A New Way to Measure Playmaking Ability

There are players who score and only score, and there are players who score and make players around them better. There is value in a player who not only scores, but also makes others around him better by distributing and facilitating. How do we separate a great all-around player who has an impact on his whole team from a guy who’s just known for his scoring ability? Introducing the harmonic mean between points and assists.


The harmonic mean between two variables is simply (2*A*B) / (A + B), where A and B are any two variables. In this case, A and B are points and assists. The harmonic mean was first introduced in sports by Bill James, when he developed the Power-Speed number in baseball. In his formula, home runs and stolen bases were the two variables. To do well, you need a lot of both.  This makes sense because the numerator in the formula grows at a much faster rate than the denominator.

The same applies in the points-assists harmonic mean (PAHM). In order to have a high PAHM, a player must have a lot of points and a lot of assists. In other words, one would expect point guards to infiltrate the top of this list and for Carmelo Anthony to not fare too well.

After running the results the first time, I noticed that players who had played more games naturally had a higher PAHM because they had more opportunities to get points and assists. In order to avoid this problem, I divided their overall PAHM by games played to get their Per Game PAHM.

2012-13 Per Game PAHM Stats:

Screen Shot 2013 08 08 at 1.17.15 PM

A few observations when we look at this table from last season:

  • As expected, the list is filled with point guards. In fact, 24 of the top 28 are point guards. This is again no surprise because point guards generally rack up assists and aren’t afraid of taking a shot. Also, the league is filled with stellar point guards today and this table reiterates that notion.
  • Chris Paul, like his fictional twin brother Cliff, is in fact great at assisting others as portrayed in the State Farm commercials.
  • Rajon Rondo is a bit of a surprise at No. 2. He didn’t play a full season but he made his way to the top of the list because of his high assist total. Just imagine how great he would be if he had a better scoring touch.
  • Kobe Bryant is 11th on this list (first among all shooting guards). So next time someone on Twitter or Facebook posts a “Kobe doesn’t pass” meme, you can swiftly respond with this stat. (More on Kobe in a bit.)
  • LeBron James is a freak, but we already knew that. He’s not only third overall in Per Game PAHM, but he’s a power forward! The next power forward on the list is Josh Smith and he’s ranked No. 40.
  • No surprise but Carmelo Anthony is not on this list. He was actually ranked No. 84 in the stat – no surprise from a guy who was criticized all year for not passing the ball.

The main takeaway from this table other than the fact that Kobe is dominating in a stat most people wouldn’t think he could dominate is the limited help the team received from Chris Duhon and Darius Morris. Once again, the 2012-13 story cannot be told without first talking about injuries. Nash and Blake missed almost half the year and were not backed up well by their third and fourth stringers (nor were they expected to be.) Nash was also 5th in the league in 2011-12 in PAHM, but he fell to 21st last year.

But let’s talk about Kobe. He recorded the highest PAHM of his career last season at 9.86 and he has a career PAHM of 8.01, which is excellent for a shooting guard. One may attribute his high PAHM to his 31,617 career points, but the fact that he’s averaged near five assists per game throughout his career definitely has a lot to do with his high PAHM. If you cut Kobe’s assist by 60 percent, it lowers his PAHM to the low 5’s.

This is intriguing because as mentioned before, most people don’t look at Kobe as a distributor, when in fact he’s been fairly good at getting his teammates involved. And when Kobe got his teammates involved, the Lakers won games.


In short, PAHM has several good uses:

  • It’s a great way to evaluate point guards. The higher a point guard’s PAHM, the more versatile they are in terms of scoring and distributing.
  • It’s also interesting to look at players that play other positions pop up at the top of the list because it shows that they are not only good scorers, but solid facilitators.
  • It’s a number that separates great players from great scorers. For instance, it says a lot that LeBron has a higher career PAHM (11.08) than Allen Iverson (10.0) even though the former is a power forward and the latter is a point guard.
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Early Start Key for Red Sox Success

Koji Uehara once again made it look very easy when he recorded his first save of 2014 as the Boston Red Sox wrapped up their first series win. The team also pounded out 14 hits. The way they won made it seem like the party from 2013 was carrying over to this year.

