Tag Archives: BIER formula

The Beard, the Brow, the Greek Freak, Lebron and Steph . . . NBA Basketball Impact and Efficiency Ratings (BIER) leaders at the break

Through games of Feb. 15, Giannis Antetokounmpo was the 3rd best player in the NBA behind only James Harden and Anthony Davis, according to Basketball Impact and Efficiency (BIER) positional ratings. Lebron James and Steph Curry rounded out the Top 5.

No one should be shocked and awed by these revelations, as the top spots in the BIER Rankings merely confirm what you and me and even casual NBA fans already know, while also confirming that BIER’s a reliable box score stats model that works. (For an explanation of BIER and its basics, see notes below this post, wherein the thorny question of whether or not the world really needs another advanced box score metric is also addressed).

Here’s the entire BIER Top 20 at the All-Star break (through games of Feb. 15):

The All-Star break made for a good stopping point for the compiling of things, so I found some time to crunch the 2017-18 season BIER numbers for every NBA player, then created a relative scoring system by position to rank the top 60-70 players (expressed as “median +”). For example: Giannis has a BIER rating of 15.91, which is 10.24 above the median (5.67) for all power forwards. James Harden’s rating is actually lower (due to missed shot volume and turnovers) but because the median for shooting guards this season is 3.005, he comes out on top in this “relative” ranking system at 11.52.

The non-centers in the first 16 are another affirmation that this BIER thing is no crackpot system — from Harden to Irving, the fans, players and coaches got the easy 12 All-Stars right, noting that Chris Paul didn’t make the mid-season party due to missed games (injury) earlier in the season.

Chris Paul (left) and James Harden have their sights set on the Warriors’ Western Conference title and a shot at winning it all this season in Houston. USA Today Sports photo. License: Standard non-commercial use.

James Harden will, in all likelihood, win the MVP this year and deserve it. A 14.53 BIER for a shooting guard is the territory of Michael Jordan, the only SG in history to record a career BIER greater than 14. That Harden doesn’t shoot as efficiently as Jordan hardly matters when the Beard is doing so much of everything else in the box score, and the Rockets have won 17 straight. And his 38% from three is the best he’s shot it since his 2012, his last year in OKC.

Anthony Davis edges out Antetokounmpo with better free throw shooting, offensive rebounding, blocked shots, fewer turnovers (the Brow doesn’t play point forward) and fewer fouls. Since I crunched these numbers, the Pelicans have won 7 straight and Davis has gone for 40+ points in three of the wins. Giannis and the Bucks have won 2, lost 6, and fallen to 8th in the East, though Giannis has been good enough to stay in the league’s top 5 or 6 rated players.

Lebron James, at age 33, is averaging 26 pts, 9 boards and 8 assists per game, feats that a 33-year-old Larry Bird nearly matched (24.3 pts – 9.5 rebs – 7.5 assists) — but Lebron is showing no signs of slowing down. The Oscar Robertson for modern times, however, turns it over a lot (4.3 per 36 – BIER is a per minute, pace adjusted model) and doesn’t rebound like the Brow or the Greek Freak — and those factors tend to offset his greater assist rate in the BIER rating. All three forwards were shooting 54% from the field at the break. 

Steph Curry laid a little low last season as he worked to integrate Kevin Durant into the Warriors offense, but Steph’s back to MVP form this season, shooting just one FG% point shy of the 50-40-90 Club — and how does he manage nearly 6 boards a game? In Houston, Chris Paul has quietly gone about his business (except for that craziness with the Clippers), and the business of Chris Paul  is to file top 5 All-Time BIER point guard numbers. CP3 is right there with John Stockton at No. 2 behind Magic Johnson, which means that Curry isn’t far behind on the All-Time list.

“Seventh? That can’t be right.” Jimmy Butler‘s having another great season, reunited with coach Thibs. T-wolves photo. License: Standard non-commercial use.

Jimmy Butler‘s career NBA offensive rating is 10th All-Time, believe it or not, and 3rd among active players (behind Paul and DeAndre Jordan). Kevin Durant is shooting 43% from three, but he’s a bit off this season — his true shooting percentage is down .04 points, from 65.1% to 64.7%. The numbers being filed by these top 9 players are unreal. (Russell Westbrook will get a full discussion below in the notes).

