  However, several high-end players had their salaries artificially capped due to the CBA rules that restrict the max salary to about $20million annually if resigned by their former club.  Moreover, we witnessed a rare circumstance where players took paycuts below their max cap (LeBron James, Dwyane Wade, and Chris Bosh) so that the team could have more money to fill out the roster. Consider that Joe Johnson will get paid more than James despite only being half the player James is.

There isn’t a perfect way to handle this designed deflation but I chose to ignore the players fulfilled the following qualifiers a) received the max allowable contract AND b) produced at least 10 WARP2.  This takes out Dirk Nowitzki, Bosh, James, and Wade —  all of which would almost undoubtedly receive bigger contracts if the CBA gave them that right.  It’s arguable whether someone would have paid higher than the max for Johnson, Stoudemire, and Rudy Gay, but their included in the Total w/o “max” price.

So, with that in mind, it seems as though the market rate has slid from $2.23 million per win to $2.01 million per win (or just $2 million) over the past week.  As I mentioned in my previous post, the 2009 summer going rate was approximately $1.49 million which means NBA teams a whole are paying about half a million dollars more for each win.

You could interpret this finding in a number of ways.  An argument can be made that agents are simply getting better at selling the product but that’s probably not something that happens collectively overnight.  It could also be a sign that front offices are desperate to pacify their anxious fans and thus, will use their enormous cap space to land someone of name-value.  Remember, fans have been promised the moon in the Summer of 2010 TM and that demand has pushed up the price.  But it’s also very possible that the impending lockout has caused more players to enter the free agency market to secure a long term contract.  In turn, the supply has been raised as well, but maybe not as much.

It’s also worth noting that the $1.49m price from 2009 was derived with the original version of WARP and thus, the price could change slightly.  However, I don’t have any reason to believe it would change the price significantly as the system adjustment was merely a minor tweak to allocate more credit to 3-point shooters for floor-spacing.

So the $750,000 premium we saw last week has been reduced down to a not-too-shabby $500,000.  The players will take it — while they can.

NBA HD: This summer’s $740K premium

July 8, 2010 in by with 8 Comments

With Joe Johnson receiving a max contract and Darko Milicic taking in $20 million from David Kahn, it seems as though teams are recklessly showering free agents with money this summer. It’s a sellers market; teams are flush with cash and promising the world to their fans.

But what do we mean when we say that a team overpaid for a free agent?  Whether you know it or not, our minds gather bundles of basketball information (How good is this player?), transfers that to a dollar amount (What is that product worth?), and compares it to the price tag (Was it a good deal?).  The wondrous mind is able to perform this function in a matter of seconds.  But let’s try to slow it down and put it on paper.

One approach is to quantify player value on the court and then observe how much that product costs on the market.  The market prices stabilize only after several deals have been made and they change from year to year as player as new money enters the market (say, a Prokhorov arrives or salary cap threshold rises) and/or the product line changes.   The product line has never been stronger and the suit pockets have never been deeper.

There are several player metrics out there that attempt to quantify player value on a scale of wins: John Hollinger’s Estimated Wins Added (EWA), Dave Berri’s Wins Produced (WP) and Justin Kubatko’s Win Shares (WS).

The player metric I’ll use for these purposes is Kevin Pelton’s Wins Above Replacement (WARP) which applies the same framework in Baseball Prospectus’ WARP to the NBA.  To account for player value, I will use the player’s WARP for the 2010 season.

So far, the going rate this summer for one WARP is $2.23 million.  This means that in this climate, a 4 WARP player would generally command about a $9 million per annum contract.  Of course, this isn’t ironclad and as shown by Chris Duhon and Steve Blake, who both received four-year contracts after contributing sub-replacement level performance last year, this model will bend going forward.