Sure, there are still 159 long games left in the marathon season. However, the series showed that the Sox may have been hammered after winning it all last year, but they took their hangover pills and are ready to play the same way they did in 2013.

No team has repeated as champions since the Yankees did so in 2000. Since then, six of the 13 champions failed to even make the playoffs. The 2005 Red Sox and the 2002 Diamondbacks made the playoffs but both were swept in their respective League Division Series. Just two – the 2001 Yankees and the 2009 Phillies were able to make it to the playoffs. These teams were established powers at the time and had the firepower to get that far.

The Red Sox, as almost every fan knows, overachieved last year. No one expected them to do what they did. Everything clicked, the bullpen got hot at the right time and they completed a worst to first season. Generally when that happens, one can expect a regression to the mean during the following season, especially when the team loses one of its best players like the Sox did with Jacoby Ellsbury. It really wouldn’t be that much of a surprise if the Red Sox slip from last season.

That said, after the first three games, the Red Sox still look like the team from last year. David Ortiz is tearing the ball up as he’s reached base seven times in his first 15 plate appearances. Xander Bogaerts continues to show signs of a promising career with an OBP of .667. The bullpen hasn’t allowed a run. And finally, the starting pitching held a powerful Baltimore Orioles lineup featuring Chris Davis, Nick Markakis, Nelson Cruz, Adam Jones, and Delmon Young to just seven earned runs over a three game span.

Even the bad looks the same. Jonny Gomes has only one hit and Mike Napoli and Will Middlebrooks have struck out for a combined seven times.

No, the Red Sox aren’t undefeated, but the way played against Baltimore was similar to the way they played all season long last year. Nothing has changed. They’re still getting contact on pitches they swing (80.4 percent contact rate – third best in the majors even though, yes, it’s a small sample size) and they’re taking the first pitch 78.3 percent of the time – fourth highest in the league.

The Red Sox have a special way of playing. They take bad pitches and swing and get contact on the good ones.  When they’re on “their game”, they end up getting W’s. It doesn’t seem to matter if Jonny Gomes or Jacoby is leading off in the lineup. The formula worked last year, and John Farrell’s boys are trying to make it work again this year.

The team is sticking to the championship script and after their first series against a pretty good Orioles team who will likely stick around until September, things are looking up. If the Red Sox are going to repeat this season, they need to stick to that script.




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Finding a Bright Spot in a Dismal Season

The buzzer sounded at the Bradley Center on a chilly spring Milwaukee night and the Los Angeles Lakers found themselves on the losing end once again in a season that just won’t end quickly enough. The 16-time NBA champions had just been swept in a season series against the Milwaukee bucks – the league’s worst team, who have a winning percentage that’s less than .200. No team has won fewer than 20 percent of their games in a full NBA regular season since the 2009 New Jersey Nets.

This pretty much summed up the Lakers woeful season, who have lost to the bad and been crushed by the best throughout the season. It’s difficult to find many positives after a season like this that’s been riddled with countless injuries or even in a loss against the Bucks, but walking out of the locker room in Milwaukee was Jordan Hill, one of the few silver linings in the Lakers dismal 2013-14 season.

Hill scored 28 points and grabbed 16 rebounds in a losing effort in just 31 minutes. He made 13 of his 17 field goal attempts. Nine of his 16 rebounds were of the offensive variety. These type of numbers aren’t an anomaly either. Hill has continuously showed this season how efficient he can be.

He missed almost a month due to injury, but in his four games back he has scored 28 points twice, which have been season highs for the power forward. He has also grabbed 14.7 percent of all available offensive rebounds, the second highest among players who average at least 19 minutes per play.