Rockets center Clint Capela represents part of the Frankenstein model for centers in the new NBA — “Frankenstein” because no player possesses all the many attributes found in the crop of young centers. Capela is quick, athletic, mobile enough to guard the 3-point line, a shot-blocker, rebounder and dunker of many lob passes — which means he doesn’t miss many shots and BIER loves that. Basketball-reference had a stat the other day about how Capela this season will become the youngest player in NBA history (age 23) to record a double-double season while shooting 65% or better. He also blocks 2.4 shots/36, 3rd among qualifying centers. (Capela also represents the part of the new NBA center model where the center doesn’t play full-time minutes, though he does qualify to be ranked here. The minimum qualification for BIER ranking is playing time of 25 mins per game, with a case-by-case minimum on number of games due to the crazy number of star players getting hurt this season).

Thought the Knicks most impactful player was Kristaps Porzingis? Nope, that guy is Enes Kanter, who’s been a high-efficiency brawler in the offensive paint in New York (his 5 OREBs per 36 is 3rd among NBA centers). Porzingis, despite the NY media glow and All-Star politics, won’t make the lists here, which should tell you there was a reason the Knicks weren’t winning before “the Unicorn” had season-ending knee surgery.

2017-18 has been Damien Lillard’s finest season, according to BIER. NBA.com photo. License: Standard non-commercial use.

But let’s talk about the players who are on the list, like Damian Lillard, on fire of late and having his best season as a pro in Portland, according to BIER; and Victor Oladipo, having a breakout year leading the Pacers into the hunt for top-4 playoff seeding in the East.

Pistons center Andre Drummond edges out Hassan Whiteside of the Heat to rank 14th, and it’s not all about offensive rebounding, though Drummond leads the league on the O-glass; it’s also about Drummond’s better passing and his theft rate. Drummond leads all qualifying centers in steals per 36 mins (1.7) and his assist rate is double the median for centers. So despite not having quickness, mobility or shot-blocking ability (like Capela) Drummond’s got an all-around floor game that any box score-based advanced stat model would love. Whiteside is all of the above as an imposing defender and rebounder but doesn’t have all-around offensive skills like some “new centers”. Based on Miami’s winning ways in January, Whiteside probably would have been an All-Star had he not missed 18  games earlier this season, though who knows — the East coaches might’ve snubbed Whiteside too, as they did with Drummond in the first-seven reserves voting. Heat point guard Goran Dragic was selected.

Surprised that Kyrie Irving — who’s flirting with 50-40-90 Club shooting season and would be the 8th player in history to join that club — isn’t ranked higher? Irving has thrived in Boston, but it’s not as though he’s transformed into a wholly different player. Other point guards, even Lillard, pass the ball more, as Irving’s assist rate is about the league median for PGs (5.5 per 36). But Irving this season is well ahead (at 10.17) of his career BIER rate (8.49).

DeAndre Jordan, in his 10th season Clippers, may not have the quickness to defend the perimeter (like Capela) but he can dunk a lob pass like nobody’s business. 10 years in Lob City have put Jordan on the Top 20 All-TIme BIER center lists, and he’s quietly had another great year as L.A. battles down the stretch for a playoff spot. The rebounding numbers for Jordan, Drummond and Whiteside are off the charts – all three centers board at nearly 17 rebs per 36. Ridiculous, but also a reflection of the all-time low offensive rebounding rates in the NBA this season. Crashing the offensive glass is a feature of bygone days in the NBA.

Is it the player or the system? Whichever it is, Kyle Anderson of the Spurs made the BIER Top 20 at the All-Star break. Photo by Ronald Martinez, Getty Images. License: Standard non-commercial use.

Who is Kyle Anderson? He’s the 24-year-old forward for the Spurs who’s been starting in place of injured Kawhi Leonard (shoulder). Anderson doesn’t shoot a lot (8 times per 36 mins) but hits a high percentage (51%), and rebounds the small forward position like it was the 1980s (7.5 per 36), while dishing out  3.6 assists and coming up with 1.8 steals/36 (2nd among SFs). He’s filling up the box score without turning it over or fouling a lot — all of which has him in the Top 20, sneaking in just above the 25 minutes per game requirement. But there’s always the nagging question for the Spurs’ small forward — is it the player or the Popovich system?

