Opportunity cost and the fast break

As a basketball fan, one of the things I enjoy most is just how many different styles of play there are, and how so many of these different styles enjoy relatively similar levels of success. When we consider different styles of basketball, the pace at which a team plays is one of the biggest things that we first notice. Some teams, such as North Carolina, really push the tempo. This makes some sense, as these teams often have significant talent advantages over their opponents, and often have players that flourish in a wide open style. Other programs, such as Wisconsin, play at a much more deliberate pace. Both North Carolina and Wisconsin often have highly efficient offenses.

This year, Rick Barnes will have a young and athletic team that appears to lack the type of size inside that he is used to. He also has the lightning quick Myck Kabongo on campus. Given these basic facts, many are clamoring for Barnes to adopt an up tempo, fast breaking approach. Barnes teams typically play somewhere near the median level for Division I when it comes to pace. But there have been some seasons (such as the T.J. Ford years) where Barnes' encouraged his teams to run. So what would be the ideal approach for a small team with a fast point guard like the one Rick Barnes has?  Does it make sense to switch to a run and gun approach?

I am always interested in trying to understand the various sorts of tradeoffs that exist in these situations. What are the advantages and disadvantages of pushing the tempo in basketball? What should we consider when debating the decision between running and walking the ball up the floor? Is either approach right or wrong? How do we analyze this?

I don't think you can ever arrive at a definitive conclusion on these sorts of things, but I think we can use the type of analysis that I will describe below to at least understand some of the tradeoffs.

The decision of tempo really starts with what approach a team wants to take on the defensive glass.  Teams can choose to send three, four, or five guys to the defensive glass.  If you only send three players to the glass, you will sacrifice some rebounding, but will also be well positioned for a fast break.  If you send all five players to the glass, then you have a much better chance of getting a rebound, but do not have a player preparing to receive an outlet pass and push the ball up the floor.

A few weeks ago The Mikan Drill had a nice post on the tempo of former Texas A&M coach (and current Maryland coach) Mark Turgeon's teams.  Turgeon's teams have typically done very well on the defensive glass.  From the article:

Turgeon focuses heavily on protecting the defensive glass and preventing offensive rebounds. His teams have not finished lower than 67th in offensive rebounds allowed since 2003 and have finished in the top 11 in the nation 4 times since then. They almost always send 4 players to rebound and often send 5 to make sure they secure the missed shot.
While this does allow them to rebound well, it does not allow them to push the tempo. At most, they have one player who is able to receive the outlet pass but it would be foolish for that one player to push the tempo when he is outnumbered. This means they are forced to slowly bring the ball up the court, which slows down the pace of the game. In collecting shot clock data for this game, I characterized possessions used within 7 seconds of the shot clock starting to be possessions used the result of transition. In the FSU game, A&M ended a possession in the first 7 seconds only 8 times out of 56 possessions (14.3%).

So here we have a classic trade off.  By sending 4 or 5 guys to the defensive glass, Turgeon increases his team's odds of getting a defensive rebound.  This comes at the cost of not being able to get out in transition.  Turgeon isn't the only coach who has teams that crash the defensive glass while playing at a very slow pace.  There are a number of coaches who seem to adopt a similar approach.  Ones that come to mind include Stew Morrill of Utah State, Bo Ryan of Wisconsin, and Brad Stevens of Butler.  Here is a video where Brad Stevens explains his approach to defensive rebounding, which basically boils down to sending all five guys to the glass and not really worrying about trying to fast break.

On the other hand, there are plenty of coaches who seem to prefer a more wide open style.  Take Turgeon's predecessor, Gary Williams, for example.  Williams' teams really looked to push the tempo, and were often not very good on the defensive glass.  (The change in style from Williams to Turgeon is going to be a shock for Maryland fans.)  Williams was an outstanding coach who won a national championship, so it isn't like his approach couldn't be made to work.