Remember the Drew Gooden contract that people drew all sorts of insta-snark?  That measures out to be the best bang for the buck deal of the summer up to this point, along with Boozer’s deal.  The years may be long on Gooden but the Bucks got the veteran big man at a steep discount most likely because of his questionable motor and perception that a oft-traded player equals a flawed player.   If he continues to produce on the court, Gooden could be a steal at this climate.

Surprise, Surprise: Darko Milicic was one of the worst deals so far this off season.  The Timberwolves overpaid about $13 million ($2.23 x 0.8 x 4) on the fringe contributor and the signing did little to change David Kahn’s rep as a showrunner.

One shortcoming of this model, as you can see with the cases of Blake and Duhon, is that a straight $/WARP calculation can produce some wonky results off of a poor season.  I looked at adjusting the WARP input to reflect an average of the past two seasons but the going rate remained nearly unchanged ($2.23 per win vs. $2.1 per win).  With that adjustment, Duhon and Rudy Gay became the summer’s worst deals.

Another assumption that this model makes is that production is constant.  Joe Johnson’s contract doesn’t look nearly as bad as it would if we considered his career arc and likely depreciation.  It’s the length that’s egregious; a two-year, $20 million is a much better deal than six-years , $120 million.

So is $2.23m/win an inflated price?  Compared to last year’s free agency, yes.  In fact, teams are paying about a $740,000 premium per win this offseason compared to last summer.  Using the same system for last year’s free agency, teams paid $1.49 million for each WARP unit in 2009.

But there’s still plenty of time for the Grand Opening excitement to calm and the price will likely slide a bit.  The other capped max contracts have yet to be handed out (Wade, LeBron, and Bosh) and their contracts will actually drive the going rate downward since they’re not paid on the free market.  The near $1 million premium may drop down to $500K or $250K by the end of summer.

But right now, players are seeing green.

NBA HD: Winging it with Length

June 17, 2010 in by with 3 Comments

The NBA draft is approaching.  Prepare for the cliches and buzzwords.

Freakish.

Tremendous.  Upside.  Potential.

Ceiling.

Length.

You’ll hear that last one probably the most. Length. Why do we care about length?  Well, extra length gives players advantages within a variety of basketball actions; deflections, live rebounds, and getting shots off requires extension above the opponent, to name a few.

Today’s post looks into the length of this year’s crop and who has notably long or short arms for their height.  It would be amusing to think of it the other way around but we don’t. This guy has the arms of a 6’2″ guy but he’s 6’8″!  He’s a giant!

Before we dig in, let me first say that Jonathan Givony’s Draft Express is our best friend and our valuable resource around draft time.  You can get all sorts of historical player measurements there.  I should also mention that they just started publishing advanced stats for college basketball.  Amazing stuff happening at Draft Express.

Anyway, the first thing I did was calculate the proportional wingspan of a player relative to his height using the prospect measurements dating back to 2000.  I used a regression to predict wingspan from player height (WITHOUT shoes on) with a sample of 916 NBA prospects.

Here we see a pretty strong linear relationship between player height and wingspan.  Want to know what your NBA prospect wingspan should be? Take 98.5% of your height in inches and add about 5.5.  My wingspan should be about 76 inches long.

Who has the longest go-go gadget arms of players that actually got drafted? Let’s take a look.

Oh my, the stars!  Not a very inspiring list, eh? Jason Maxiell had the most “freakish” arms as he’s one of those guys who can touch his knees without bending over.  Fingertip to fingertip, he is 10 inches longer than head to toe.  All told, his wingspan is about six inches longer than we’d expect and proportional for a 6-9 guy.  His extra wingspan is partly responsible for his rebounding rate we’d typically see from a center.

The rest of the list has some big time busts who may or may not have been overrated by their length.  Saer Sene got drafted 10th overall, Fred Jones 14th overall, and Shelden Williams 5th.  As we saw in Game 6, freakishly long arms cannot guarantee a successfully converted dunk in the biggest game of your life (right, Shelden?).  Marvin Williams, the second overall pick in 2005, sits just outside this list as his wingspan was 4 inches longer than we’d expect.