Otto Porter is a super-efficient shooter at forward (49-40-84%) and one of the reasons the Wizards kept winning when John Wall went down with a knee injury at the end of January. In his 5th season, Porter’s a strong wing defender who rebounds his position (7.3 per 36) and has the 3rd-best SF steal rate (1.8/36). In the Wizards recent win in Milwaukee, Porter stole the ball three times while turning it over 0 times. The 0 turnovers were no happy accident — he rarely turns it over, just once per 36 mins while playing catch-and-shoot with the Wizards All-Star guards. Porter is averaging a career best 15.1 pts per game this season.

Karl Anthony Towns is one of the few centers in the league actually making a high enough % of his 3-point attempts to be out there shooting them. Towns was shooting 55-42-86% on FGs-3pt-FTs at the All-Star break and his numbers have actually improved slightly since then. No center in the history of the NBA has shot the ball from the outside as well as Towns, who is only going to get better.

That’s the Top 20, and here’s the next 20, where the BIER calculation didn’t fail to produce some surprises.

Orlando traded Elfrid Payton to Phoenix for a 2nd round pick, even though he’d found ways to minimize his poor outside shooting while maximizing the rest of his game. Photo by Zimbio. License: Standard non-commercial use.

Elfrid Payton and Rondae Hollis-Jefferson ahead of All-Stars like Paul George, Bradley Beal and Kemba Walker? They play NBA games in Orlando and Brooklyn, and there are some young players on those teams filling up box scores and finding their games in the league. The BIER formula does what it does.

Payton was easily the biggest surprise for me — and the Magic traded him to the Suns last month for a 2nd round pick, so I wasn’t expecting him to show up here. The problem with Payton (the marvel of his hairdo notwithstanding) is that he can’t shoot; but unlike a lot of guys who can’t shoot in the NBA, Payton has figured out how avoid throwing up bad shots. He shoots 50%, has made 35% of his threes this season, and as a taller point guard has high rebound and assist rates. Orlando just didn’t want to pay him this summer after his 4-year rookie contract expired, but Phoenix might be a good fit given the young guns on the Suns.

Steven Adams — the unsung hero on the Thunder — leads off “the next 20” rankings  and is having a monster season for OKC. Adams’ OREB rate is 2nd only to Drummond among centers, and OKC leads the NBA in offensive rebounding (28.3% rate). Somebody’s gotta save all those possessions Westbrook, Paul George and Carmelo toss at the rim, and there are a lot of those — but it all evens out in the rebounding and 2nd chance points, where Adams is 3rd in the NBA at 4.6 per game. Adams gets 14 pts and 9 rebs a game in a full time (32 mpg) role. (He also joins Antetokounmpo, Porter, Rudy Gobert and Oladipo as players from the much-maligned 2013 draft who have steadily improved to the point where, now in their 5th seasons, they’re bonafide players to be reckoned with in the league.)

BIER says Ben Simmons of the 76ers should win Rookie of the Year (and he probably will), averaging an all-around 16.9 pts – 8 rebs – 7.6 assists/36. BIER likes even better the break-out shooting season Darren Collison is having for the Pacers, and Collison is the 3rd point guard in rankings flirting with a “50-40-90 Club” season. With Oladipo at No. 13 and Collison at No. 24, suddenly the Pacers have one of the most efficient and impactful backcourts in the league, so far rating better than Derozan-Lowry, Wall (injured)-Beal and Lillard-McCollum.

From there we see a string of All-Stars led by Demar Derozan, having another great season in Toronto, his running mate Kyle Lowry, and Kevin Love — eight All-Stars in all ranked 25th-39th. I didn’t have the heart to classify Kevin Love as a center, so I split the difference making him a half-center, half-power forward. Basketball-reference has Love playing center 98% of the time this season, but Love’s a center in name only — 40% of his shots were threes (before another injury sidelined him). I also split the difference with Draymond Green, who alternates between power forward and small forward with Kevin Durant (also spit). Few — if any — teams play “positionless basketball” but the Warriors are one that does with their forwards. And the Cavs? Let’s just say that deciding to play without a center doesn’t make Keven Love a center. He’s been a stretch 4 power forward his entire career.

At No. 29 Tyreke Evans in Memphis got back to the 20-5-5 numbers he put up when he beat out Steph Curry and Brandon Jennings for the 2010 Rookie of the Year award. Good numbers, though I can’t help but wonder if Evans will ever be able to put up those numbers for a team that wins games. In Brooklyn, BIER finds a player in the rough in Rondae Hollis-Jefferson, a steadily improving 3rd year forward who, if he ever learns to shoot the three (he’s hitting just 26% this season), could develop into a star given the strength of the rest of his game.

