I had a typo in one of my spreadsheet formulas, which was screwing up the possession usage data in the Georgetown players' skill curves. I've corrected the figures and accompanying text - the story has changed a bit now, especially as it relates to Austin Freeman and the other returning players, so if you've already read this article, you might want to re-read the last section.

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For better or for worse, the media, the fans and even the Georgetown Athletic Department have embraced the notion that this season's Hoya team will be led by it's three McDonald's All-Americans: Greg Monroe (soph), Chris Wright (junior) and Austin Freeman (junior).

These are the only three returning players that we credit with positive net points (created more points than they allowed) from last season, so it seems natural that they would become the core of the team.

A trio of players leading the team is not new. During the JTIII era, there have been typically three players who use ≥22% of available possessions each season. If all players shared the ball equally, we'd expect a possession usage of 20%, so in effect the offense is usually dominated by three guys.

.Player%Poss%MinORat2004-5 Bowman 24.2 82.7 112.4 . Green 23.8 84.0 111.5 . Hibbert 25.3 39.3 89.2 . Cook 20.3 80.1 102.3 2005-6 Green 25.4 80.7 102.7 . Hibbert 25.6 59.6 120.9 . Bowman 24.6 70.7 101.0 . Cook 18.1 76.8 113.0 2006-7 Green 24.9 83.0 114.4 . Hibbert 22.8 65.7 130.8 . Summers 22.0 65.7 101.8 . Wallace 18.9 80.2 119.7 2007-8 Hibbert 25.9 66.0 120.5 . Summers 23.8 67.5 104.0 . Sapp 22.7 66.4 105.5 . Wright 21.9 42.4 97.7* . Freeman 18.1 63.9 115.9 2008-9 Summers 24.4 72.0 104.0 . Monroe 22.9 76.0 110.9 . Wright 21.3 81.5 107.2 . Freeman 19.4 74.3 115.6 *Wright missed 18 games his freshman year, so his usage stats aren't easily compared to his teammates.

Usually, the next man in line for possessions is much more efficient offensively than at least one of his more aggressive teammates. Last season the "next man in line" was more efficient than all three players who were ahead of him.

That man was Austin Freeman. It's also worth noting that he was able to keep a high offensive rating despite having his 3FG shooting accuracy drop from 40% to 31% from his freshman to sophomore season. One could reasonably hope that he will be even more proficient this year.

There are two fundamental hurdles that he - and any player looking to step into a bigger role - must overcome. We'll call them inertia and marginalism. Each of these concepts is fundamental to a pair of questions we'll ask about Austin Freeman coming into this season:

- Can Austin Freeman increase the rate at which he uses possessions, to become a go-to offensive player rather than just a complementary one?
- Will there be a cost in his offensive efficiency if he does use more possessions?

Inertia

A couple of years ago, Ken Pomeroy posted an article on Basketball Prospectus noting that

[o]nce a player demonstrates himself to be a role player, it's unlikely he'll ever be a go-to guy and, therefore, a superstar. It's not quite a law in college basketball, but players who are not very involved in the offense tend to stay that way. Any major changes in a player's usage are usually the result of filling the hole left by a departing possession eater.I found this point compelling, so much so that I wrote about this each of the past two pre-seasons, and here I am doing it again.

As an aside, an important point to keep in mind during this discussion is that we are discussing usage rate (a percentage), not possessions used (a counting stat). As players receive more minutes of playing time, their counting stats will naturally increase. But here we are concerned with how their rate statistics change, which should better indicate a change in behavior or ability.

Greg Monroe and Chris Wright appear naturally predisposed toward using possessions - Wright has used ~22% of available possessions each of the first two seasons, and Monroe was using more than 23% last year. This was a good thing last season, as both were more efficient than the team overall, especially when looking at performance versus Top 100 opponents. In fact, they were the second and third best option on offense in those games. The most efficient offensive player, whether you look at vs. Top 100 teams, conference games or even all games, was Austin Freeman.

Can we expect that Freeman will use significantly more possessions this year? First, let's see if we learned anything from his freshman to sophomore growth.

From the table above, we see that the Hoyas went into last year with only one possession-eater lost (Hibbert) and three returning (Summers, Sapp and Wright). So possessions were available, but there wasn't a wholesale change at the top.

To understand the year-to-year change in possession usage a typical Big East player experiences, we can take a look at all Big East players from 2005-2008 and fit a line through their possession usage rates from one year to the next. I've attached a figure from last year's article - you'll need to go back and read that post to understand all of what's going on in it, but for now all we care about is the solid black line that is fitted to the circles (click on the figure to enlarge).

