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Using Principal Component Analysis to Identify High Quality Wide Receivers
Image via BMWard_2000/Flickr
Image via BMWard_2000/Flickr

RotoViz utilizes a lot of different metrics in an attempt to explore and discover patterns relating to fantasy football. When all the metrics are in agreement, things are easy. However, the metrics aren’t always in agreement. Stedman Bailey, for example, had great production metrics last year, but perhaps there were some red flags concerning his physique. This makes finding patterns more complex.

College production is great. Being a beastly athlete is great. Putting all the valuable information together to make an overall assessment, that’s tricky. One option is through visualization. To utilize many of the metrics endorsed by RotoViz, we then need to employ a dimensionality reduction technique. An often used technique is principal component analysis (PCA) which creates principal component (PC) variables from the input variables (i.e. the metrics). The principal components try to explain as much variance as possible in the underlying variables, orthogonally.

I decided to run a PCA on the following familiar variables, for which I had data available: Market share yards (MSYDS), market share touchdowns (MSTD), games dominated (GMSDOM), age (MAXAGE), dominator rating (DR), freak score (FS), explosion score (xplo), and height (HT).

PCA Biplot

biplot

This biplot illustrates the loadings of the different variables that I churned through the PCA algorithm, for the first two principal components (i.e. the two PCs explaining most of the variance). The first PC clearly represents production, while the second PC represents physique. The third PC, which is not illustrated, mostly represents age. The two first PCs account for almost 63% of the variance in the data.

 

Thoughts about the zoomable graph above:

– Clearly, you want to move towards the lower-left corner. This should be expected after seeing in which directions the variable loadings went in the biplot.

– Megatron is a beast. His combination of production and physique is unparalleled.

– There has been a lot of talk about the depth of this class. If one were to look at players that were below (remember, below is good) on both PCs, this class has 12 drafted or undrafted players in this lower-left quadrant. Last year’s class had just one player: Keenan Allen.

– There is an obvious survivorship bias as I only plotted drafted players available in my data set from previous years. Even so, the lower-left quadrant has 8 drafted players from this year’s draft compared to one from last year’s draft.

– RotoViz favorite Quincy Enunwa looks to be perhaps the most promising late-round prospect this year.

– UDFA gems are Eric Thomas (Colts), Brandon Wimberly (Jaguars) and Colin Lockett (Bengals). Although, Wimberly is a soon-to-be 25 year old whilst Lockett is listed as a TE. Conclusion: Go get Eric Thomas in the last round of your deep rookie draft.

Show Me More

Now, this might be a nice illustration, but how can you use this graph to make actionable decisions? One idea would be to create a frontier on this graph to decide between players. I might investigate this further later on, but for now I will create an arbitrary rule as my frontier. For illustration purposes I set the initial frontier as the area below the (0,0) point.* Note different scales on the graphs.

