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# Advanced Stats Analysis: Percentage Magnitude Index

### Michael Chua

Michael Chua is a basketball statistics expert from the Philippines. He has worked as a student manager for the University of Wisconsin Men's basketball team. He is also the basketball program consultant for his high school alma mater, Shanghai American School, in China.

Impact of Percentages

Percentages

Dwight Howard's atrocious performances from the free-throw line can drive his Lakers into the ground. Coincidentally, not a single Howard owner in any head-to-head fantasy league can win free throws most weeks.

In my previous article, I discussed the importance of dynamics. While the idea is beneficial for counting categories, percentage categories (field-goal and free-throw percentages) follow a different set of rules.

The percentages categories are a significant factor in head-to-head leagues because they account for two categories in weekly matchups, enough to decide a win from a loss. Therefore, it is essential for owners to understand the nature of how percentage categories accumulate within the context of head-to-head leagues.

A common mistake made by inexperienced managers is to base a player's contribution in percentage categories solely on the raw percentages themselves. Although I am an advocate of simplicity, raw percentages fail to tell the whole story. Within a limited scope of evaluation, a player like J.J. Redick (.901 percent) would be deemed more valuable in free throw contribution than James Harden (.855 percent). While Redick is unquestionably an asset for free throws, his impact falls short of Harden's.

Percentage categories are calculated by dividing the sum of shots made by the sum of shots attempted, not by computing the average of player percentages. Therefore, raw percentages are insufficient in determining a player's true value.

While this may not be rocket-science, it is still often overlooked by first-timers. Experienced managers are wise to take into consideration the magnitude of shot attempts, in addition to the raw percentages, when gauging a player's impact in percentage categories. However, the question still remains as to how one can quantify the impact in a tangible form, and how the impact can be compared with that of other players.

Percentage Magnitude Index (PMI)

Percentage Magnitude Index (PMI) is a statistical measurement of a player's impact on percentage categories (field goal and free throw). PMI, as its name suggests, takes into account a player's shooting percentage as well as the magnitude of shot attempts. Due to the nature of basketball, accumulation patterns for field goals and free throws differ greatly. Therefore, separate algorithms are used for calculating field goal and free throw PMI. A PMI with an absolute value less than 1.00 implies a player's insignificance in a particular percentage category in a head-to-head matchup, due to either a lack of shot attempts, or a percentage that is too neutral to have an impact. A PMI with an absolute value greater than or equal to 1.00 implies a player's significance in a particular percentage category in a head-to-head matchup, either positive or negative.

PMI can be relatively compared intra-category, but not necessarily inter-category. Positive and negative PMI can be compared by calculating for absolute value. PMI is stackable; therefore, the sum of PMI for multiple players can be calculated to evaluate a group of players or an entire team.

Players with a significant PMI (absolute value greater than or equal to 1.00) can be tagged as percentage saviors, killers, or padders. Saviors are scarce, and can singlehandedly "save" a team in a percentage category, in the absence of a killer. Their overarching positive impact on a category makes them invaluable in head-to-head leagues. Killers, their counterparts, do the opposite. Killers can singlehandedly "kill" a team in a percentage category, in the absence of a savior. Essentially, their opposing polarities cancel each other out. Despite having such a negative impact on percentage categories, killers often produce well in volume categories. Therefore, it is not uncommon for managers to take on percentage killers, considering the tradeoff that reaps benefits in other categories. This is where padders come into play. Padders can "pad" a category, helping a savior to nullify the effects of a killer. In fact, it is a wise strategy to stack a team with multiple padders, regardless of a killer's presence, to create a buffer that can ensure victory even in off-weeks. Refer to the PMI-Tag Scale below.

 Percentage Magnitude Index (PMI) Tag Description Greater than or equal to 2.00 Savior Polarizing positive impact Between 1.00 and 1.99 Padder Noticeable positive impact Between -0.99 and 0.99 None Negligible impact Between -1.99 and -1.00 None Noticeable negative impact Less than or equal to -2.00 Killer Polarizing negative impact

Below, players are ranked by best and worst PMI for both percentage categories (field-goal and free-throw). All statistics are based on games played this season, as of January 24, 2013.