Hill has limitations. He’s not the next Dwight Howard or Roy Hibbert. Defensively he’s not the greatest player in the world as evidenced by his defensive rating of 106. That said, this could be a product of the system he plays in which doesn’t stress defense at all as evidenced by the 16 consecutive games they allowed 100 or more points from early January until February.

Defensive deficiencies or not, Hill is a guy that the Lakers need to try to retain in the offseason. He only makes $3.5 million this year and he’s a high energy player the Lakers could sign for a couple of years for a good price. His rebounding abilities and constant energy are reason enough for the team to bring him back.

Just think about it for a second. Hill has been subjected to awful minutes by D’Antoni this year. He’s getting only 19 minutes per game – fourth-lowest on the team. Shawne Williams and Ryan Kelly are averaging more minutes than Hill. If a player is producing and not getting minutes there’s no doubt that this could lead to frustration. The fact that Hill still is playing hard and producing despite not getting the minutes he deserves is a testament to his character and focus.

Finally, concerns that giving Hill big minutes would tire him out and diminish his productivity are false. Hill’s best games have come when he gets big minutes. His per 36 minutes are incredible because he grabs a lot of rebounds in very few minutes but when he does play over 30 minutes, his numbers are consistent. When he plays 30 minutes or more, Hill averages 11.3 rebounds and 16.6 points. These are starter type numbers.

It’ll be interesting to see if this would keep up if Hill had a central role on a winning team. Guesses are that he can easily be a high energy guy off the bench and average 25-30 minutes per game. Whether he fits in a D’Antoni type system remains to be seen, but there’s no doubt Hill deserves more minutes because of his production. If he continues to not get them, then he may kiss L.A. good bye come summertime.

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NCAA March Madness: Finding the Upsets in the Bracket

Every year around this time we all become college basketball experts. We act like we’ve watched every single Wofford game and pick them in our brackets for a massive upset even though most of us don’t even know where Wofford even is. (No, seriously, where is it?)

If you’ve ever been in a bracket pool, you definitely know that picking an upset is extremely challenging. If you don’t know much about the sport, sometimes it’s just best to go chalk because at least the percentages are on your side.

However, with some research it’s possible to make smart, educated upset picks that could help you get to the top of your bracket or make your wallet fatter.

Research done by ESPN’s Peter Keating, shows that upsets are generated by teams who do the following things well: make threes, grab offensive rebounds, force turnovers, and prevent their opponent from doing the same.

Making threes is an obvious one. If a team is efficient from downtown, they are scoring 1.5 times more than the average basket. The value of each shot goes up and if they’re successful at it, they’re going to put plenty of pressure on their opponent.

Grabbing offensive rebounds is important because it essentially gives a team another opportunity to score and keeps the ball out of the opponent’s hands. The best defense is to not even allow an opponent to have the ball. The more offensive rebounds a team gets, the more they give themselves a chance to score. It’s also important to note that most offensive rebounds occur near the basket. So if a player grabs the ball in the paint and shoots it from there, it’s most likely going to be a high percentage shot.

Finally, forcing turnovers are essential for lowly ranked teams because they give teams more possessions and like offensive rebounds, they keep the ball away from the other team. Also, turnovers can lead to fast break opportunities, which can lead to easy points.

It’s also key for teams to prevent other teams from making threes, grabbing offensive rebounds, and forcing turnovers. If a team isn’t known for making threes or grabbing offensive rebounds, but they have a strong perimeter defense and clean up the glass defensively, that’s going to help them get a win in the tournament.

Looking at the upsets in just the first day of this year’s tournament, we can see that these characteristics hold true for some of the underdogs.

No. 11 Dayton held No. 6 Ohio State to just two offensive rebounds and just three 3-pointers in their 60-59 shocker. Dayton wasn’t amazing at either of the categories during the regular season, but Ohio State was woeful in both 3-point shooting (241st in the country) and offensive rebounds (258th in the country).

As you continue to pick winners in the Sweet 16, Elite Eight, and Final Four, it’s wise to continue to look at these numbers even though the teams will be more evenly matched. Generally speaking, teams that can efficiently and consistently maximize the value of their shots and increase the number of possessions are going to win more games than others.