Some other notable extra wingspans: LeBron +0.5″. Thabeet +0.6″.  Durant +3.3″.  Beaubois +4.0″.

Let’s head over to the short arm prospects or as I like to call them, the capital T’s (just look at a capital T).  These guys have shorter arms than we’d expect given their height.

Martynas Andriuskevicius played only 9 minutes in his NBA career, way back in 2005 but he deserves a shot out here.  His arms were over six inches shorter than we’d expect given his 7’1.25″ height.  In reality, he has the wingspan of a 6’6″ guy.  Yes, observant reader, Fred Jones has a longer wingspan than Marty Andy.  For your information, he grabbed four rebounds in 9 minutes which translates to a crisp 17.8 rebounds per 40 mins.  Sample size be damned.

We have some pure shooters (Redick, Kapono) as well as some truly undersized point guards (Maynor, Jordan).  Redick relies on his hops more than most shooters since he wasn’t gifted with long arms. He got away with it in college but he’s taking threes at a much slower rate in the NBA, granted, for several different reasons.  Perhaps one of them is that he has the arms of a 6-footer.

Some notable curbed wingspans: Jon Brockman -3.7″, Chris Kaman -4.1″, Stephen Curry -3.0″, Jared Dudley -3.2″

While we’re at it, let’s go ahead and pull up the go-go gadgets arms and T’s of this crop of 2010 prospects.  First, the long arms:

And the T’s:

Looks like I’ve snooped out the market inefficiency that Coach K has been exploiting for years.  Short armed scorers.

In the future, expect some application of these measurements to NBA production to test their significance in predicting professional success.

NBA HD: Inching For A Rebound

May 21, 2010 in by with 4 Comments

In last week’s post, I looked at the relationship between team height and rebounding.  It’s a good jumping off point to investigate the value of height in today’s game.  Building from that, I’d like to tighten my focus and hone in on the play-by-play data.  Aaron Barzilai graciously publishes play-by-play lineup data on his website basketballvalue.com and I’ll be playing around in that sandbox today.

Looking at the lineups, how much did a height advantage affect rebounding?

This approach improves upon last week’s analysis in a couple ways.  To start, we’re looking at play-by-play lineup data as opposed to overall rebounding numbers on a season-level.  This allows us to look into detailed matchups and focus on units rather than full rosters.  Secondly, I’m solely looking at the 3, 4, and 5 positions to better reflect those who affect rebounding the most.  In last week’s study, a few people pointed out that Derek Fisher’s smallness skewed the Lakers height numbers even though he doesn’t really matter on the boards.  (Perhaps the best solution is to weight the effective height by position).

The way the data is presented in the basketballvalue format is as follows:

Which ten players were on the floor? How many possessions were they on the court for?  How many offensive and defensive rebounds did each unit have?

Before I dove headfirst, I made some qualifications.  The units would have to have at least 30 possessions on the floor together.  Thirty possessions isn’t a whole lot (a little more than a quarter’s worth of a basketball game) but with the players held constant, it seemed like a fair line in the sand.  This qualifier eliminates about 63,000 lineup units and leaves a remaining sample of 326.

From there, I calculated the average height of the 3,4, and 5 players on each team and compared them to their opponent.  The widest margin of average height between two lineups was 10 inches or 3.3 inches per player (Grizzlies vs. Rockets). We’ll take a closer look at that matchup later.