Best Field-Goal Percentage Magnitude Index (PMI)

 Rank Player FGM FGA FG% PMI Tag 1 LeBron James 10.2 18.6 .550 +6.96 Savior 2 Kevin Durant 9.6 18.5 .520 +4.31 Savior 3 Dwight Howard 5.9 10.3 .576 +3.45 Savior 4 David Lee 8.2 15.7 .522 +3.41 Savior 5 Chris Bosh 6.6 12.2 .543 +3.15 Savior 6 Tyson Chandler 4.4 6.6 .673 +3.14 Savior 7 Blake Griffin 7.3 13.8 .529 +3.12 Savior 8 Tony Parker 7.9 15.1 .520 +3.07 Savior 9 Serge Ibaka 5.9 10.6 .560 +3.07 Savior 10 Brook Lopez 7.5 14.4 .521 +2.90 Savior 11 Al Horford 7.0 13.3 .528 +2.89 Savior 12 Dwyane Wade 7.7 15.1 .512 +2.58 Savior 13 Thaddeus Young 6.7 12.9 .519 +2.32 Savior 14 J.J. Hickson 5.1 9.3 .551 +2.22 Savior 15 Tiago Splitter 3.9 6.4 .603 +1.96 Padder 16 Robin Lopez 4.8 8.7 .548 +1.91 Padder 17 Kenneth Faried 4.9 9.0 .543 +1.90 Padder 18 Tim Duncan 7.0 13.9 .505 +1.88 Padder 19 Nikola Pekovic 6.3 12.4 .511 +1.82 Padder 20 DeAndre Jordan 3.7 6.2 .599 +1.80 Padder

Note that Tyson Chandler is ranked sixth in field-goal PMI despite taking only 6.6 shots per game. This is because his whopping .673 shooting percentage from the field more than makes up for the low number of shots he takes.

Worst Field-Goal Percentage Magnitude Index (PMI)

 Rank Player FGM FGA FG% PMI Tag 1 Kevin Love 5.8 16.6 .352 -8.50 Killer 2 Raymond Felton 6.5 16.4 .396 -5.22 Killer 3 Monta Ellis 7.1 17.5 .404 -5.19 Killer 4 Dion Waiters 5.4 14.2 .378 -5.11 Killer 5 Russell Westbrook 7.9 18.9 .418 -4.65 Killer 6 J.R. Smith 6.2 15.5 .400 -4.50 Killer 7 Andrea Bargnani 6.0 15.2 .398 -4.48 Killer 8 Brandon Jennings 6.7 16.5 .409 -4.35 Killer 9 Eric Gordon 5.7 14.5 .396 -4.25 Killer 10 Rudy Gay 6.7 16.4 .410 -4.23 Killer 11 Byron Mullens 4.4 11.9 .371 -4.09 Killer 12 Bradley Beal 4.8 12.4 .390 -3.54 Killer 13 Deron Williams 5.6 13.7 .405 -3.40 Killer 14 Klay Thompson 5.8 14.0 .410 -3.25 Killer 15 Jameer Nelson 5.6 13.7 .411 -3.09 Killer 16 Damian Lillard 6.5 15.4 .423 -2.99 Killer 17 Paul Pierce 6.4 15.0 .422 -2.92 Killer 18 James Harden 7.7 17.8 .434 -2.91 Killer 19 Paul George 6.4 15.2 .424 -2.86 Killer 20 Dirk Nowitzki 5.0 12.3 .408 -2.71 Killer

Note that many of the worst field-goal percentage killers such as Kevin Love and Russell Westbrook are still valued highly in all leagues because of their contributions in other categories. This is why many managers choose to draft killers despite their low field-goal percentage.