This year Duke and Louisville are among a few of the schools that were in the top 100 in all three categories. Duke and Louisville are playing in the same region this year and are No. 3 and No. 4 seeds, respectively. They are expected to go deep but it’ll be interesting to see if they can pull off mini-upsets as underdogs if they play the No. 1 and No. 2 seeds in the Sweet 16 because of the fact that they’re good at those essential categories.

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Despite Struggles, Jackie Bradley, Jr. Deserves Starting Spot in Center

A year ago at this time, Jackie Bradley, Jr. was putting on a show in Fort Myers. In one particular game against the Miami Marlins, Bradley came a triple away from the cycle, hit a home run, and raised his spring average to an astronomical .519. His performance was so phenomenal last spring that the team made the bold move of putting the rookie in their starting lineup on Opening Day. However, Bradley hit just .097 in April and was sent back to the minors before even the calendar turned to May.

In hindsight, the Red Sox fell for a player who was hot during Spring Training and made the mistake of thinking that it would translate to regular season success. A year later, the Red Sox are on the verge of making the same mistake if they give Grady Sizemore the starting spot in center field on Opening Day.

Sizemore came to Fort Myers with limited expectations. He hasn’t played since 2011 and his career has been riddled with injuries since 2009. After being an All-Star and winning a Gold Glove and a Silver Slugger back in 2008, Sizemore has been an afterthought. For the Red Sox, signing Sizemore was a low-risk, high-reward proposition.

Fortunately for the Sox, in the early stages it looks like the investment may pay off. Sizemore has been a pleasant surprise in March. He’s hitting .381 and is outplaying Bradley, who is having a frustrating spring batting below the Mendoza line. Bradley’s struggles throughout last season and during spring training this year coupled with Sizemore’s solid play has given Grady a case to be the starting center fielder on Opening Day. However, Sizemore is nowhere near ready to take on those duties.

Sizemore only has 21 at-bats this spring and from his eight hits, seven of them are singles. He also hasn’t driven a single run and has just one walk. He hasn’t shown that he can sustain this little hot streak he is having over a long period of time. Bradley hasn’t exactly been lighting it up, but it’s way too early to award Sizemore with anything at this point when he hasn’t proven he can be consistent over a large sample size.

It’s important for the Red Sox to have Sizemore earn the starting center fielder spot, rather than just handing it to him because his competition is struggling in spring training. Sizemore will get plenty of opportunities to prove to John Farrell that he has made a healthy recovery and returned to form. It’s encouraging for everyone that his comeback has started without a hitch and he’s heading in the right direction. But until he shows consistency in terms of both staying healthy and production, the starting spot is still Bradley’s.

Even though Bradley’s spring numbers aren’t anything close to stellar, Farrell has made it clear that batting averages aren’t going to be the make or break. Bradley is starting to show solid plate presence. In a recent at-bat against the New York Yankees’ Michael Pineda, Bradley fouled off several pitches before striking out on a questionable called third strike that could have been a bit high. It went down as an out, but his approach to the plate is a positive attribute that is not measurable.

Bradley also has an advantage defensively, which is another characteristic that isn’t as easy to measure as offense. His youth and speed gives him an edge over Sizemore, who is now 31 and hasn’t played in a full season since 2008. Bradley showed signs of athleticism earlier this week when he made an impressive catch at the wall with the sun in his face off an Alfonso Soriano blast.

Things can obviously change if Bradley’s offensive struggles pour into the regular season and Sizemore’s production remains consistent. It’s critical that the team doesn’t weigh spring statistics too heavily.

It’s also important to note, that Bradley’s performance was significantly better than what Sizemore is doing this year. From players who received at least 20 at bats last spring, Bradley led the team in batting average, runs, RBIs, and walks. Sizemore isn’t doing any of that. Everybody fell in love with Bradley. Boston was coming off one of the most disappointing seasons in franchise history and Bradley offered a beacon of hope. So yes, they overreacted, but it’s fair to say that with that kind of performance, a lot of teams would have caved in, too.