The typical Big East player will increase his usage from one year to the next, so long as he used less than 22% of possessions in the previous year. Players who used more than 22% of possessions the previous season tend to use less. Moreover, we can use that fitted black line to actually estimate how many more possessions a player would be expected to use the next season.

Austin Freeman went into last season having used 18.1% of possessions as a freshman. Based on historical Big East growth rates, we expected him - on average - to use 18.9% of possessions as a sophomore. He actually exceeded that by a bit (19.4%). So it looks like Freeman is fairly well-described by our little model, or perhaps we're being a bit conservative.

This season, the Hoyas again have lost one possession eater (Summers) and return two (Wright and Monroe), so we'd expect about the same change or increase in usage from the returning players.

If we apply the model towards next season, we'd only expect Freeman to use 20.0% of available possessions, which would frankly be a bit disappointing in light of his offensive ability. Let's take this a bit further. Because we are über-geeks here, we can actually predict what his usage rates would be under favorable (75th percentile) and extraordinary (95th percentile) conditions, just as Pomeroy did.

Assuming the model is good for Freeman, an increased usage to the magical 22% rate - both the seeming natural usage rate for players and the top tier for players in the Georgetown offense - has about a 1 in 4 chance of happening this season. It's tempting to say that he'll likely take more than 20% of possessions, since he used more than predicted last year (or to say that there is better than a 1 in 4 chance he'll get to 22%), but I'm a bit hesitant to draw this conclusion from one data point (his change from freshman to sophomore year).. Year 2 Year 1: 19.5% Expectation . Average 20.0 75th percentile 22.0 95th percentile 25.5

Marginalism

Throughout the above discussion, we were only concerned with the percentage of possessions Austin Freeman might use this year, with the hope that he might increase his usage rate more than expected. The assumption is that a sharp increase in possession usage by Freeman would help the team because he is the team's most efficient scorer. Taking some of Summers' and Sapp's possessions and scoring on them at Freeman's rate will help the offense.

But if Freeman takes more possessions and shots, would he remain as efficient a scorer? As a player takes more and more possessions from his teammates, does his efficiency decrease, and by how much?

The law of marginal utility (i.e. "diminishing returns") should be familiar to anyone who's had to suffer through an economics class. Simply, as a resource is increasingly available or used, the utility of each quanta of the resource decreases. In plainer English, the more abundant an item, the less its value. Think crop prices, or water rates.

To my best knowledge, this idea of marginal return was first applied to basketball by Dean Oliver, who wondered if players were more offensively efficient when they used fewer possessions. He discusses this in his book Basketball on Paper, and, to this end, he looked at three NBA players: Jerry Stackhouse, Michael Jordan and Georgetown's very own Allen Iverson via what he calls "skill curves" (I've reproduced his plot here):

To my way of thinking, he's got the axes backwards (usage rate is the independent variable and therefore should be on the X-axis) but the conclusions from the data are still clear. I'll flip the axes to make my point, though (and ignore that red line for a moment):

As players increase their usage - the percentage of possessions they use - they become less efficient.

However, it's not a smooth curve, but rather a sigmoidal fit (an S-curve), so that there is a big jump between efficient usage and inefficient usage. That notch varies from player to player, and Jordan's greatness shows up by where his notch is: he can produce a 120 offensive rating (1.2 pts. per poss. used) even while using more than 30% of available possessions.

There is a common criticism of Oliver's work, summarized recently by Kevin Pelton over at Basketball Prospectus:

This is all well and good, but is this information applicable to Austin Freeman, or the Hoyas more generally?

To find out, I compiled efficiency vs. usage stats for the past three seasons for Georgetown, much like Oliver did. I don't have the energy, and probably not the skills either, to redo Witus' work. Here, I simply compiled offensive rating vs. poss. usage rate for each player in each game, using my HD Box Score program, which should be more accurate than using the traditional box score calculations.

The data tends to be quite a bit more noisy than Oliver's plots, mainly because there aren't nearly as many games to sort through. Oliver looked at 2 NBA seasons (164 games), while I have data for 88 Georgetown games over the last three years. I've also used relatively narrow "bins" or ranges of possession usage to average - I'm using increments of 2.5% (e.g. averaging games with 15% - 17.5% poss. used). I've done this so each player's skill curve will have at least 8 points. I've included standard deviations for each bin to help indicate that noise - a point with no error bars is from a single game.