Nuggets center Nikola Jokic is No. 30 in the BIER rankings and joins the Clipper’s Lou Williams as the top Western Conference players snubbed in the 2018 All-Star selection. USA Today photo. License: Standard non-commercial use.

Nikola Jokic is another center to be reckoned within the new model for center play, representing the 7-footers with mad guard skills. Jokic posted the fastest triple double in NBA history in Milwaukee just before the All-Star break and has all-around numbers at 16.9 ppg, 10.6 rebs and 5.9 assists per game. He’s also one of only a handful of qualifying centers shooting in the neighborhood of the NBA avg. of 36.1% behind the arc. The Joker was shooting 36.3% at the break. Al Horford, Towns, Love and Pau Gasol are the others, a list of 5 that looks a bit too forward-ish to really reflect a “centers shooting threes” trend, if making the 3-pointers has anything to do with it. (This is a topic begging for a separate blog).

Paul George shows up here at No. 35, and relative to other small forwards he’s Top 4 — and shooting 43% from three this season in addition to being one of the best defenders in the league. He was the 8th reserve All-Star selected by the West coaches, and BIER confirms this a fair choice. Never has a borderline All-Star received as much media attention as George does, however, and I think nearly every NBA broadcaster who’s seen Lou Williams play lately has said that “Lou Williams should have been an All-Star”. BIER also confirms this, and Lou’s ahead of George at No. 26 in the BIER ranking.

Is Toronto center Jonas Valanciunas really shooting 44.6% from three and why is he on this list? Well, he’s not on the list really, and he’s taking fewer than one 3-pointer a game, so he’s not really on that list either, nor his he playing the minimum of 25 mins per game. I included both Valanciunas and Boston’s Greg Monroe (who also hasn’t qualified) because they have so much in common as so-called “dinosaur” centers and their BIER numbers are so nearly identical that it’s just interesting to look at. At the end of the day, Valanciunas and Monroe are more efficient scorers and better rebounders than the vast majority of the centers in the league; and when they’re in the game, they contribute big impact numbers despite neither Boston or Toronto prefers to play inside-out.

Jrue Holiday closes out the Top 40, which makes a lot of sense in light of Holiday finding a next level to his game in New Orleans playing with Rajon Rondo and Anthony Davis in the absence of injured DeMarcus Cousins. Holiday’s averaged 21.7 pts and 7.6 assists since Cousins season ended Jan. 26, and he’s raised his 3-point shooting to 35% on the season.

Where oh where, Boozy Bango the Bucks fan wants to know, are Eric Bledsoe and Khris Middleton? They appear in the next 20, with Bledsoe ranked No. 49 and Middleton at No. 58, which seems to point to where the Bucks are at — struggling to beat other playoff teams, falling to 8th in East, losing three out of 4 to the Pacers and all three of their scheduled games to the Heat. Not that Top 50 for Bledsoe isn’t good, or that No. 58 is a dishonor for Middleton — All-Stars Al Horford (53), John Wall (55) and Klay Thompson (56) populate the 41-60 rankings. It’s just that Horford, Wall and Thompson probably shouldn’t have been named All-Stars this season, according to BIER — and the Bucks have not been quite good enough. Here’s the the next 22:

Wait, what is this BIER thing?

And do we really need another advanced box score metric? Of course we don’t need it, not really, and it can be a real headache if you want to get down to the nitty-gritty of assist rates and other adjustments, like the horrific free throw shooting of so many centers. But you don’t have to worry about the headaches because the editorial board chains J.D. Mo to his laptop a few times a month and has him sort it all out until he’s got a headache. (Unfortunately, the board can’t always get him to write anything, or a blog like this one would have appeared last year at the All-Star break, the first time he ran the whole league through the BIER model).

All hubris noted, the justification for BIER can be found in the flaws of other models such as John Hollinger’s infamous PER (the one ESPN bought), NBA 2K, and a lot of the fantasy scoring systems, where volume scoring is valued over efficient scoring. PER commits a major statistical no-no in that it bases missed shot value on offensive rating (points per possession) instead of on basketball’s basic 2-point scoring system. The main factor defining the offensive rating is whether or not shots go in the bucket, so there’s a causal relationship there. If most of the league shoots poorly, which happened in the dead ball era, it follows that possession value drops (which it did, all the way down to 1.04 pts per possession) and a little less is deducted with each miss. Bad shooting is rewarded. Conversely, good shooting is punished in PER because good shooting leads to a higher offensive rating which results in a higher missed shot value.

