There’s this thing in math called the Golden Ratio. You, of course, know The Golden Ratio as Ace of Base’s fifth album, but it’s also a relationship between two numbers that shows up all over the place in art and nature. It basically means that, for two numbers, the proportion of the sum to the larger number is equal to the proportion of the larger number to the smaller number. (Please don’t quit on me now.)

I don’t know how to do a square root in WordPress to show the whole equation, so let’s just agree that the Golden Ratio is about 1.62. It shows up in the facade of the Parthenon and, supposedly, in the geometric compositions of plants and animals, like this angelfish:

So it’s fitting that the Golden Ratio also applies to the ideal shot chart of a man who was named after a fish: Brandon Bass.

In last night’s breakout game, Bass took five long jumpers, three short jumpers, and five FGA at the rim, plus five more that led to shooting fouls. That’s a departure from a typical Brandon Bass outing: he usually takes more than twice as many jumpers (8.1 per game this season) as he does shots at the rim (2.6, although we don’t have numbers for the times he was fouled).

The year long ratio between Bass’s jumpers and FGA at the rim this season was 3.11. I submit that, for the rest of the playoffs, he should seek to make his jumpers/rim FGA exactly what it was last night: 8/5 = 1.6. The Golden Ratio, almost. So if he takes six jumpers, he should balance it out with about four attempts at the rim. If he takes 10, he needs to go to the rim at least six times. I’m talking about shot chart numbers, so none of these ratios include his rim attempts that draw a foul, meaning he should actually be going to the rim a few more times than that.

Attacking the rim more often suits Bass for a number of reasons. First: Rondo rewards cutters. Bass, like Bradley, is almost always the third or fourth option on the floor. Defenders will sag off him, especially because of hit reputation as a jump shooter. But last night he betrayed his defender’s trust by cutting to the rim several times, and he was paid in dunks.

Second: he can get there on his own. If Bass gets the ball within five feet of the rim, he’s mobile enough to put it on the ground and spin-bump his way into better position. He does this with such wild, reckless joy I wonder why he doesn’t more often.

Third: he has fat strength. Have you ever played basketball against an actual fat person? Not fat like that Sixer fan: just a really beefy dude. Because fat guys are really, really tough to defend at the rim. Their extra circumference gives the ball that much extra protection when they put the ball up, so you as a defender find yourself struggling to get your hands anywhere near the shot, even if you’re the same height as the big guy. If the dude has any level of finesse, he’s either dinking layups in uncontested or getting fouled.

Bass isn’t fat, per se. But he’s very, very broad. Look at his shoulder-to-shoulder width sometime: he’s built like a soda can. So when he’s in good position and he goes up strong at the rim, defenders on his shoulders can struggle to find the ball without slapping his arm, especially undersized guys like the ones peppering the Philly roster.

So for the reasons above, Bass should try to hit that 1.61 ratio when he divides his jumpers by his rim FGA after the game. Bass’s jumper is obviously important. Defenders need to account for it. It’s also so aesthetically kooky it’s travels full circle to beautiful: the leg kick, the full topside coverage of the left hand, the 110-degree lean his body takes in the air. So it’s important for a lot of reasons. But as the Stockton-Webber team pointed out many times last night, Bass’s rim work should give him more open looks on his jumper, as his jumper will likewise give him a little edge when he takes that one hard dribble to the rim.

How bad had it gotten for Bass? A guy who had averaged 33.8 minutes per game and 13 ppg in the regular season? Before Game 5, the former LSU star had played a grand total of 13 seconds of a fourth quarter against Philadelphia in Games 1-4 combined. It should also be noted those 14 seconds were at the end of game 4, when Philly had already secured the win. That’s four playoff games where a guy who had been a pretty integral part of the team’s regular season success didn’t even have a chance to see the floor in crunch time. For this entire series, Doc had been sending him out for a few minutes of the third quarter and that was that.

Now, I’m not attacking Doc for this. Besides the fourth quarter of Game 4, all of his decisions involving Bass were defensible. Still, it makes you wonder whether Bass had some frustration brewing heading into last night, a game where the team desparately needed his additional offensive punch and some improved defense to get over the top with Avery Bradley sidelined. After the game, Bass reflected on how he responded to the late-game benchings.

“With the leadership we have on this team,” Bass continued. “These guys encourage you to work hard, get your shots up, and watch more film and I took heed to it. I saw where I was open and I saw where I could be better on defense and it led to me being better tonight.”

And had there been any frustration building up over these past four games with the reduced court time? (just 24 minutes per game this series). The bait was laid out for Bass right there but he didn’t come close to biting.