Best Free-Throw Percentage Magnitude Index (PMI)

 Rank Player FTM FTA FT% PMI Tag 1 Kevin Durant 8.4 9.3 .910 +17.44 Savior 2 James Harden 8.5 10.0 .855 +12.24 Savior 3 Kobe Bryant 6.5 7.8 .838 +5.96 Savior 4 Carmelo Anthony 6.4 7.8 .824 +4.73 Savior 5 Chris Paul 4.0 4.5 .897 +3.70 Savior 6 Ramon Sessions 4.8 5.7 .841 +3.32 Savior 7 John Wall 4.9 5.9 .829 +2.96 Savior 8 Kevin Martin 3.5 3.8 .912 +2.95 Savior 9 Deron Williams 4.1 4.7 .861 +2.89 Savior 10 Eric Gordon 4.5 5.5 .833 +2.74 Savior 11 Kyrie Irving 4.3 5.1 .841 +2.66 Savior 12 Jamal Crawford 3.4 3.9 .878 +2.37 Savior 13 Russell Westbrook 5.6 7.0 .803 +2.33 Savior 14 Stephen Curry 3.2 3.6 .894 +2.31 Savior 15 Marc Gasol 3.4 3.9 .875 +2.30 Savior 16 Darren Collison 3.1 3.5 .881 +1.96 Padder 17 DeMar DeRozan 3.9 4.7 .831 +1.94 Padder 18 Kyle Lowry 3.8 4.6 .833 +1.92 Padder 19 O.J. Mayo 3.2 3.8 .861 +1.89 Padder 20 LaMarcus Aldridge 4.1 4.9 .822 +1.80 Padder

Note that Kevin Durant and James Harden are by far the best free-throw percentage contributors in head-to-head leagues. In addition to shooting high percentages, they are league leaders in free-throw attempts as well.

Worst Field-Goal Percentage Magnitude Index (PMI)

 Rank Player FTM FTA FT% PMI Tag 1 Dwight Howard 4.8 9.6 .504 -35.30 Killer 2 Josh Smith 2.0 4.0 .510 -5.99 Killer 3 Kevin Love 5.6 7.9 .704 -5.93 Killer 4 Omer Asik 2.3 4.3 .551 -5.83 Killer 5 Blake Griffin 3.5 5.5 .640 -5.66 Killer 6 DeAndre Jordan 1.4 3.3 .428 -5.36 Killer 7 Kenneth Faried 2.3 3.7 .607 -3.21 Killer 8 Tyson Chandler 3.2 4.7 .681 -2.83 Killer 9 Andre Iguodala 2.1 3.5 .614 -2.75 Killer 10 Greg Monroe 3.4 4.8 .695 -2.49 Killer 11 Andre Drummond 0.9 2.2 .418 -2.45 Killer 12 JaVale McGee 1.8 3.0 .590 -2.33 Killer 13 Thaddeus Young 1.5 2.7 .566 -2.14 Killer 14 Gerald Wallace 2.4 3.7 .667 -2.03 Killer 15 Tristan Thompson 1.9 3.1 .624 -2.02 Killer 16 Al Horford 1.6 2.7 .585 -1.94 None 17 LeBron James 4.7 6.4 .738 -1.89 None 18 J.J. Hickson 2.1 3.3 .652 -1.85 None 19 Dwyane Wade 4.7 6.4 .740 -1.77 None 20 Paul Millsap 3.6 5.0 .725 -1.62 None

Note Dwight Howard's free-throw PMI of -35.30. Because PMI is stackable, a fantasy team with Howard would hypothetically need Durant (+17.44), Harden (+12.24), and Kobe Bryant (+5.96) just to become an average free-throw percentage team. A team with Josh Smith (-5.99), however, can overcome a free-throw percentage deficit with just Bryant alone. This shows how negatively polarizing Howard is with free throws, and why owners can never expect to win that category in normal situations. A wise strategy for Howard owners is to buy low on other free-throw percentage killers, considering the tradeoffs that would provide productive numbers in other categories, such as field-goal percentage, rebounds, and blocks.

Conclusion

Understanding the importance of raw percentages as well as the magnitude of shot attempts is vital in dominating percentage categories. Always be sure to equip your team with saviors and padders to compensate for any killers you may decide to take on. Remember, the best saviors can carry their team to victory, no matter how cold and unforgiving the week may be.