All of that said, Sizemore playing well is tremendous news for a team that is trying to replace Jacoby Ellsbury. Competition is never a bad thing. Neither is depth. With Sizemore producing, it becomes important for Bradley to play well, too, and this bodes well for the team as a whole. Also, when was the last time a team stayed healthy from April thru September? Having both on the team gives the Red Sox one of the deepest outfields in the league along with Daniel Nava, Shane Victorino, and Jonny Gomes.


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Have A Heart: Red Sox Enter 2014 With Most Powerful 3-4-5 Punch in AL East

The human heart is essential for life. It pumps blood through our system and without it, a person can’t live.

The same applies to the heart of a baseball order and a team’s success. A team could have a flailing heart that could lead to a dead offense, much like the Miami Marlins had last year with no-namers like Derek Dietrich, Marcell Ozuna, and Justin Ruggiano hitting in the heart of the order during parts of the year.

Or they could be like the Boston Red Sox who will once again have a heart that’s as potent as a decathlete’s. No cardiac arrest here. It’s a heart that is unrivaled in the AL East and it will fuel the team to another year of offensive success and a deep postseason run.

The Red Sox bring back their 3-4-5 combination from last year. Dustin Pedroia hit third in 147 games last season and he has settled in nicely in that spot after spending much of his early career hitting in the No. 2 spot. Pedroia has consistently put up solid contact numbers as he got a piece of 87.2 percent of the pitches he faced last season – 7th best in the AL. He also hit a respectable .296 last season from the three spot and those kind of numbers set things up perfectly for clean-up hitter David Ortiz.

Ortiz spent 121 of his 135 total games in 2013 from the clean up spot and to put it simply, he raked. He was the beat of the heart as evidenced by his phenomenal World Series performance when he hit .688 with two home runs. Ortiz proved once again that he has plenty left in the tank and his presence in the heart of the lineup gives the Red Sox a valuable edge over other teams.

Finally, Mike Napoli rounds out the heart with an extremely patient and disciplined approach to the plate that worked wonders for the Red Sox last season. Napoli hit in the No. 5 spot 84 times last season – most on the team – but he actually wasn’t that impressive from that spot. In fact, he hit better from the cleanup spot with a .942 OPS – over a 100 points better than his OPS from the five spot.

Napoli’s value comes in terms of taking pitches. He took 4.57 pitches per plate appearance last season – 0.28 pitches per plate appearance more than the next guy on the list, Adam Dunn.

So what?

Dunn took 0.28 pitches per plate appearance more than Ryan Zimmerman. However, there are also 32 other guys separating Dunn from Zimmerman. Napoli is at another stratosphere in terms of taking pitches and that patience pays off because it raises the pitch count for starting pitchers.

If the Red Sox took an EKG, it would show that they had healthy and boisterous heart. The combination of contact, power, and patience in the Red Sox heart of the order sets the tone for the rest of the lineup, but they have some competition in the AL East.

The New York Yankees  are looking at a projected heart of the order featuring Carlos Beltran, Mark Teixeira, and Alfonso Soriano. All three of these guys have hit clean up numerous times at one point of their careers and they will provide nightmares for pitchers throughout 2014.

However, it’s an aging heart. The Yankees’ heart is like a marathon runner who is in incredible shape, but let’s face it – he’s 55 years old and his body isn’t what it used to be. It breaks down more often. He doesn’t recover as quickly. He’s just old.

Meanwhile, the Baltimore Orioles have more punch in the middle of the order with Chris Davis, Adam Jones, and Nelson Cruz. It’s young, powerful, and scary. The trio combined for 94 home runs last season and they will rival the Red Sox for the best 3-4-5 punch in the AL East.

Both of these hearts are significantly better than the Tampa Bay Rays, who are projected to have Evan Longoria, Wil Myers, and Matt Joyce hitting from the 3-4-5 spots. It’s a heart that can have some bursts, but it gets tired quickly. These three players have pop as they combined for 62 home runs last season, but none of them hit over .260.