We'll start with Roy Hibbert and Jon Wallace, combining their junior and senior seasons. Here, Witus' expected decline rate is now indicated by the dashed gray line.

We don't see the notch - the big and sudden drop in efficiency at high usage rates - but there also aren't the extremely high usage rates that the NBA stars can reach. What we do see is that the decline looks very different for the two players.

Hibbert - a high usage player - was incredibly efficient at virtually every usage rate (and I have no idea why he has that drop when he used less than 10%), good for about a 130 Off. rating when using between 12% and 33% of possessions. His efficiency finally starts to drop at extremely high usage rates (>35%), but even this part of the curve is being drive by a single game (against Michigan, Nov. 2007).

Wallace - a low usage player - has a very different skill curve. There's a lot more noise in his data, which I believe is attributable to his high dependence on 3pt shooting. He also suffered from a much steeper drop in efficiency as he used a higher percentage of possessions. If we fit a line to his curve (not shown) we'd see that his expected offensive rating drops below 100 around 25% of possessions used. And since he was surrounded by other skilled offensive players, it makes intuitive sense that we'd not want him to use much more that 20% of possessions, which was his natural behavior.

Next up are Sapp and Summers, for whom I have the last three seasons. I've left the Witus line at the same location as for the Hibbert/Wallace plot, to allow for easy comparison.

While Summers was a forward and Sapp a guard, the slopes of their efficiency curves are quite similar. They both shot about half of their shots from outside (Sapp: 428/811 3FGA/FGA = 52.8%, Summers: 411/838 = 49%) at about equal proficiency (Sapp: 34.5% 3FG, Summers: 35.1%) over their careers, so this may not be entirely surprising. Once again, we see no notch in their curves, but a decline in efficiency at increasing usage not as steep as for Wallace. Sapp, especially, showed a steady drop paralleling the Witus line, although he seems to have an upward notch at the 25% usage rate. I wonder if this is the effect Pelton discussed; Sapp - who I think was always under-appreciated for his basketball sense - may have been more adept at recognizing and exploiting a favorable matchup.

At even moderate usage (>15%), neither player showed an area of high efficiency (>120 off. rating), but Summers did post some very high off. ratings at the lowest usage bins (although those were highly variable). This is not to say that these were poor offensive players - a 120 off. rating is very good - but neither looked to be a consistently great offensive player, even when not required to carry the load.

Now that we've got some context, let's take a look at how Austin Freeman has performed over the last two seasons.

Freeman's curve is a bit harder to make sense of, as he's got that big drop in efficiency when using 17.5-20% of possessions. In a bit of a statistical fluke, most (7 of 9) of the games that make up this bin are from his freshman year, and that dip seems to be due to his freshman games (his two sophomore games in the bin are amongst the three best of the bin). More on year-to-year improvement below.

Ignoring that dip, we see that Freeman can be an elite offensive player when he's using less than ~22% of possessions, operating at the level of Hibbert and Wallace rather than Summers and Sapp. Also, it's apparent that Freeman does not do well when he takes on a higher load - above 22% of possessions used his off. rating drops below 100, i.e. to a mediocre level.

So here we are faced with a conundrum - Freeman has been anointed to be one of the big 3 players for the Hoyas this season, but his offensive game suffers greatly when he steps into the high usage (>22%) role.

I'll now add Wright and Monroe to Freeman's graph:

As you can see, Monroe also has the drop in his skill curve, although his looks to drop below a 100 off. rating somewhere around 27% of possessions used.

Chris Wright's curve is a complete mess. That huge drop at low usage rate is the average of two games against Pitt, including the 2008 BET when he put up 0 points created in 30 possessions played. But even ignoring that point, his skill curve just doesn't seem to obey the rules of efficiency vs. usage. I don't know if this is a result of the 18 games he missed during his freshman year or his inconsistent outside shooting, but I'll refrain from further comment until we get another season to add to the database.

Am I underselling Freeman's potential for this year?

There is one critical point that I've been ignoring here: year-to-year improvement. Unlike Oliver and Witus, we aren't discussing mature NBA players, but college kids who are still developing their skill sets and learning a complicated offensive scheme.

To address this, I've come up with a simplistic plot. I've taken all Big East players for the 2005-2008 seasons who played at least 10% of available minutes, and found the difference between their current and previous year's poss. usage and off. rating. For example, looking at Austin Freeman:

The markers are color-coded by Year-2 offensive rating and sized by Year-2 percent minutes played. The fitted line (with the fit weighted by % min) is the black line, with the 75% and 95% prediction bands in blue and gray, respectively.