1st

First Round Principal Component Analysis

NAMEDPMAXAGEFORTYWTHTFSxploMSYDSMSTDDRGMSDOMFPG
Calvin Johnson221.34.3523977100.4176.40.510.540.522012.7
Aj Green422.44.4821175.666.3160.50.410.370.391612
Julio Jones621.94.3422074.884.7173.50.310.230.271111.8
Andre Johnson321.54.412307482.11710.330.340.341010.7
Larry Fitzgerald320.34.4822574.973.5173.70.450.580.521910.7
Demaryius Thomas22224.3822475.283.6161.20.70.540.622110.2
Percy Harvin2220.64.3919271.154.1152.40.270.350.3169.9
Dez Bryant2420.94.522247466.8163.60.540.670.6139.4
Reggie Wayne30224.451987253.4154.30.270.520.469.4
Roddy White2723.24.4620773.260.7161.90.50.540.5289.1
Hakeem Nicks29214.5121272.857.6149.50.460.380.42138.9
Dwayne Bowe2322.34.5122174.266.51580.320.330.32168.8
Jeremy Maclin1920.64.4519872.153.7157.30.270.280.2888.5
Justin Blackmon5224.4620772.960148.40.320.490.4178.4
Santonio Holmes2521.84.3518870.654.7165.60.370.50.44168
Michael Crabtree1021.34.5221573.460.2144.10.220.450.34127.9
Lee Evans1322.84.3919770.956.7154.50.410.480.44167.4
Santana Moss1621.54.3118169.652.3172.40.260.140.227.3
Roy Williams7224.4821174.563.9157.90.390.380.38186.8
Javon Walker2023.14.3821074.874.2165.50.330.20.2616.8
Kendall Wright2022.14.4919670.244.3159.50.370.40.38196.6
Cordarrelle Patterson2921.74.3321673.981.41650.20.160.1826.6
Tavon Austin821.84.2817468.548.61520.30.310.3116.5
Kenny Britt3020.34.521874.9671610.430.150.29136.4
Michael Floyd1322.14.422074.678.2158.50.340.430.38216.2
Braylon Edwards321.94.4521074.967.2162.50.460.510.48226.1
Donte Stallworth1321.14.3819772.160.3157.30.360.480.4276.1
Koren Robinson920.74.6121173.548.1161.50.320.440.3855.6
Deandre Hopkins2720.64.512147359.41510.350.580.46115.6
Mark Clayton2222.54.4119370.451144.50.260.20.23115.5
Robert Meachem2722.34.392147474.1158.50.380.380.38115
Rod Gardner1523.14.4821974.268.4160.50.410.20.305
Charles Rogers221.54.4820274.457.7152.40.490.450.47154.7
Michael Jenkins2921.64.421776.580.3150.50.320.230.28134.6
Darrius Heyward Bey721.94.2521073.685.4164.50.310.330.32104.5
Ashley Lelie1921.84.2919774.675.4164.20.350.490.42144.5
Reggie Williams920.54.5622575.867159.40.350.430.39134.4
Anthony Gonzalez3222.34.441937251.31610.270.190.2364.3
David Terrell821.74.4321375.171.7163.30.440.580.5174
Michael Clayton1521.24.6720974.843.3148.50.320.290.3133.9
Bryant Johnson1721.74.4621474.467.2158.60.360.170.2673.5
Ted Ginn921.64.3817871.246.6140.60.270.270.2793.2
Troy Williamson721.64.3220373.473.1161.50.380.450.42112.9
Craig Davis3021.34.4120073.161.3170.60.270.110.1932.7
Freddie Mitchell25224.4618571.442.9159.50.460.40.4372.6
Mike Evans720.44.5323176.876163.20.280.280.286NA
Sammy Watkins420.64.4321172.865.31600.350.350.3511NA
Brandin Cooks2020.34.3318969.855.51560.350.490.4215NA
Odell Beckham1221.14.4319871.253.9160.50.330.220.286NA
Kelvin Benjamin2822.94.612407773.9141.50.240.340.291NA