So which approach is better?  Is it better to send three players to the glass and get out and run in transition?  Or is it better to send four or five guys to the glass and limit second chance opportunities for the other team?  Of course, I can't really answer this question in a general sense, but I think it is interesting to at least try.  Analyzing this situation will highlight some of the various factors that should influence you decision about which approach is "best."

Before I dive into this analysis, I want to point out that which approach a coach should choose probably should depend a lot on the style of play that they know how to teach, and the types of players they are typically able to recruit.  Take a guy like Bo Ryan for instance.  Before taking over at Wisconsin, he was a ridiculously successful Division III coach.  Once he got to Wisconsin, he suddenly was able to recruit a different sort of athlete.  But despite the presence of great open court players such as Devin Harris, Ryan has basically stuck to his preferred style of play.  And this probably makes sense.  Ryan got where he is by coaching in a particular style.  Switching styles now might not be such a good idea, as his whole approach to the game and how he teaches it would have to change.


We can do some really simple back of the envelop calculations to try to understand the benefits of sending four or five players to the defensive glass, and the cost teams that do not do this potentially incur.  This will be the cost that a typical fast breaking team needs to make up on offense.  Let's consider a simple case.  A really good defensive rebounding team, like Butler in the 2010-2011 season, will typically allow the opposition to only get about 28% of the available offensive rebounds, using the kenpom.com numbers.  Median allowed offensive rebounding percentage for a team is around 32%.  I am going to make the assumption that by adopting the rebounding strategy of teams such as Butler, you will get Butler-like results.  So it makes sense to compare a median level defensive rebounding team to Butler to see what the difference in points per possession this makes to a defense.  An example of a team near the median in 2010-2011 was Georgetown, so I will just use their basic rebounding statistics for my estimates.

Now I have to introduce a second assumption, which turns out to be really useful for making this analysis go.  It will greatly simplify the math required.  I am going to assume that all offensive rebounds in a game come on missed field goal attempts, and none come on missed free throw attempts.  This assumption will simplify the analysis greatly, and is almost correct.  (Watch a game some time and keep track of how many offensive rebounds come on missed free throw attempts.  I have done this a few times, and for a typical NCAA game there might only be one or two such offensive rebounds.)  If we do this, we will end up with an offensive rebounding percentage (OR%) that is defined somewhat differently than the approach used at kenpom.com.  By my definition, OR% is

OR% = ORB/[FGA x (1-FG%)]

where ORB is offensive rebounds, FGA if field goal attempts, and FG% is field goal percentage.  Using this method, the 2010-2011 Butler team had an opponent OR%= 26.1%, and Georgetown had an opponent OR%=29.6%.

Calculating points per possession

Now it is time for a little math.  In this section, I am going to develop a formula that can be used to see how changing rebounding rate will affect the points scored per possession.  Feel free to skip ahead to the next section if you aren't interested in the details.  Recall our basic possession estimation formula.

POSS = FGA + 0.475 x FTA - ORB + TO

With a bit of algebra, and the definition of OR% I have presented above, we can rearrange this equation to give

FGA/POSS = (1 - TO/POSS)/[1+0.475 x FTA/FGA - (1-FG%) x OR%]

Feel free to check that out for yourself.  This equation is the reason that I have redefined OR%, and made my assumption about offensive rebounds only coming on missed field goals.  You can't get to a relationship like this without this sort of approach.  This relation defines the number of field goal attempts per possession that a team gets in terms of turnover rate, the ratio of free throw attempts to field goal attempts, FG%, and OR%.  We can also write the following sensible equation that relates points a team scores to shooting percentages and the number of shots taken

Points = (2 x eFG% + FT% x FTA/FGA) x FGA

where eFG% is the effective field goal percentage, which accounts for the difference in point values between two point and three point shots, and FT% is the free throw percentage.  We can combine our equations to get a useful tool for estimating points per possession

Points/POSS = (1-TO/POSS) x (2 x eFG% + FT% x FTA/FGA) /
[1+0.475 x FTA/FGA - (1-FG%) x OR%]

That is a very handy formula.  It may look like gobbly gook, but it is useful.  It enables us to estimate the effect of changes in OR% on points per possession.  (It also enables us to do many other sorts of estimates.)  