The evidence is not promising. That line has a negative slope, just as Witus saw for NBA players. Ours has a gentler slope, but still shows that a 1 percent increase in possession usage from one season to the next will cost an average Big East player about 0.78 points in off. rating.

All I can offer is that the correlation is extremely weak: the 1σ uncertainty of that slope is 0.73, which is to say that it is just barely significant. To put it another way, of the 274 player-seasons we're looking at here, 80 showed an improvement in offensive rating while increasing possession usage. Or take a look at Chris Wright, who improved his offensive rating 9.5 points (97.7 to 107.2) with a drop of only 0.6 points in usage (21.9 to 21.3).

Could inherent talent (using, e.g. RSCI ranking as a metric) help some players to improve offensively in spite of increased usage? That study will have to wait for another day.

As players increase their usage - the percentage of possessions they use - they become less efficient.

However, it's not a smooth curve, but rather a sigmoidal fit (an S-curve), so that there is a big jump between efficient usage and inefficient usage. That notch varies from player to player, and Jordan's greatness shows up by where his notch is: he can produce a 120 offensive rating (1.2 pts. per poss. used) even while using more than 30% of available possessions.

There is a common criticism of Oliver's work, summarized recently by Kevin Pelton over at Basketball Prospectus:

Most past efforts [to understand efficiency vs. usage in the NBA] were tripped up by the problem of looking at usage on a game-by-game basis. Naturally, players will use more possessions on nights where they have a more favorable matchup, so it is not surprising that these studies actually found that players' efficiency rose as their usage increased.More recently, Eli Witus expanded greatly upon this pioneering work by comparing high-usage and low-usage lineups for the 2007-8 NBA season, to find a relationship between player usage rates and efficiency without the confounding effect described by Pelton. I won't go into much detail here - the article may be a bit advanced for non-geeks - but the upshot was that he found that, if a player increases his usage rate by 1%, his efficiency will decrease by 1.25 points. This result is that red line added to the graph above. While it doesn't apply to Jordan, this new analysis actually shows good agreement with Oliver's work with "normal" NBA superstars.

This is all well and good, but is this information applicable to Austin Freeman, or the Hoyas more generally?

To find out, I compiled efficiency vs. usage stats for the past three seasons for Georgetown, much like Oliver did. I don't have the energy, and probably not the skills either, to redo Witus' work. Here, I simply compiled offensive rating vs. poss. usage rate for each player in each game, using my HD Box Score program, which should be more accurate than using the traditional box score calculations.

The data tends to be quite a bit more noisy than Oliver's plots, mainly because there aren't nearly as many games to sort through. Oliver looked at 2 NBA seasons (164 games), while I have data for 88 Georgetown games over the last three years. I've also used relatively narrow "bins" or ranges of possession usage to average - I'm using increments of 2.5% (e.g. averaging games with 15% - 17.5% poss. used). I've done this so each player's skill curve will have at least 8 points. I've included standard deviations for each bin to help indicate that noise - a point with no error bars is from a single game.

We'll start with Roy Hibbert and Jon Wallace, combining their junior and senior seasons. Here, Witus' expected decline rate is now indicated by the dashed gray line.

We don't see the notch - the big and sudden drop in efficiency at high usage rates - but there also aren't the extremely high usage rates that the NBA stars can reach. What we do see is that the decline looks very different for the two players.

Hibbert - a high usage player - was incredibly efficient at virtually every usage rate (and I have no idea why he has that drop when he used less than 10%), good for about a 130 Off. rating when using between 12% and 33% of possessions. His efficiency finally starts to drop at extremely high usage rates (>35%), but even this part of the curve is being drive by a single game (against Michigan, Nov. 2007).

Wallace - a low usage player - has a very different skill curve. There's a lot more noise in his data, which I believe is attributable to his high dependence on 3pt shooting. He also suffered from a much steeper drop in efficiency as he used a higher percentage of possessions. If we fit a line to his curve (not shown) we'd see that his expected offensive rating drops below 100 around 25% of possessions used. And since he was surrounded by other skilled offensive players, it makes intuitive sense that we'd not want him to use much more that 20% of possessions, which was his natural behavior.

Next up are Sapp and Summers, for whom I have the last three seasons. I've left the Witus line at the same location as for the Hibbert/Wallace plot, to allow for easy comparison.