For each lineup, I gathered their offensive, defensive, and total rebounding percentages during that time period. So, for example, a dataset may read as follows:

Westbrook, Sefolosha, Durant, Green, Krstic
Frontcourt avg height (Durant, Green, Krstic): 82.0 inches
ORR,DRR,TRR: 30.4%, 87.5%, 53.8%
vs.
D.Williams, Miles, Matthews, Millsap, Boozer
Frontcourt avg height: 79.3 inches
Margin: 2.7 inches
Possessions: 48

So, here we see that this particular Thunder unit made the most of their height against this specific lineup of the Jazz, grabbing 53.8 percent of all rebounds and locking up the defensive boards in partifular (87.5 pct).    Boozer and Millsap are known as talented board cleaners but against the Thunder height,they couldn’t make up the difference.  But not all matchups work in the taller team’s favor.  Digest:

Conley, Mayo, Gay, Randolph, Thabeet
Frontcourt avg height (Gay, Randolph, Thabeet): 83.0 inches
ORR, DRR, TRR: 10.5%, 72.2%, 40.5%
vs.
Brooks, Martin, Ariza, Scola, Hayes
Frontcourt avg height: 79.7 inches
Margin: 3.3 inches
Possessions: 36

Here, we see that the far superior team (in terms of height) got worked on the boards by their smaller foes.  In this matchup, the Grizzlies missed 19 shots but only recovered 2 of those missed shots.  That’s quite an accomplishment for a team giving up 10 inches underneath.  Once again, we bow down to Chuck Hayes’ rebounding prowess.

But these are just two of the 326 matchup pairings that lasted 30 possessions.  What does it look like when we look at all observations in the sample?

Here, we have all 362 lineups and their total rebounding percentages.  As you can see by the positive trendline, the taller the frontcourt, the more rebounds collected (p<.0001).  Earth-shattering stff, I know.  But how much does an inch help? We can use that handy regression equation:

Total Rebounding Percentage = 0.0165*(Height Advantage) + 0.4983

So, for every inch gained in Height Advantage, meaning each frontcourt player has an inch on average on their opponent, we would predict the total rebounding percentage to increase by 1.65 percent.  What’s 1.65 percent? For reference, the Thunder are the sixth best rebounding team in the NBA according to TRR and they are 1.69 percent better than average.   All else equal, having an inch on your opponent matters, but it won’t guarantee a rebound.  In case you were wondering, the lone blue dot on the bottom right represents the Memphis Grizzlies lineup mentioned above.

How about strictly looking at offensive rebounding? Does height more critical on the offensive boards?

It doesn’t appear that height margin matters more on the offensive boards than overall, given that they have nearly identical coefficients (0.01645222 vs. 0.01645211 to be exact).  Like overall rebounding, an inch in average height advantage tends to lead to 1.65 percent more offensive boards.  Any interesting matchups? As you can see on the graph, some units failed to get a single offensive rebound (0.0% ORR).  Who were they? For fun, let’s take a gander:

Curry, Ellis, Maggette, Hunter, Tolliver (-1.7")
vs.
Nash, Richardson, Hill, Stoudemire, Lopez
11 rebounds
31 possessions
-
Rondo, Allen, Pierce, Garnett, Perkins (-1.3")
vs.
B.Davis, Butler, Thornton, Camby, Kaman
13 rebounds
35 possessions
-
Udrih, Greene, Casspi, Thompson, Hawes (+0.3")
vs.
Fisher, Bryant, Odom, Gasol, Bynum
12 rebounds
31 possessions
-
Fisher, Bryant, Artest, Gasol, Bynum (+1.0")
vs.
Foye, Miller, Butler, Jamison, Haywood
9 rebounds
32 possessions

You got the obvious Warriors Nellieball lineup but you also have the Lakers on both ends of the deal.   I’m not surprised that the Odom, Gasol, Bynum lineup grabbed all 12 available rebounds even with Donte Green at the 2.  That’s a ridiculously tall lineup.  However, I didn’t expect the Lakers to be on the losing end of the deal against the pre-trade Wizards.  Interesting stuff, I say.

On the offensive end, it still holds that the taller your frontcourt, the more offensive boards you will tend to collect.  Let’s finish up with the defensive side of the boards.

Again we see a positive relationship with height advantage and rebounding rates but the coefficient here is greater (0.0175).  This means that an inch advantage on the defensive end tends to increase defensive rebounding percentage by 1.75 percent.  This contradicts my finding in last week’s exercised that showed that team minutes-adjusted height had almost a completely random correlation with defensive rebounding rate.