“I wasn’t really frustrated,” Bass explained. “I trust Doc and his coaching ability. For me, I just stay ready and on a night like tonight, I was able to help.”

So simple, yet so refreshing to hear. And that’s the great thing about this team right now. You have a bunch of guys that know their roles, stay patient, don’t make excuses and don’t show frustration. Bass didn’t get down about his benching, he just took it as a cue to play harder and smarter.

The same goes for Greg Stiemsma last night. While he was spotty on the defensive end at times, the Steamer responded to a DNP-CD in Game 4 with 10 crucial points in Game 5 on 5-of-5 shooting, including eight big points in the first half which helped keep Boston in the game at the time.

Bass and Stiemsma are terrific representatives of the locker room makeover this team experienced in the offseason that is paying extreme dividends now. Instead of dealing with big egos and guys seeking attention, you have players committed to a team concept and also a couple bench guys whose voices are respected and heard in that locker room as Bass explained:

“At half, we were struggling defensively, Doc didn’t think we were playing for each other,” Bass said. “Then Reverend Dooling stepped up and gave us a little sermon and let us know we had to play for each other and in the second half we decided to do it.”

That’s a pretty tough locker room to be heard in, but Keyon is obviously a guy who has that cache. You can’t put a price on that on this kind of veteran team. A guy like Dooling getting through to the likes of Ray Allen and Paul Pierce as well as the younger guys in Bass and Rajon Rondo. That says a lot.

Brandon, like the rest of his teammates, is buying in though. He isn’t getting caught up in individual accolades either. After scoring a season-high 27 points and setting a postseason high for most points scored in a quarter in the NBA this season, Bass was given the opportunity to reflect on the accomplishment.

“I haven’t thought too much about. For me, it’s hard work. My motto is God, grind and greatness and grinding is what got me to this point and it’s what I’m going to continue to do.”

That grinding mantra has been the rallying cry of the Celtics, since they turned around their season at the All-Star Break. And now, thanks to Bass and company they have a chance to ride it into the Eastern Conference Finals.

With that said, we have a little bit of an issue. Hollins has been terrible in this series. Not just bad, but terrible. It’s not his fault entirely (see above) but it’s a major problem with no easy solution in the interim.

Let’s start with some numbers. Ryan Hollins has played 55 minutes in this series overall. Over those 55 minutes his has a plus/minus of -38, including a -15 during the Game 3 blowout win in Philadelphia. Those numbers don’t tell the whole story, but are indicative of how little Ryan has been able to do while out on the floor. He has been good for about an alley-oop or a offensive putback each game (averaging 2.8 points per contest) and that’s fine. Fans shouldn’t expect anything from him on the offensive end, because that’s not his job. He posted up and took a fadeaway jumper at the end of a quarter in Game 3 and that’s a shot I never want to see him attempt again.

My issue with Hollins is the rebounding, or lack there of. Coming into town, the center historically had one of the worst defensive rebounding rates for any center in the league, grabbing a mere 10.1 percent of all rebounds. He improved on that atrociousness slightly upon arriving in Boston, finishing the regular season at 12.2 percent rate, a pretty awful number overall but again progress. I wasn’t complaining.

We arrived in the postseason though and the bottom has fallen out for Hollins on the defensive glass. Through 10 postseason games, Hollins has the second worst defensive rebounding rate on the entire team, grabbing just 6.6 of all available defensive rebounds when he’s on the floor. That’s a 50 percent drop from his regular season number, and puts him just above Mickael Pietrus during the postseason. That’s pathetic, even with the small sample size.

In 55 minutes of floor action, he has grabbed just 3 total rebounds (2 on the defensive end). For a team that struggles with rebounding enough as it is, that’s unacceptable. The guards have been stepping up on the glass, as has Paul Pierce (except for Game 4). Hollins has not.

Despite this, Doc Rivers continues to have a bit of a love affair with the guy. He played fairly well against Atlanta in that series and his athleticism is obviously useful against the speedy Sixers. Still, the Celtics are compromising themselves and their rebounding when he is out there (especially if KG isn’t, but that’s any big on the roster at this point not playing with KG).

There is really no easy solution to his problem. Despite his awfulness, Hollins is playing more and more minutes (10, 14, 16, 15 in Games 1-4 this series). And to be fair to Doc, Greg Stiemsma has been nearly just as bad (-19 in 23 minutes this series). The Steamer will rebound however (27.1 percent rebounding rate this postseason) but he’s been turning the ball over (20 percent turnover rate) and it’s unclear whether he can keep up with the speedy Sixers guards with his banged up feet as Doc has appeared to lose confidence in him. Despite it all, Steimer rebounds and after the DNP-coach’s decision in Game 4, I bet he gets another chance tonight in the first quarter of Game 5.

