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Advanced Stats Analysis: Percentage Magnitude Index

Michael Chua

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.

Saviors, Killers, and Padders

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)TagDescription
Greater than or equal to 2.00SaviorPolarizing positive impact
Between 1.00 and 1.99PadderNoticeable positive impact
Between -0.99 and 0.99NoneNegligible impact
Between -1.99 and -1.00NoneNoticeable negative impact
Less than or equal to -2.00KillerPolarizing 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)

RankPlayerFGMFGAFG%PMITag
1LeBron James10.218.6.550+6.96Savior
2Kevin Durant9.618.5.520+4.31Savior
3Dwight Howard5.910.3.576+3.45Savior
4David Lee8.215.7.522+3.41Savior
5Chris Bosh6.612.2.543+3.15Savior
6Tyson Chandler4.46.6.673+3.14Savior
7Blake Griffin7.313.8.529+3.12Savior
8Tony Parker7.915.1.520+3.07Savior
9Serge Ibaka5.910.6.560+3.07Savior
10Brook Lopez7.514.4.521+2.90Savior
11Al Horford7.013.3.528+2.89Savior
12Dwyane Wade7.715.1.512+2.58Savior
13Thaddeus Young6.712.9.519+2.32Savior
14J.J. Hickson5.19.3.551+2.22Savior
15Tiago Splitter3.96.4.603+1.96Padder
16Robin Lopez4.88.7.548+1.91Padder
17Kenneth Faried4.99.0.543+1.90Padder
18Tim Duncan7.013.9.505+1.88Padder
19Nikola Pekovic6.312.4.511+1.82Padder
20DeAndre Jordan3.76.2.599+1.80Padder

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)

RankPlayerFGMFGAFG%PMITag
1Kevin Love5.816.6.352-8.50Killer
2Raymond Felton6.516.4.396-5.22Killer
3Monta Ellis7.117.5.404-5.19Killer
4Dion Waiters5.414.2.378-5.11Killer
5Russell Westbrook7.918.9.418-4.65Killer
6J.R. Smith6.215.5.400-4.50Killer
7Andrea Bargnani6.015.2.398-4.48Killer
8Brandon Jennings6.716.5.409-4.35Killer
9Eric Gordon5.714.5.396-4.25Killer
10Rudy Gay6.716.4.410-4.23Killer
11Byron Mullens4.411.9.371-4.09Killer
12Bradley Beal4.812.4.390-3.54Killer
13Deron Williams5.613.7.405-3.40Killer
14Klay Thompson5.814.0.410-3.25Killer
15Jameer Nelson5.613.7.411-3.09Killer
16Damian Lillard6.515.4.423-2.99Killer
17Paul Pierce6.415.0.422-2.92Killer
18James Harden7.717.8.434-2.91Killer
19Paul George6.415.2.424-2.86Killer
20Dirk Nowitzki5.012.3.408-2.71Killer

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)

RankPlayerFTMFTAFT%PMITag
1Kevin Durant8.49.3.910+17.44Savior
2James Harden8.510.0.855+12.24Savior
3Kobe Bryant6.57.8.838+5.96Savior
4Carmelo Anthony6.47.8.824+4.73Savior
5Chris Paul4.04.5.897+3.70Savior
6Ramon Sessions4.85.7.841+3.32Savior
7John Wall4.95.9.829+2.96Savior
8Kevin Martin3.53.8.912+2.95Savior
9Deron Williams4.14.7.861+2.89Savior
10Eric Gordon4.55.5.833+2.74Savior
11Kyrie Irving4.35.1.841+2.66Savior
12Jamal Crawford3.43.9.878+2.37Savior
13Russell Westbrook5.67.0.803+2.33Savior
14Stephen Curry3.23.6.894+2.31Savior
15Marc Gasol3.43.9.875+2.30Savior
16Darren Collison3.13.5.881+1.96Padder
17DeMar DeRozan3.94.7.831+1.94Padder
18Kyle Lowry3.84.6.833+1.92Padder
19O.J. Mayo3.23.8.861+1.89Padder
20LaMarcus Aldridge4.14.9.822+1.80Padder

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)

RankPlayerFTMFTAFT%PMITag
1Dwight Howard4.89.6.504-35.30Killer
2Josh Smith2.04.0.510-5.99Killer
3Kevin Love5.67.9.704-5.93Killer
4Omer Asik2.34.3.551-5.83Killer
5Blake Griffin3.55.5.640-5.66Killer
6DeAndre Jordan1.43.3.428-5.36Killer
7Kenneth Faried2.33.7.607-3.21Killer
8Tyson Chandler3.24.7.681-2.83Killer
9Andre Iguodala2.13.5.614-2.75Killer
10Greg Monroe3.44.8.695-2.49Killer
11Andre Drummond0.92.2.418-2.45Killer
12JaVale McGee1.83.0.590-2.33Killer
13Thaddeus Young1.52.7.566-2.14Killer
14Gerald Wallace2.43.7.667-2.03Killer
15Tristan Thompson1.93.1.624-2.02Killer
16Al Horford1.62.7.585-1.94None
17LeBron James4.76.4.738-1.89None
18J.J. Hickson2.13.3.652-1.85None
19Dwyane Wade4.76.4.740-1.77None
20Paul Millsap3.65.0.725-1.62None

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.
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