In the end, conventional theory holds true that it helps to be taller in order to grab rebounds. However, it’s not as strong of a correlation as I expected.  Of course, height doesn’t explain all the variation in rebounding rates because there are other factors that contribute to rebounding: wingspan, vertical jump, horizontal jump, reaction time, positioning, etc.  I like that this study holds the lineup personnel constant but I would always like to get a larger sample size. But that has it’s drawbacks too.  When we increase the requirement threshold, we lose reliability.

How do we reconcile this study with last week’s that said height mattered more to offensive rebounding?  Last week’s looked at the forest rather than the trees.  I only had 30 teams in the sample size and the height effects could have been clouded in the aggregate numbers.  Additionally,  in this post, I tried to improve the validity of the measure by only looking at the frontcourt height rather than the whole five.  Perhaps a weighted height would be the best option, giving more weight to the bigger position and less weight to the point guard position.  For another time.

Again, have to thank Aaron for providing such a helpful resource.  Assist point to you, sir.

NBA HD: Time for Time of Possession

May 6, 2010 in by with 2 Comments

It seems as though I stumble upon a new basketball advanced stats site every week.  I found statsbynumbers.com after it was linked to in the APBRmetrics forum last Tuesday and I’ve been very impressed with what I’ve seen.  So far, the founder of the site has uploaded the post season data and will be publishing regular season data soon.  Each box score on the site is packed with data found in the play-by-plays, some of which you can’t find anywhere else.

In today’s post, I’m particularly interested in the Time Of Possession box.   Haven’t seen this in an NBA box score before.  NFL, yes, but this is new territory for basketball analysis as far as I can tell.  The number tells us how long each team controlled the possession for the game.  For example, in the box score from Suns-Spurs Game 1, we find that the Spurs had possession of the ball almost 2 minutes longer than the Suns did (24 mins 51 seconds vs. 23 mins 09 seconds).  Simple stuff but has some interesting implications for our understanding of pace.

Typically, when we talk about a team’s pace, we usually refer to the number of possessions in a game and then we aggregate those possessions over the course of a season to get a team’s average pace.  So the Golden State Warriors play at ludicrous speed and their average possessions per game of about 103 reflects their lead foot in the automotive proverbial sense of the phrase.  Contrast that with the Blazers who play at a slow crawl (90 possessions per game).

But on an individual game level, the possession total has minimal interpretation value.  If a regulation game lasted 100 possessions, we know it was up-tempo but we wouldn’t know who stepped on the gas.  We can make judgments from our prior knowledge of each team’s typical pace but often times that misses the mark.

That’s where Time of Possession comes in. Turns out, time of possession can vary wildly in the same game.  In Game 3 of the Lakers-Thunder series, the Lakers had the ball 5 minutes and 38 seconds longer than the Thunder.  That’s a half a quarter’s worth of time!   Like I said, statsbynumbers.com only has this year’s playoff data up on the site but that didn’t stop me from digging deep into the numbers.  For each game, I gathered each team’s time per possession and their total time of possession listed.

Who had the quickest one-game pace of the playoffs so far?  That would be Denver when they lost by 3  to Utah in Game 2 of their series, averaging just 13.7 seconds per possession in that contest.  Here are the top ten fastest of the postseason:

That Utah – Denver series was fast wasn’t it? They both like to play up-tempo basketball so it’s not a surprise to see track meets when they went head-to-head.  Also interesting was that Chicago’s time per possession in their Game 4 was slower than Cleveland’s Game 2 dud against Boston even though Chicago saw seven more possessions.  92 possessions may seem like a methodical pace but actually Cleveland did their best to speed up that game.

I expected the top ten to be filled with teams on the wrong end of a blowout since, anecdotally, teams down big like to get quick shots off to extend their breathing room.  But we have some close wins here as well as some routs.

How about the slowest performances of the playoffs?

