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rocketeli
11-24-2012, 05:38 PM
I'm looking forward to the game tonight so that's got me thinking about Duke basketball topics in general
It seems every year people start posting their worries about "depth" and the sports-yak types start yakking about how "Coach K likes a short bench" or always "shortens his rotation." It seems to me that Duke doesn't play any shorter a rotation than other successful ball program in general...but can I prove it?
First, let's posit that there can be no greater success in a given year than to win the NCAA basketball tournament and be crowned National Champions.
Therefore, I looked at the last 15 years of NCAA basketball winners and looked at the minutes played per gam (mpg) for each player on the roster. (This info is actually not much work to find) I broke the stats down into players playing an average on 15min or more and players achieving double figures (10mpg or better) for each team.
I prepared the following table with the results
year NCAA Champ Team Coach #player 15+ mpg 15mpg player + player 10+ mpg
201 KY Calipari 6 7
2011 UCon Calhoun 7 7
2010 Duke Coach K 7 8 (O czyz was averaging 10mpg before he transferred which would make 9)
2009 UNC Williams 7 9
2008 Kansas Self 7 8
2007 FLA Donovan 7 7
2006 FLA Donovan 7 8
2005 UNC Williams 8 8
2004 Ucon Calhoun 7 8
2003 Syracuse Boeheim 7 8
2002 Maryland GWilliams 7 7
2001 Duke Coach K 6 8
2000 Mich St Izzo 6 10
1999 Ucon Calhoun 7 8
1998 KY Smith 6 9

Observations:
1. The modal number for really meaningful minutes (set here at 15mpg) for a national championship is 7. for 4 teams the 15mpg amount was 6 and for one team 8 so there was little variance around the mean as well. For players total players in double figures minus 15mpg + guys the range was 0 to 4 but the most usual scenario was a difference of +1 which occurred 7 times.
2. This is a veritable hall of fame collection of coaches--they seem to have all arrived at the conclusion that if you play your best players and sit your less talented ones on the bench, you will win more games. Guess that's why they make the big bucks.
3. Duke is not an outlier in terms of minutes played per player or length of (used) bench. In fact the smallest total number of players in double figures belongs to Calipari in 2012. Maybe we can retire this meme, which I have no doubt is used to some effect in recruiting against us by our rivals?

MarkD83
11-24-2012, 06:41 PM
Thanks for the analysis.

The only thing that worries me as a Duke fan is that the "meme" that Duke has a short bench can be used against us in recruiting. However, there has been an epidemic of transfers in college basketball lately (not just at Duke). Perhaps the players which transfer hear that a team plays 9 or 10 players and then go to that team and find out they don't play. Would Duke benefit if that 9th ot 10th guy came to Duke and then transfered?

uh_no
11-24-2012, 06:42 PM
While somewhat enlightening, the chosen number of minutes (15 and 10) are somewhat arbitrary and make the analysis somewhat contrived.

The question we want to ask is, what determines whether someone is in the rotation or not? Sometimes that is very fuzzy. It would seem that if you ordered players on a team by playing time, there should be a point when you say "this guy was in the rotation and this guy was not" You used 15 and 10 minutes, but how do we know that the team didn't have a handful of people at 9 minutes? In essence, we don't.

I think a better way to do this would be to ask the question "what does the distribution of minutes look like across the team"

To do this, we'd start by ordering players by minutes played and graphing the minutes played vs player, which should yield some monotonically decreasing graph. While we could look at this graph and figure out how minutes are used, we'd like 1 or 2 individual metrics to describe usage.

The next step is to calculate the expected value, in other words, from a high level, how for a given minute, what is the average index of the player who used that minute. You do this by sorting the values for minutes played for each player on the team (highest to lowest) and then for each minute value, mutliply the value by its place in the list (1 for the highest minute value, 2 for the next highest.....N for the Nth highest) finally dividing the sum of all those by the number of players:

(1*minutes(1)+2*minutes(2)+.....N*minutes(N))/200

The higher this number, the more deep the minutes are distributed. This is a good starting point. For teams such as our 2010 title team, the number will be somewhere around 3.5. A team with 10 guys playing 20 minutes scores 5.5. A team with 5 guys playing 40 minutes each scores a 3.