Oh, the adjustments made to correct for this problem! But once those are done, PER remains relevant only within each season. When you hear NBA analysts criticizing advanced metrics for “tailoring” to the changing game, PER is what they’re talking about, to say nothing of the arbitrary downgrading of all things rebounding that occurs within the PER formula. It’s as though Hollinger chose Kobe’s side in the Kobe-Shaq conflict of the early 2000s and form-fit his formula to justify it, at a time when Shaq was so dominant it was almost boring. One hears less talk of PER now as advanced stats geeks and saber-metrics pros have moved on to better measures, and the search for the Holy Grail model of Basketball analytics goes ever onward.

Why not simply keep shooting independent of the offensive rating and create a scoring system that conforms to basketball’s 2-point basic scoring system? BIER does this by letting the rebounding rate decide what to deduct for a missed shot and multiplying by two to create 2-point values out of the percentages, similar to the Win Score/Game Score model used at Basketball-reference.com — but also uses some of the genius parts parts PER (specifically the assist adjustment for made shots). BIER is Frankenstein, constructed off of the best parts of PER and the more sensible WS game score formulae.

For example: The current leaguewide rate for the defense rebounding missed shots is 77.6%, the all-time high in the NBA. Because percentages are on a whole-of-one value, multiply .776 x 2 to conform to basketball’s 2-point scoring base and get 1.552 — this is the hit a shooter takes when he (or she) misses a shot in the 2017-18 season. The defensive rebounder is awarded (2 – 1.552 = 0.448), and the possession ends. Conversely, if the offense grabs the miss, the rebounder who saved the possession is effectively canceling out the missed shot, so that’s + 1.552 for the rebounding player but the -1.55 stays with the shooter as the possession continues. A -1.55 seems like a big deduction for a missed shot, but with offensive rebounding at an all-time low, the numbers are only a reflection of the changing game. A shooter who misses 2/3 three-pointers will end up in the negative, but that’s OK. 33% 3-point shooting does not usually win games given the league average at 36.1%. The game itself says the 33% shooter is digging his (or her) team a hole.

In practice (using current league-wide numbers), if a shooter goes 3 out of 10 from 3-point-land, the shooter scores +7.782 in both PER and BIER (after a basic assist adjust), but PER deducts only 5.9 for the misses to keep our volume shooter ahead + 1.88 even though the shooter is (probably) losing the game for his team. BIER deducts 7 x 1.55 for the misses, or 10.85, leaving our volume shooter minus – 3.07. By then, the shooter is probably on the bench or, if still in the game, being frozen out by his point guard, who’s looking for more efficient scoring. Kobe Bryant shot like this often, but Kobe got to the line 8-10 times a game in his prime and did a lot of other things on the court to help his Lakers win. Still, PER helped the volume shooters of the deadball era (Kobe, Tracy McGrady, Paul Pierce, Michael Redd et. al) look a lot better than they were.

The rates are adjustable within BIER, of course, and Russell Westbrook and the OKC Thunder are a great example of this — the Thunder lead the league in offensive rebounding at 28.1%, so when Westbrook misses, J.D. Mo uses the OKC rebounding number (minus-1.44) instead of the leaguewide number. About 64% of Westbrook’s shots are unassisted, so when the assist adjustment in BIER is applied to Westbrook (as part of the 2-point system), the assist rate of (1 – .6325 = 0.3675) is used, the lowest assisted basket rate I’ve seen this season.

But let’s not get ahead of things. At this point it should be noted that BIER in-season numbers are adjusted for both the pace and the assist rates of each team, and are expressed per 36 mins. It’s not a good idea to adjust for rebounding rates except in rare circumstances such as OKC, where the rebounding is part of their offensive strategy. Most teams don’t do this, and it would be another statistical no-no to reward good offensive rebounders with a lower OREB value, so the leaguewide rates for rebounds are always used and missed shot value adjusted only in rare cases (again, missed shot value = DREB rate x 2, and missed shot value = OREB value). Let’s introduce some terms and the first part of the formula.