The other guy that should come into play here is Brandon Bass. The starting power forward has played just 24.3 minutes per game in this series and while he has had his ups and downs, there is no way I want him playing that little with Hollins playing that much. Doc hasn’t shown the willingness to go small defensively with Bass at the 5 (yet) in a C’s small lineup but ultimately rebounding-wise, that may be the lesser of two evils here. Bass may not be able to guard Spencer Hawes at the 5, but he has shown the ability to handle Lavoy Allen, Elton Brand, and Thaddeus Young in short stretches. As long as Hawes or Brand/Allen isn’t out there, Doc shouldn’t be afraid to go small with Bass at the 5 in a pinch with Garnett resting.

Whatever the decision may be tonight, one thing is clear. If you are a center, you need to grab rebounds. Heading into the most pivotal game of the season for the C’s tonight, Hollins needs to bring his rebounding shoes or he should stay on the bench.

Game 4
Celtics @ Sixers
8:00 PM EDT
ESPN
Wells Fargo Center

Offensive Efficiency:
Boston: 94.0 points per 100 possessions (11th)
Philadelphia: 95.6 points per 100 possessions (10th)

Defensive Efficiency:
Boston: 90.4 points allowed per 100 possessions (1st)
Philadelphia: 91.7 points allowed per 100 possessions (3rd)

Probable Sixers Starters: Jrue Holiday (PG), Evan Turner (SG), Andre Iguodala (SF), Elton Brand (PF), Spencer Hawes (C)

View From The Opposing Bench: Philadunkia

THUMBNAIL

For Game 4, I joined Chris Forsberg over at ESPNBoston to break down what to expect in Game 4. Here’s a sampling of what we covered in our game of 2-on-2. You can check out the full post at ESPNBoston

1. Predict the unpredictable: Can the C’s carry their momentum from Game 3 over to Game 4 and take a commanding 3-1 lead?

Robb: I like their chances of maintaining the momentum. This team hasn’t made it easy on themselves all season, but after Game 3 you have to think the C’s smell blood. They know a 3-1 series lead all but puts away Philadelphia for good. Plus, with Miami having their hands full with Indiana on the other side of the bracket, a quick wrap to the series could bring several days off, which is plenty of motivation for the ailing members of the roster. Besides the added rest incentive, I just think the C’s worst basketball of the series is behind them. They won’t replicate their nearly perfect Game 3 effort, but Kevin Garnett can’t be stopped, Mickael Pietrus has rediscovered his shot, and the C’s have made defensive adjustments that will be tough for the Sixers to counter heading into Game 4.

Forsberg: We hear so much about the importance of peaking at the right time in sports. Well, I don’t know if it’s possible for the Celtics to peak considering the lingering injuries they’re battling, but I wonder if — apologies for an awkward sounding phrase — they can consistent at the right time. All season we’ve been seemingly waiting for this team to build off quality performances. And yet they always seem to let off the accelerator a little bit, making things just a bit more difficult on themselves. Friday’s Game 4 is a chance to all but lock up this series, build off the boundless confidence that seems to exist after Game 3. Heck, with another effort like Wednesday night, the Celtics could consider printing up some Pacer-like T-shirts with Green Swagger on it for later in the playoffs. You get the feeling this team is locked in and focused, but they gotta show it. It’ll also be interesting to see how Philadelphia responds to this adversity; they’ve rebounded from each previous playoff loss with a win, but can they keep up the trend in Game 4?

Playoff Offensive Efficiency
Philadelphia: 101.7 points per 100 possessions (17th)
Boston: 98.9 points per 100 possessions (24th)

Playoff Defensive Efficiency
Philadelphia: 96.6 points allowed per 100 possessions (3rd)
Boston: 95.5 points allowed per 100 possessions (2nd)

Probable Sixers Starters: Jrue Holiday (PG), Evan Turner (SG), Andre Iguodala (SF), Elton Brand (PF), Spencer Hawes (C).

View From The Opposing Bench: Philadunkia

Thumbnail: Ray Allen and Paul Pierce are in. And in case you missed them earlier today, here are our series predictions…..