This can be broken, though, as we can (however unlikely) have a team where one or two players get a huge number of minutes while the next 8 get medium minutes which looks identical to a team where the top 7 players play all the minutes equally per the metric i just derived....so how do we come up with a metric which differentiates these two cases? We can compute the kurtosis of minutes away from the top minute getter. This is effectively just the same as the above number, except we take the 4th power of the index

4throot((1*minutes(1)+2^4*minutes(2)+...N^4*minute s(N))/200)

Similar to the above number, the higher the number, the more deeply they are distributed. But in this case, we effectively nullify the amount that the starters play and get a good idea of how deeply the bench is used.

Between these two numbers we will get an idea of both overall how are the minutes distributed, as well as how deeply the bench is used.

If I get a chance I will run a couple teams through this metric to get some baseline numbers and see if we can actually gain something out of this.

This has the added benefit of giving a much more fine grained output than simply number of players who played x minutes.

rocketeli
11-24-2012, 07:21 PM
While somewhat enlightening, the chosen number of minutes (15 and 10) are somewhat arbitrary and make the analysis somewhat contrived.

The question we want to ask is, what determines whether someone is in the rotation or not? Sometimes that is very fuzzy. It would seem that if you ordered players on a team by playing time, there should be a point when you say "this guy was in the rotation and this guy was not" You used 15 and 10 minutes, but how do we know that the team didn't have a handful of people at 9 minutes? In essence, we don't.

I think a better way to do this would be to ask the question "what does the distribution of minutes look like across the team"

To do this, we'd start by ordering players by minutes played and graphing the minutes played vs player, which should yield some monotonically decreasing graph. While we could look at this graph and figure out how minutes are used, we'd like 1 or 2 individual metrics to describe usage.

The next step is to calculate the expected value, in other words, from a high level, how for a given minute, what is the average index of the player who used that minute. You do this by sorting the values for minutes played for each player on the team (highest to lowest) and then for each minute value, mutliply the value by its place in the list (1 for the highest minute value, 2 for the next highest.....N for the Nth highest) finally dividing the sum of all those by the number of players:

(1*minutes(1)+2*minutes(2)+.....N*minutes(N))/200

The higher this number, the more deep the minutes are distributed. This is a good starting point. For teams such as our 2010 title team, the number will be somewhere around 3.5. A team with 10 guys playing 20 minutes scores 5.5. A team with 5 guys playing 40 minutes each scores a 3.

This can be broken, though, as we can (however unlikely) have a team where one or two players get a huge number of minutes while the next 8 get medium minutes which looks identical to a team where the top 7 players play all the minutes equally per the metric i just derived....so how do we come up with a metric which differentiates these two cases? We can compute the kurtosis of minutes away from the top minute getter. This is effectively just the same as the above number, except we take the 4th power of the index

4throot((1*minutes(1)+2^4*minutes(2)+...N^4*minute s(N))/200)

Similar to the above number, the higher the number, the more deeply they are distributed. But in this case, we effectively nullify the amount that the starters play and get a good idea of how deeply the bench is used.

Between these two numbers we will get an idea of both overall how are the minutes distributed, as well as how deeply the bench is used.

If I get a chance I will run a couple teams through this metric to get some baseline numbers and see if we can actually gain something out of this.

This has the added benefit of giving a much more fine grained output than simply number of players who played x minutes.

Yes I agree--by simplifying with arbitrary cutoffs a lot of more subtle info isn't captured. Having seen the actual data I can say that most of the usage patterns are strikingly similar with some outliers. For example Michigan state used a lot of players, with several over ten approaching 15 while KY in 2012 really only used 6 heavily. However, I think minutes per game is a good metric in and of itself for gauging impact, because if you don't get in the game very often, it means you're not all that important in terms of how you are used.

Duke of Nashville
11-24-2012, 08:50 PM
The only thing that concerns me about the way the bench is operating this year is the amount of points being scored from it. Our 6th and 7th men whoever it will end up being (Tyler or Marshall Probably) hopefully can pick up the points scored. Eventually, whether it be due to health or just an off night, not everyone will be able to score as well as they are right now. It would be nice to have those 6th and 7th players pick up the scoring pace. When we are playing a defensive minded team cough...Louisville...cough it would be nice to have some other options to rely on....

-jk
11-24-2012, 08:55 PM
If you're going to delve this deeply, uh_no, I think you have to limit your analysis to either games against top 100 kenpom teams or games where the margin is in single digits with less than two minutes to play. These limits were, of course, arbitrarily chosen.

-jk

Kedsy
11-24-2012, 08:58 PM
The only thing that concerns me about the way the bench is operating this year is the amount of points being scored from it. Our 6th and 7th men whoever it will end up being (Tyler or Marshall Probably) hopefully can pick up the points scored. Eventually, whether it be due to health or just an off night, not everyone will be able to score as well as they are right now. It would be nice to have those 6th and 7th players pick up the scoring pace. When we are playing a defensive minded team cough...Louisville...cough it would be nice to have some other options to rely on....