  • Made shot value = 2 or (3 for 3-point shots), one for free throws
  • Point value (or scoring) is expressed at the beginning of the equation as ptsper36
  • Missed shot value is 1.55
  • First part of the equation is: ptsper36 – [(field goal attempts – field goals made) x 1.55]

Why points per 36? The purpose of BIER is to compare players within a season, and also to compare players’ career numbers. Who’s better, Lebron or Bird? Who’s having the better season, Lebron or Giannis? Is Anthony Davis putting up better all around numbers than James Harden? And so on. The super-duper stars play about 36 mins per game, so using per36 stats just makes sense. Also, by equalizing every player to 36, BIER shows which part-time players are having the highest impact, and impact is an important part of BIER. There is an additional calculation J.D. Mo has been making lately to undo the per36 numbers and get a real-BIER based on how many minutes players are actually on the court, but typically when BIER is used in the blog (as in the rankings above) it is expressed as the per36 BIER number. Yes, everything is adjusted for pace, equalized at 100 possessions per game.

The assist adjustment is Hollinger’s PER adjustment, which enables any stat geek to run the numbers using the box score stats, avoiding the problem of needing to know which made shots were assisted and which were unassisted. An assist has a value of 0.7 in BIER (and PER), with the idea that the assist value is taken away from the scorer and given to the passer within the 2-point model. Many assists aren’t worth 0.7 points, being the result of the ball moving around the perimeter to the open shooter or simply an exercise of typical team offense, but some assists (like lob passes to dunking 7-footers or behind-the-back passes on the break) are worth the price of admission, so the hope is that it balances out. The 0.7 value seems sensible and fair, and it’s the standard value used in other systems, so I adopted for BIER.

Not knowing which baskets in a box score are assisted or unassisted means the formula has to assign an assist rate to calculate an average assist adjustment for every made shot. This can be the leaguewide 2017-18 assist rate of 0.58, a basic 0.6 or a more detailed rate depending on how much work one feels like doing. This is why the editorial board chains J.D. Mo to his laptop and has him calculate the assist rates for each team as well a special assist rate for point guards. Each point guard or high assist player (like point forwards Lebron James, Giannis Antetokounmpo and Draymond Green) in the charts above has a separately calculated assist rate, which is how Westbrook’s 0.3675 assist rate was arrived at.

The calculation of the assist adjust = made shots x 0.7 x assist rate. Westbrook makes 9.5 shots per 36, so multiply 9.5 x 0.7 x 03675 = 2.444. This is subtracted from Westbrook’s points per 36 at the start of the equation:

25.3 – (assist adjust of 2.444) – [(FGA 21.4 – Made FGs 9.5) x 1.44] = 5.724

Because Westbrook misses a lot of shots (11.9 per 36) and shoots just 44.4%, he’s doing a lot of work to end up +5.724, while a 55% shooter like Lebron James, Anthony Davis or Giannis Antetokounmpo will generate a higher + value given fewer shot attempts. This is the efficiency side of BIER. All three forwards ranked higher than Westbrook on the above BIER Top 20.

How are three point shots calculated in BIER? Missed or made threes are not part of the formula because they are accounted for in the per36 points scored at the beginning of the formula. In the BIER spreadsheets, columns for 3-pointers made, attempted and the % are included because it’s instructive to see what a player’s shooting from downtown, but there’s no need to treat missed 3-pointers any differently than a missed layup. Both the points and the made FGs are already accounted for in the formula, and missed threes are calculated along with the 2-point misses in FGA-FGs.

Free throws attempted and made are divided by two, right? Yep, and the next step after figuring out the assist adjust and the missed shot deduction is to calculate the missed free throws deduction. A first missed FT, however, is always rebounded by the team offense and a 2nd (or 3rd) missed FT is almost always rebounded by the defense — so how do we account for this in the rebound rate/missed shot value? The only available source out there seems to be a study by 82games.com that said 86.1% of missed free throws are rebounded by the defense. That’s a rate for a contested missed free throw rebound, obviously, and it’s an older study from the early 2000s — but it’s the only research I’ve found. I also couldn’t think of any justification for reducing the deduction of a missed free throw by taking into account the unknown % of missed first FTs, so the 86.1% rebound rate is applied in BIER for all missed free throws.