Finally, the Toronto Blue Jays will sport Jose Bautista, Edwin Encarnacion, and perhaps a platoon between Brett Lawrie, Melky Cabrera, and Adam Lind. Bautista and Encarnacion combined for 65 home runs last year and they should be able to provide more pop this year. However, the lack of an established No. 5 guy this year means that the Jays will do plenty of experimenting.

At the end of the day, the Red Sox have the most balanced heart of the order in the AL East. The Yankees are old, the Jays have question marks, and the Rays are fledgling. The Orioles will be extremely interesting but their success hedges on whether or not Davis can repeat his masterful performance from last season when he hit 42 home runs.

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Penguins Return From Olympic Break With Plenty of Questions

When the Olympic break began, the Pittsburgh Penguins were sitting on top of the Eastern Conference with the conference’s best record. Now with Sidney Crosby, Chris Kunitz, Jussi Jokinen, and Olli Maatta returning with some hardware from Sochi, it’s time for the team to resume their NHL schedule Thursday night against the Montreal Canadiens.

However, the announcement of Paul Martin’s hand injury and the fact that there is no timetable for Kris Letang’s return from his stroke means that the Penguins will be shorthanded defensively during the final stretch. With Martin and Letang out for the foreseeable future, the Penguins will have to rely on young defensemen like Robert Bortuzzo and Simon Despres as they gear up for the playoffs. Considering the fact that Maatta is also only 19, Pittsburgh may be sporting three defensemen under the age of 24. This inexperience in the back end could end up harming the Pens in the long run.

As the Penguins have learned well over their last few playoff runs, a strong offense, which the team has once again, cannot propel a team to the Stanley Cup. They need to have an excellent defense as well. The Penguins were plagued with poor defensive and goaltending performances in the playoffs in 2011 and 2012. Ironically, last season it was their offense that was stymied as they only managed to score two goals in the Eastern Conference Finals against Boston. However, considering they have two of the best players in the league in Sidney Crosby and Evgeni Malkin, it’s unlikely that that problem will repeat itself this time around.

A bigger cause for concern will be the defense. They need to protect the Penguins’ goaltending situation as much as possible. Goaltender Marc-Andre Fleury hasn’t exactly been any good in the playoffs over the last two years. Last season, he was pulled in favor of backup Tomas Vokoun, who is still out with a blood clot. The year before, he was horrendous with a .834 save percentage and a goals against average of 4.63 in a 4-2 series loss to Philadelphia. Those six games produced 56 goals and as a result it was also the highest scoring series in NHL playoff history. All of this means that the losses to Martin and Letang will put even more pressure on Fleury, who has an awful track record over the last few years.

The Penguins can’t find themselves in track meets with their opponents in the playoffs. They may have the best offense in the Eastern Conference with a 186 goals scored this season, but goals are going to be harder to come by the deeper they get into the playoffs. Most successful teams have great goaltending in the deep stages of the playoffs. Last season, Tuukka Rask of the Boston Bruins played a major role in holding the Penguins to two goals in the Eastern Conference Finals. The year before, Jonathan Quick of the Los Angeles Kings was lights out with a .946 save percentage, three shutouts, and a 1.41 goals against average.

The point is, it becomes more difficult to score goals in May and June. This means that the Penguins will be in deep trouble if Martin and Letang aren’t able to return at a 100 percent level by then. Their defense has to be able to protect the Penguins’ shaky goaltending situation and be able to take some pressure on the explosive offense.

All of that said, the Penguins have already dealt with numerous injuries on the defensive side this year. The only defenseman to have played all 58 games thus far is Matt Niskanen. This means that guys like Bortuzzo, Despres, and even lesser experienced players like Philip Samuelsson and Brian Dumoulin have all gotten their feet wet in the NHL level.

But still, the Penguins would much rather have proven NHL veterans in the lineup when the playoffs roll in.

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