2nd3rd

2nd & 3rd Round, Principal Component Analysis

NAMEDPMAXAGEFORTYWTHTFSxploMSYDSMSTDDRGMSDOMFPG
Anquan Boldin5422.34.7221672.637.9147.50.350.410.381010
Keenan Allen7620.54.482067460.1155.90.40.440.42129.9
Desean Jackson4921.14.3516969.840.8154.50.260.250.26149.8
Greg Jennings5222.24.4219771.154.1153.50.450.360.4219.7
Alshon Jeffery4521.94.4821674.967.8160.60.330.350.34149.6
Mike Wallace8422.44.2819972.472.71690.290.220.26119.3
Steve Smith7421.64.411846942.4159.50.390.130.2629.1
Ty Hilton9222.14.3418369.550.1151.70.360.320.34168.7
Torrey Smith5821.94.4120472.963.31670.370.310.3498.4
Eric Decker8722.64.4721775.170.5166.90.50.330.42187.8
Randall Cobb6420.44.4619170.244.2148.50.310.250.2897.6
Jordy Nelson3622.54.5121774.664.81540.470.490.48167.1
Sidney Rice4420.34.5120075.555.9148.50.340.20.27136.7
Deion Branch6522.44.4719169.140.81530.440.370.496.4
Terrance Williams7423.34.482087460.9141.50.410.330.3756.4
Titus Young4421.44.4317471.439.11580.290.230.26106.3
Aaron Dobson5921.44.3721074.875.3151.80.180.080.13136.3
James Jones7822.74.5420772.851.31430.410.350.3876.3
Antonio Bryant6320.74.5718873.237.31580.330.420.38106.1
Nate Burleson7121.34.5119772.547.6168.50.470.480.48176.1
Chris Chambers5222.34.3321071.672.81790.450.250.3536
Mario Manningham9521.64.5918171.827.61490.450.40.43155.9
Robert Woods4120.74.4220172.459.3150.50.280.240.2685.7
Kevin Curtis7424.44.4218671.147.21580.380.340.3605.7
Mike Walker79224.3520973.874.6157.50.410.290.35115.7
Chris Henry8321.64.51977656.2161.80.480.610.54145.6
Golden Tate6021.34.4219970.253.51550.380.540.46155.5
Brandon Lafell7823.24.5821174.553.41510.340.460.465.5
Eddie Royal4221.64.3918469.645.81600.220.30.2685.3
Donnie Avery3323.64.431927149.61700.380.240.3175.2
Reggie Brown35244.4519673.655.7169.50.30.240.2725.2
Steve Smith5121.74.4419771.853.31580.310.30.3115.2
Bernard Berrian78234.581837332.51660.230.20.2285.2
Leonard Hankerson7922.74.420973.568.81530.390.570.48144.9
Devery Henderson5021.84.5919871.537.6142.40.270.320.384.7
Chris Givens9622.14.3519871.162141.50.390.330.36114.7
Jabar Gaffney33214.4819373.150163.90.260.360.31134.6
Rueben Randle6320.74.5521074.956.71520.390.310.35104.5
Dexter Mccluster3620.44.5317268.821.7145.50.210.120.1674.3
Justin Hunter3421.54.361967670.2175.50.280.180.2364.2
Mohamed Sanu8322.44.6221173.547.11620.390.320.36114.2
Mohamed Massaquoi5022.14.621073.548.5163.50.230.260.24104.1
Earl Bennett7020.74.4820971.556.21360.380.150.26133.9
Emmanuel Sanders8222.84.418670.948.7165.50.380.290.34163.9
Reche Caldwell4822.74.3919471.856.6161.50.250.250.2543.8
Harry Douglas8423.24.5117671.231.71510.330.30.3243.8
Marquise Goodwin7822.14.2118368.962.41740.120.160.1453.8
Snoop Minnis7723.84.5717172.825.5152.50.310.280.303.8
Josh Reed3621.64.5221070.249.7146.30.490.280.3893.7
Early Doucet8122.24.5920972.146139.40.260.190.2293.6
Stephen Hill4320.74.282157690.5172.50.410.290.3593.5
Robert Ferguson4120.94.4820573.257.4156.50.380.50.4453.4
Brandon Jones9622.34.4220873.465.81510.110.070.0933.4
Austin Pettis7822.64.5620974.654.5153.50.230.260.24123.3
Jordan Shipley8424.14.619371.233152.50.390.410.433.3