Lakers opened up that Oklahoma City series by running through their sets and not letting their youthful opponents dictate their style of play.  Eventually, the Lakers were going to find their holes in the defense through patience and crisp passing.  In this one, the Lakers had the ball for over four minutes longer than the Thunder.

Portland was the slowest team in the NBA and they certainly didn’t give in to the Suns up-tempo style of play in Game 5.  On average, the Blazers drained the shot clock to 6 seconds remaining on every play in that game.  Didn’t expect to see two teams lose by double digits near the top of this list but the teams themselves (Charlotte and Portland) didn’t shock me.

Watching Game 7 of the Milwaukee – Atlanta game was like taking an Ambien.  Also, it’s worth noting that Game 3 of the Lakers – Thunder series featured some of the slowest and fastest tempos of the playoffs with the Thunder winning the battle by 5 points.

Comparing the two lists, we find that about five seconds separated the fastest time per possession to the slowest.  We don’t have regular season data on hand to look at the Denver vs. Portland games but Phoenix sufficed as a tortoise vs. the hare matchup– Phoenix had a faster average pace than Denver during the regular season.

Let’s take a step back and look at the fastest average time per possession of the playoffs.  Remember, this is a small sample, especially in the case of Charlotte who played just four games in the playoffs.

Phoenix finished the regular season with a faster tempo than Denver, but only by a nose.  In the postseason, the Nuggets actually paced the field before their first round exit.  Some other notables on this list include Boston matching Phoenix and Lakers not letting the fast pace of the Jazz and Thunder rush their triangle offense.

I’m not sure time of possession will stick in our basketball vernacular anytime soon but it undoubtedly adds some valuable information.  As we’ve seen, the number of possessions can mislead us into thinking that each team followed the same speed, which simply isn’t true– just look at Game 3 of the Lakers vs. Thunder series.  With more data in the regular season, we could analyze how teams respond to dissimilar styles of pace more accurately.  In general, do teams mold to their opponent’s pace or do they proudly go in the opposite direction? How does a coaching change affect their team’s tempo?  Which teams keep their tempo most consistently? All these questions are fair game, thanks to the assembly of data from statsbynumbers.com.

NBA HD: Offensive Orientation and Re-Estimating ORR

April 30, 2010 in by with 7 Comments

Carl Landry came up in a conversation I had recently.

In his rookie season in 2007-08, Landry grabbed 15.5 percent of the Rocket’s missed shots while he was on the floor, a rate that placed him atop the list of every player in the NBA.  Remarkably, the Rockets found a guy in the second round of the draft who immediately stepped in as the best mess cleaner in the NBA.  Not three years down the road. Immediately.

And two seasons later, Landry is a below-average offensive rebounder at his position.

As surprising as it might be, Landry isn’t a vacuum around his basket anymore.  His offensive rebounding rate (ORR) could be micro-graphically illustrated by the backslash on the keyboard in front of you.  From 15.5 percent in 2007-08, his ORR slid down to 10.3 percent in his sophomore campaign, and 8.5 percent this past season.  But if we focus solely on his brief stint for Sacramento, his ORR stood at 7.1.  If you’re scoring at home, you’ll notice that his once elite offensive rebound production has been slashed in half.

One can look at these numbers and arrive at several conclusions.  ”Carl Landry can’t rebound anymore.“… ” Carl Landry is a phony.“… “Please, stop talking about this new-fangled stat, ORR. You sound like a damn fool.” … “OK, so what’s your point?”

Well, I think we’re missing an important piece of the puzzle: Carl Landry isn’t playing around the basket offensively anymore.   Sacramento has the Purdue alum playing further away from the rack and as a result, he has shot long twos twice as often as he did in Houston.  So he may not grab as many offensive rebounds but that doesn’t necessarily mean he’s no longer skilled as an offensive rebounder. This is an important distinction.