How much does a team have to improve on offense by getting out in transition to make up for the loss of defensive rebounding?

Let's use NCAA median values to see the effect of better rebounding on a team's defense.  In this case median levels are TO/POSS=0.2, eFG%=0.492, FT% = 0.695, FG%=0.435, and FTA/FGA=0.38.  So a team that rebounds like Butler (opponent OR% = 0.261), but otherwise defends at a median level will allow on average 0.967 points per possession.  An otherwise identical team that rebounds like Georgetown (opponent OR%=0.296) will allow on average 0.985 points per possession.  This is a difference of nearly 0.02 points per possession, or about 1 point in a 65 possession game.  This allows us to create a simple estimate of the benefit of sending 5 guys to the defensive glass, if you can be as effective as Butler is with this strategy.

Let's assume that by sending only 3 guys to the defensive boards, a team allows approximately an extra 0.02 points per possession on defense (in other words, they achieve a median level of defensive rebounding).  But this decision also allows that team to get out in transition, potentially improving offensive efficiency.  How much of an efficiency gain on offense is needed to make up for this difference.

The answer is easy here; by getting out in transition a team needs to make at least an extra 0.02 points per possession on offense just to make up for the loss of defensive rebounds.  This is simply the breakeven point.  To make this strategy worthwhile, the offense should do even better.  Let's assume that playing an up tempo style has essentially no effect on a team's ability to get offensive rebounds or avoid turnovers (based on correlation analysis with kenpom.com data, this seems to be true at least on average).  The offensive benefits that a team would derive from fast breaking could then only come from improvements in shooting efficiency (as measured by true shooting percentage).  By getting out in transition, how much of an increase in true shooting percentage is needed?  Let's assume that a typical NCAA team on offense gets about 1 point per possession on average.  Let's assign this team NCAA median values for eFG% (0.49), FT% (0.69), and FTA/FGA=0.376.  This gives that team a true shooting percentage of 0.525.  To boost their offense by 0.02 points per possession, they would need to raise their TS% to 0.536.  There are a different ways to improve true shooting percentage.  One way is to shoot more free throws. Generally teams score more efficiently from the free throw line, and some teams that fast break a lot get to the line at a pretty high rate (there is a really weak correlation between adjusted tempo and free throw shooting rates). But to add 0.02 points per possession, our hypothetical team needs to get to the line a lot.  To increase TS% to 0.536, our hypothetical team would need to get their FTA/FGA = 0.51 (assuming they shoot an NCAA Division I median free throw shooting percentage).  No team in Division I shot free throws at this high of a rate last season.  So the boost in trips to the line cannot really make up for what a team gives up by not sending five guys to the defensive glass.  In other words, if you cannot gain a significant increase in eFG% by getting out in transition, you are better off just sending all 5 defenders to the glass.  It is no surprise that stat friendly coaches such as Brad Stevens adopt this approach.

How large of an increase in eFG% is required to pay for the cost of giving up some defensive rebounds?  Let's assume that getting out in transition had no effect on free throw trips, but a team was able to employ this strategy to increase eFG%.  To raise TS% from 0.525 to 0.536, a median level team would need to raise its eFG% from 0.490 to about 0.502.  This is a pretty sizable improvement in offensive efficiency, although it certainly isn't unreasonable.  It is equivalent from going from median level for eFG% to roughly the top third in NCAA Division I. Again, this is simply what is required to break even with the strategy of sending all five guys to the defensive glass.

I am not trying to argue that all teams are better off sending five men to the glass and then walking the ball up the floor.  But it seems that the costs of the fast break incurred on the defensive glass are not often considered.  A fast break approach seems to make the most sense if you have a few big guys that can clean up the defensive glass without a lot of help from the guards.  A small team might be better off sending their point guard to the defensive glass than it is trying to get the point guard in position to push the tempo.  Otherwise, that "small-ball" fast break team really needs to have superior open court players to make up the difference on offense.