Ryan DeGama: The Celtics will win this series, but with Paul Pierce unlikely to approach 100% against the hyperathletic Andre Igoudala and Ray Allen a question mark for game one, it’s going to prove tougher than many are expecting. If the Celtics can control tempo (no turnovers!) and force Philly to grind it out, the Sixers are going to struggle to score against this Boston halfcourt defense. TheRajon Rondo-Jrue Holiday matchup is not as clear a win for the Celtics as you might think, especially if Rondo takes quarters off or plays them badly, the way he did last series. Nobody expected the Celtics to have homecourt in round two but it might prove the difference. Boston in 7.

Michael Pina:  The Celtics will move on for myriad reasons (skill, experience, etc.), but what I’m most looking forward to in this series is Avery Bradley’s true coming out party. Due to a sudden shoulder injury and an unfavorable matchup against the 6’8? Joe Johnson, Doc Rivers wasn’t able to utilize his feisty, small backcourt in the first round. Against Philadelphia, a team that likes to run on the backs of Lou Williams, Jrue Holiday, and Evan Turner, Boston’s emerging weapon will finally make his presence felt.

The Sixers have youth, overwhelming athleticism, and confidence now that they’ve made their first bit of playoff progress in about a decade. If you believe professional sports is a bottom line business, then the bottom line with Philadelphia is that they beat Chicago in six games. But if you want to break down that series as a way to learn what might happen in this one, what really happened is they squeaked past a Bulls team that was missing its two best players. It wasn’t an eighth seed defeating one of basketball’s premier contenders. This was a borderline playoff team that had its hands full with a lottery bound roster of role players. This isn’t a case of my overlooking Philadelphia in anticipation of a showdown with Miami. It’s my belief that the Sixers simply aren’t all that good. Boston in 5.

Brian Robb: Philadelphia is a tough little team to figure out. The key to this series as Doc Rivers already articulated will be the turnover game. The Sixers are the best in the league this postseason at not coughing up the ball, and like Atlanta, they have the athleticism to force turnovers at an impressive clip as well (top-10 in regular season). The issue for them is no one can score the ball with any regularity. If you thought Boston’s offense was ugly, take into account only Spencer Hawes and Lavoy Allen averaged above 42 percent shooting from the field against Chicago in six games of action. The Sixers also hit 24.7 percent of their 3-pointers in that series, and Boston is one of the best at defending beyond the arc.

Philadelphia survived against Chicago because they were able to get to the line at an impressive clip against an undermanned Bulls team. In the regular season however, they were the worst team in the league at getting to the charity stripe (free throws per field goal attempt), so given the small sample size, I don’t expect this getting to the line trend to continue against a superb Boston defense. Putting it all together, I don’t think Philly can score enough to win four games in this series. Boston’s injuries will play a factor and make the series longer than it should be, but if Pierce, Allen and Bradley can stay on the floor and contribute, Boston gets it done. Boston in 7.

Brendan Jackson:  This series is going to be really hard to predict.  The Sixers don’t have the individual talent the Hawks had, which leaves the Celtics without anyone around which to specifically design their defensive game plan.  What sounds like a good thing actually has a tendency to cause the Celtics to become complacent on the defensive end when they think a lesser player has the ball.  The biggest problem with this approach is that while the Sixers are a collection of less-than-stars, they’re all still pretty good, not to mention young, athletic, and defensive minded.

Against the Bulls, a few players stood out as real x-factors.  Both Jrue Holiday and Spencer Hawes showed flashes of brilliance against the Bulls and provided an offensive spark when no flint seemed available.  I’m looking forward to see if Hawes has the same success against Kevin Garnett as he did against Carlos Boozer and a hobbled Joakim Noah.  Or is Holiday can do as well with Avery Bradley checking him.

Despite being embarrassed more than once by the Sixers in the regular season, the Celtics should win this series pretty handily.  Both the Sixers and Celtics struggle to score in the half-court and are both elite defensive teams.  Luckily for the C’s, if it comes down to the Celtics or the Sixers needing to score, the easy money is on the C’s to convert.  This series could be prove to be the Sixers welcoming party into the league of really good teams or it could be evidence of how a lesser team made it past a injury-depleted Bulls team.  I’m leaning towards the latter.  Celtics in 6.

Hayes Davenport:  Game is starting so I need to be quick: I think the Sixers are uniquely equipped to challenge the Celtics based on two assets: youth and depth. Both contribute to Philly’s speed, longevity, and injury tolerance. The Celtics are clearly the better team, but as we’ve seen all season and into the playoffs, they’ll go entire games playing far under their potential, so they could play an extended series against pretty much any team. I don’t think Philly’s going to make it through, but I do think it’s going to drag on. Celtics in 7.