I bring up the case of Carl Landry because I was looking at the great work of Terrance Laney (@bbstats on Twitter) and I noticed something interesting about the players who ranked at the bottom of his position and height adjusted total rebound rate list (in laymen’s terms, who rebounds better or worse than you’d expect given their height and position).  In the bottom 10, you find players like Dirk Nowitzki, Andrea Bargnani, Channing Frye, Zydrunas Ilgauskas, Rashard Lewis and Matt Bonner.  Notice a common bond?  That’s right, perimeter shooters who happen to be very tall.

So are these tall marksmen the least skilled rebounders in the NBA or has their shooting repertoire pushed them away from the rebounding zone?  I think it’s more of the latter.  In some cases, ORR isn’t the best proxy for rebounding ability in the same way that field goal percentage isn’t as good of a proxy for shooting efficiency as effective field goal percentage for 3-point shooters.

With that in mind, I went back to the drawing board with the help of the indispensable Ed Kupfer and modeled a new expected ORR using a logistic regression that adjusts for position (PG, C, PF, SF, SG, F), height( in inches) and percentage of shots on the perimeter (PerPct) which is simply the percentage of shots outside 16 feet.   Why do we add the perimeter factor? We’re looking to isolate skill from the factors unrelated to offensive rebounding ability so this accounts for the perimeter shooters who don’t grab offensive boards because of their outside offensive orientation.  For example, Carl Landry could still be a worthy offensive rebounder even though he has migrated to the perimeter.  The model can be seen here for those who care to see the details.

So let’s take a look at the player’s who went above and beyond what we would expect given their position, height, and their shooting orientation.

Without context, a 14.2 ORR is extraordinarily impressive but after you consider that Jordan Hill took almost half his shots from the perimeter, he looks even better.  As a Knick, Jordan Hill collected tons of offensive rebounds and he might have been even more underrated than his 14.2 ORR would suggest, given his orientation on the Knicks offense.  Some might see Jordan Hill as a deal throw-in but he possesses a knack for offensive rebounding not unlike his Rockets predecessor Carl Landry.

Coming up on his 36th birthday, Antonio McDyess can still bring it.  He’s an above-average offensive rebounder even for his position and as the 8th most frequent long two taker in the NBA, his offensive rebounding rate in San Antonio is absolutely superb.  All things considered, we would expect his offensive rebounding rate to be half of what it actually is.  Impressive.

Interestingly enough, Zydrunas Ilgauskas finds himself as one of the leaders here despite ranking poorly as a rebounder in Laney’s study.  Why? Like McDyess, he’s a perimeter shooter disguised as a big man.  He cleans up the glass much better than this model would expect.

And how about the trailers?  The players below don’t rebound nearly as much as this model thinks they should.

Etan Thomas might be the Thunder’s highest paid player but this presents another reason why he has barely gotten any run recently.  He hugs the basket on offense and yet he doesn’t offer much in the way of getting second chance opportunities.  Having taken just 12 shots outside 10 feet his year, we would expect Thomas to have more boards with his rim-centric habitat.

Whereas Ilgauskas shines in this light, Dirk Nowitzki still rates as a poor rebounder on the offensive end.  80 offensive rebounds in 3,039 minutes still carries a stench even with the perimeter game adjustment that lowers his expected rate from 9.6 percent to 6.6 percent.  This is his lowest ORR since his 2002-03 season in which he, not coincidentally, posted his highest 3-point frequency of his career.

Whenever we engineer new basketball stats, we try to strip away the luck and circumstance that blemishes the current ones.  If we want to isolate the offensive rebounding skill, it helps to find out who hangs around the rim and still can’t get a board, not just those who are tall.  Perimeter shooting percentage won’t perfectly estimate a player’s offensive orientation but until we put microchips in every player’s shoe, there will always be a margin of error.  Still, this is a big step in that direction.  If you’d like to see the whole dataset, I’ve uploaded it here on Google Docs.  I’d also like to salute Ed and Terrance again for their inspiration and assistance. Cheers.

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