Here’s what the free throw calculation looks like:

(Free throws attempted – Free throws made)/2 x (2 x 0.861) or (FTA – FTM)/2 x 1.722

Westbrook attempted 6.9 FTs per 36 and made 5 through games of Feb. 15, so we calculate his misses, divide by two to convert one point FTs to the basic 2-point framework of the game, then multiply the misses by the 2-point scale defensive rebounding rate (FTA 6.9 – FTM 5) = 1.9 / 2 to get 0.95 x 1.722 = 1.636

The missed FT value is also subtracted from the points per 36 at the beginning of the formula. Westbrook’s scoring per36 gets cut down to a + 4.088. Put it all together and the scoring efficiency part of the formula looks like this (using leaguewide rebounding rates):

PTSper36 – (FGM x 0.7 x team AssistRate) – [(FGA – FGM) x 1.55] – [(FTA-FTM)/2 x 1.722]

The rest of the formula is fairly straightforward. Values of offensive and defensive rebounds, assists, steals and blocked shots are added — turnovers and fouls are subtracted.

  • Offensive rebounds (OREBs): 1.55
  • Defensive rebounds (DREBs): 0.45
  • Assists: 0.7
  • Steals: leaguewide points per possession (1.086)
  • Blocked shots: 0.57 x leaguewide pts per possession = 0.61 or just 0.6
  • Turnovers: – leaguewide pts per possession -(1.086)
  • Fouls: For ever foul committed, the opponent ends up shooting 0.852 free throws. Remarkably, this rate has changed only by one-thousandths over the last 40 NBA seasons.

Here’s the entire formula:

PTSper36 – (FGM x 0.7 x team AssistRate) – [(FGA – FGM) x 1.55] – [(FTA-FTM)/2 x 1.722] + OREBs x 1.55 + DREBs x 0.45 + Assists x 0.7 + STLS x 1.086 + Blocks x 0.6 – TOVs x 1.086 – PFs x 0.852 = BIER unadjusted for pace.

All BIER ratings are pace-adjusted to 100 possessions per game, so a player who plays at a pace of 95 will adjust up 100/95 — the pace played is the denominator. This number (1.05 in this example) is multiplied by “unadjusted BIER” arrived at above. Westbrook’s unadjusted BIER through Feb. 15 was 11.38. The Thunder play at a 96.1 possessions per game rate, so to get to BIER100 multiply 11.38 x 100/96.1 = 11.84, the number in the Top 20 chart above.

The highest career BIER player rating in NBA history is an estimated 18.98 recorded by Wilt Chamberlain (1960-1973), estimated because box score stats were not complete until 1977 when turnovers were added. Offensive/Defensive rebounds, blocked shots and steals were added to box scores in 1974. The highest career BIER since 1977 belongs to Magic Johnson at 17.49 and then Charles Barkley with a 17.18, the best career rating for a forward in NBA history. Sir Charles was a highly efficient scorer who passed the ball more than most remember and really was the Round Mound of Rebound (his 3.9 OREBS per 36 were absurdly great).

Michael Jordan finished his career at 14.58. No other shooting guard comes close. Larry Bird (14.51) and Lebron James (13.95 at the start of this season), the never-ending comparison, lead the small forwards of NBA history (though both did/have done time at power forward) with Lebron due to close the gap with a 15+ BIER this season. Kevin Durant (12.68 entering 2017-18) is so far a Top 5 BIER small forward in NBA history, just ahead of great mid-range shooter Adrian Dantley but still a full point behind Julius “Dr. J” Erving (13.59).

Chris Paul (13.8 – 2nd pg behind Magic), James Harden (11.16 – 5th, sg) and Anthony Davis (14.65 – 2nd pf behind Barkley) are the other current players who began the season in the Top 5 All-Time career BIER at their respective positions, though Davis in just his 5th year hasn’t played long enough to be ranked All-Time. Steph Curry (career 11. 49) in his 9th year has the tenure, and could possibly move ahead of Oscar “the Big O” Robinson in 5th on the All-Time point guards list, for the time being anyway.

BIER may be tough on players who don’t make shots or do much other than shoot, due to the current high 1.55 deduction for missed shots, but isn’t that what an advanced box score rating system should be? The NBA’s very best players are having no trouble posting historic numbers in BIER — or any other metric — and if the average and below average players score low, then the system is doing its job.

— J.D. Mo