I've always thought that the concept of bench scoring is something they made up for TV. Assuming a team has a relatively consistent offensive efficiency, who cares who scores the points? If for some reason Mason gets shut down point-wise, for example, there would appear to be plenty of opportunity for Seth or Ryan or Rasheed or Quinn to step up and score more than usual. Why should we care if the extra points come from the starters or from the reserves?

Indoor66
11-24-2012, 09:02 PM
I've always thought that the concept of bench scoring is something they made up for TV. Assuming a team has a relatively consistent offensive efficiency, who cares who scores the points? If for some reason Mason gets shut down point-wise, for example, there would appear to be plenty of opportunity for Seth or Ryan or Rasheed or Quinn to step up and score more than usual. Why should we care if the extra points come from the starters or from the reserves?

I am completely with you on this. What difference where the points come from. Seems to me this is a talking point by the TV guys to fill time and sound well prepared and erudite.

Greg_Newton
11-24-2012, 09:05 PM
I assume it comes from the NBA, where it (obviously) matters a lot, as teams have to play long stretches without any first teamers in. Agree that it doesn't make a tactical difference in college as long as your scoring is diverse enough within your starting lineup.

Newton_14
11-24-2012, 09:07 PM
If you're going to delve this deeply, uh_no, I think you have to limit your analysis to either games against top 100 kenpom teams or games where the margin is in single digits with less than two minutes to play. These limits were, of course, arbitrarily chosen.

-jk

That's a great point, actually. Over the years, K uses a drastically different rotation in the cupcake games, vs the games against formidable competition. Throwing out the cupcake games will tell the story. To make it easy, you could just use all games after Jan 1. That keeps you from having to choose which games to throwout on a game by game basis.

For me, "rotation player" means guys that play in both halves, every single game. Not sure how you measure that, but sitting on the pine the entire 2nd half is definitely not in the rotation to me. WHich means for now, I do not consider Amile as a rotation player. He does play in the first half of every game, but not always the 2nd half. I do think he gets there this year though.

Obtaining DNP-CD does not happen for players in the rotation either, unless injury. As an example, in 2010, Mason and Miles were rotation players, Ryan and Andre were not.

But we all have a different measure for who's in and who's not.....

uh_no
11-24-2012, 09:24 PM
If you're going to delve this deeply, uh_no, I think you have to limit your analysis to either games against top 100 kenpom teams or games where the margin is in single digits with less than two minutes to play. These limits were, of course, arbitrarily chosen.

-jk

The question is, how closely is our late season distribution modeled by the overal minutes for the entire season? On the one hand, we certainly play different rotations in different situations. On the other hand, the other rotations may prove inconsequential over the course of the season. I don't rightly know what the correlation is.

I think If one were to go ahead and do this, a good starting point would be distributions used by teams in the NCAA championship. Now, that is, of course, arbitrarily chosen :), but we can make a seemingly sound assumption that the rotations used by teams in the tournament are the "correct" rotations. Fortunately, the arbitrary choices we're making here only affect the number of data points, not how we represent the results.

Kedsy
11-24-2012, 09:24 PM
To make it easy, you could just use all games after Jan 1. That keeps you from having to choose which games to throwout on a game by game basis.

Not sure using post-Jan 1 would do it. My observation is the minute distribution for 25+ blowout games in January and February is pretty similar to the early season games.

Duke of Nashville
11-25-2012, 12:42 AM
I've always thought that the concept of bench scoring is something they made up for TV. Assuming a team has a relatively consistent offensive efficiency, who cares who scores the points? If for some reason Mason gets shut down point-wise, for example, there would appear to be plenty of opportunity for Seth or Ryan or Rasheed or Quinn to step up and score more than usual. Why should we care if the extra points come from the starters or from the reserves?

Right...

However you look at it bench scoring matters at some point, right? Maybe it's just easy to overlook this statistic or maybe it doesn't matter.

It 2009-2010 we scored on average around 15 ppg from the bench....

Miles Plumlee 5.2
Andre Dawkins 4.4
Mason Plumlee 3.7
Ryan Kelly 1.2

In 2012-2013 we are at 7 ppg...