While Summers was a forward and Sapp a guard, the slopes of their efficiency curves are quite similar. They both shot about half of their shots from outside (Sapp: 428/811 3FGA/FGA = 52.8%, Summers: 411/838 = 49%) at about equal proficiency (Sapp: 34.5% 3FG, Summers: 35.1%) over their careers, so this may not be entirely surprising. Once again, we see no notch in their curves, but a decline in efficiency at increasing usage not as steep as for Wallace. Sapp, especially, showed a steady drop paralleling the Witus line, although he seems to have an upward notch at the 25% usage rate. I wonder if this is the effect Pelton discussed; Sapp - who I think was always under-appreciated for his basketball sense - may have been more adept at recognizing and exploiting a favorable matchup.

At even moderate usage (>15%), neither player showed an area of high efficiency (>120 off. rating), but Summers did post some very high off. ratings at the lowest usage bins (although those were highly variable). This is not to say that these were poor offensive players - a 120 off. rating is very good - but neither looked to be a consistently great offensive player, even when not required to carry the load.

Now that we've got some context, let's take a look at how Austin Freeman has performed over the last two seasons.

Freeman's curve is a bit harder to make sense of, as he's got that big drop in efficiency when using 17.5-20% of possessions. In a bit of a statistical fluke, most (7 of 9) of the games that make up this bin are from his freshman year, and that dip seems to be due to his freshman games (his two sophomore games in the bin are amongst the three best of the bin). More on year-to-year improvement below.

Ignoring that dip, we see that Freeman can be an elite offensive player when he's using less than ~22% of possessions, operating at the level of Hibbert and Wallace rather than Summers and Sapp. Also, it's apparent that Freeman does not do well when he takes on a higher load - above 22% of possessions used his off. rating drops below 100, i.e. to a mediocre level.

So here we are faced with a conundrum - Freeman has been anointed to be one of the big 3 players for the Hoyas this season, but his offensive game suffers greatly when he steps into the high usage (>22%) role.

I'll now add Wright and Monroe to Freeman's graph:

As you can see, Monroe also has the drop in his skill curve, although his looks to drop below a 100 off. rating somewhere around 27% of possessions used.

Chris Wright's curve is a complete mess. That huge drop at low usage rate is the average of two games against Pitt, including the 2008 BET when he put up 0 points created in 30 possessions played. But even ignoring that point, his skill curve just doesn't seem to obey the rules of efficiency vs. usage. I don't know if this is a result of the 18 games he missed during his freshman year or his inconsistent outside shooting, but I'll refrain from further comment until we get another season to add to the database.

Am I underselling Freeman's potential for this year?

There is one critical point that I've been ignoring here: year-to-year improvement. Unlike Oliver and Witus, we aren't discussing mature NBA players, but college kids who are still developing their skill sets and learning a complicated offensive scheme.

To address this, I've come up with a simplistic plot. I've taken all Big East players for the 2005-2008 seasons who played at least 10% of available minutes, and found the difference between their current and previous year's poss. usage and off. rating. For example, looking at Austin Freeman:

I've compiled all available player-seasons (n=274) in this graph:SeasonPoss %ORat2007-8 18.1 115.9 2008-9 19.4 115.6 Diff. +1.3 -0.3

The markers are color-coded by Year-2 offensive rating and sized by Year-2 percent minutes played. The fitted line (with the fit weighted by % min) is the black line, with the 75% and 95% prediction bands in blue and gray, respectively.

The evidence is not promising. That line has a negative slope, just as Witus saw for NBA players. Ours has a gentler slope, but still shows that a 1 percent increase in possession usage from one season to the next will cost an average Big East player about 0.78 points in off. rating.

All I can offer is that the correlation is extremely weak: the 1σ uncertainty of that slope is 0.73, which is to say that it is just barely significant. To put it another way, of the 274 player-seasons we're looking at here, 80 showed an improvement in offensive rating while increasing possession usage. Or take a look at Chris Wright, who improved his offensive rating 9.5 points (97.7 to 107.2) with a drop of only 0.6 points in usage (21.9 to 21.3).

Could inherent talent (using, e.g. RSCI ranking as a metric) help some players to improve offensively in spite of increased usage? That study will have to wait for another day.

Re: Hibbert drop when used less than 10% - could this be his deep foul trouble games, where he drew a few offensive fouls (turnovers) and barely scored?

ReplyDeleteGood call.

ReplyDeleteI didn't go back to look at the individual box scores, but I can see from my spreadsheet, looking at offensive possessions played (not used), he averaged 30 possessions for games with less than 10% poss. used, and averaged more than 38 possessions played for every other bin.