Tyler Thornton 4.0
Amile Jefferson 1.8
Josh Hairston 1.2

Two totally different offenses but I would say bench scoring wouldn't have mattered as much in 2010 as it could be in 2013. We are running faster with Quinn at the point and the 2010 offense was all half court with set plays and offensive rebounding. With three freshman and a sophomore off the bench. This year has two Junior and a freshman scoring about half the amount in 2010.

Maybe it doesn't matter and we do keep up 90% of the scoring from our starters. It's just something that is sticking out to me as an area in need of improvement.

tele
11-25-2012, 01:29 AM
Right...

However you look at it bench scoring matters at some point, right? Maybe it's just easy to overlook this statistic or maybe it doesn't matter.

It 2009-2010 we scored on average around 15 ppg from the bench....

Miles Plumlee 5.2
Andre Dawkins 4.4
Mason Plumlee 3.7
Ryan Kelly 1.2

In 2012-2013 we are at 7 ppg...

Tyler Thornton 4.0
Amile Jefferson 1.8
Josh Hairston 1.2

Two totally different offenses but I would say bench scoring wouldn't have mattered as much in 2010 as it could be in 2013. We are running faster with Quinn at the point and the 2010 offense was all half court with set plays and offensive rebounding. With three freshman and a sophomore off the bench. This year has two Junior and a freshman scoring about half the amount in 2010.

Maybe it doesn't matter and we do keep up 90% of the scoring from our starters. It's just something that is sticking out to me as an area in need of improvement.

I also think it does matter if you are getting bench scoring or not, but it matters less if you have balanced scoring from your starters, like all five in double figures.

Also if you are interested in substitution patterns when looking at the number of players in a rotation then the summaries described by uh no would help, but if you are interested in use of bench players then you can't assume that the 7 or 8 player rotation averages are made up of the same players for a given team. A team might use 8 or 9 different players as starters at different times over the course of a season but just have a 7 or 8 player rotation for each game. This can be a more effective way to develop bench strength than having more players in a rotation. You may have noticed Coach K does this with his lineups and rotations.

Kedsy
11-25-2012, 01:31 AM
Right...

However you look at it bench scoring matters at some point, right? Maybe it's just easy to overlook this statistic or maybe it doesn't matter.

It 2009-2010 we scored on average around 15 ppg from the bench....

Miles Plumlee 5.2
Andre Dawkins 4.4
Mason Plumlee 3.7
Ryan Kelly 1.2

In 2012-2013 we are at 7 ppg...

Tyler Thornton 4.0
Amile Jefferson 1.8
Josh Hairston 1.2

Two totally different offenses but I would say bench scoring wouldn't have mattered as much in 2010 as it could be in 2013. We are running faster with Quinn at the point and the 2010 offense was all half court with set plays and offensive rebounding. With three freshman and a sophomore off the bench. This year has two Junior and a freshman scoring about half the amount in 2010.

Maybe it doesn't matter and we do keep up 90% of the scoring from our starters. It's just something that is sticking out to me as an area in need of improvement.

Well, first of all, Miles started 24 games in 2009-10, so I'm not sure how he counts as "from the bench." Second, you didn't integrate DNPs into your calculations, so the actual contributions to team bench scoring from Andre, Mason, and Ryan are lower than you're reporting. Third, you're giving us exactly one data point to compare this year's team and this year's team has only played 6 games. And fourth, just because the 2010 team had more bench scoring than this year's team doesn't mean that team won the natty based on bench scoring or that the statistic is meaningful. For example, in our two Final Four games in 2010, our bench scored a total of 7 points in the two games combined, including a Jordan Davidson three-pointer in garbage time. So it doesn't sound like bench scoring was so important in the Final Four that year, in any event.

In our six game run in the 2010 NCAA tournament, our team averaged 7.3 bench points per game, which is pretty much the same as this year's team has achieved in the six games so far. Coincidence? Probably. Different situation? Certainly. But it should show that bench scoring isn't necessary to succeed.

Wander
11-25-2012, 12:20 PM
Bench scoring or minutes aren't important as season-long statistics. It's important in specific games where a starter is injured or in foul trouble. Take the Baylor game in 2010 as an example - Andre Dawkins didn't play or score much in the second half of the season, but still played extremely well when he was called upon in the Elite 8 because of foul trouble. Just because we don't play someone major minutes now doesn't necessarily imply they can't be ready to play in an emergency situation.

Kedsy
11-25-2012, 12:26 PM
Just because we don't play someone major minutes now doesn't necessarily imply they can't be ready to play in an emergency situation.

Yes. This is exactly my point. Depth on a basketball team is how many players on the team would be capable of playing well when the call arises. It doesn't mean they have to play good minutes every game.