Arrelious Benn3921.34.572197356.31450.220.080.1543.2
Ryan Broyles5423.64.5719270.133156.20.340.40.37133.2
Antwaan Randle El6222.14.4919169.639.8156.30.1800.0903.1
Quincy Morgan3323.24.4821172.860.1152.20.440.650.5503.1
Devin Hester5723.24.4119070.649.71620.1600.0803
Jason Hill7621.74.3220472.571.91600.220.380.3193
Damian Williams7721.64.5219772.646.81460.390.330.36122.9
Tj Graham6922.44.3418871.457.3153.50.230.270.2562.8
Travis Benjamin10021.94.3117269.947.21470.220.10.1692.7
Keary Colbert6221.64.4420172.658.1145.50.260.240.25102.6
Deon Butler91234.3118270.454.5142.50.250.190.22102.5
Andre Davis4722.44.4219473.557.3162.50.330.280.3152.4
Kelley Washington6523.24.4222374.577.7150.70.40.080.2442.4
Darius Watts54224.6918873.424.6155.70.310.610.46252.3
Mark Bradley3922.94.3720173.466.7167.50.180.20.1902.3
Chad Jackson3620.84.3221372.978.4160.50.330.280.3172.1
Tim Carter4622.24.3219071.961.71650.280.20.2442
Stedman Bailey9222.14.4619370.245.5151.50.360.550.46212
Andre Caldwell9722.74.3520472.268.21570.270.240.2661.9
Brian Robiskie3621.14.4620974.965.5158.60.260.290.28131.8
Malcolm Kelly5120.94.6822475.853.8144.20.250.210.23131.8
Billy Mcmullen9522.84.5421075.659.8161.70.280.070.1881.8
Derek Hagan8221.34.4520873.863.51600.270.190.2381.8
Jerrel Jernigan8321.54.4618568.937.5154.50.210.170.1991.8
Dwayne Jarrett4520.34.622197657.5167.80.30.440.37181.6
Sinorice Moss44224.381856844159.40.220.30.2641.6
Teyo Johnson63214.5924777.481.6150.30.230.520.3871.5
Devin Thomas3421.14.421573.973.41540.440.270.3661.4
James Hardy41224.4521777.476.9156.50.370.60.48191.4
Brandon Tate83214.4618371.942.7152.30.350.370.3661.4
Maurice Stovall9020.94.5721776.462.21570.270.230.2581.1
Devier Posey6822.94.3921173.671.4159.50.430.330.3891
Taylor Jacobs4421.64.4920572.454157.90.370.420.460.8
Patrick Turner8721.64.5922377.165.5152.40.230.290.2660.8
Bethel Johnson4523.84.382017160.5165.50.220.20.2100.6
Roscoe Parrish5522.54.3717069.839.4150.40.260.240.2560.6
Courtney Roby6821.94.4118972.152.2162.50.450.480.46100.5
Allen Robinson6120.34.622074.657.31660.460.310.389NA
Cody Latimer5621.24.4421574.570.8163.80.30.270.297NA
Davante Adams53214.5621272.952.7162.50.320.480.413NA
Jarvis Landry6321.14.7720571.523.3138.50.380.420.410NA
Jordan Matthews4221.54.4621275.167.9155.50.550.310.4326NA
Marqise Lee3922.14.5219271.841.81650.340.180.2617NA
Paul Richardson4521.64.417572.4451620.430.480.4513NA
Donte Moncrief9020.44.422174.478.3171.50.260.260.2612NA
Dri Archer9722.34.2617367.848.51600.180.220.29NA
Josh Huff8622.24.5120671.250.6151.50.310.370.349NA

Lt_UDFA

Late Round and UDFA, Principal Component Analysis

NAMEDPMAXAGEFORTYWTHTFSxploMSYDSMSTDDRGMSDOM
Jalen Saunders10421.271234.4416568.8827.02441560.30.220.2613
Bruce Ellington10622.378084.4519769.3847.2092159.50.230.250.247
Shaquelle Evans11522.835624.5121373.2559.2998156.50.220.350.2856
Martavis Bryant11822.054794.4221175.7572.79661630.210.140.1752
Kevin Norwood12324.293154.481987454.59041540.190.280.2350
Ryan Grant14223.021924.6419972.3835.0304144.50.440.320.3810
Devin Street14622.668494.5519874.8849.15721610.360.330.34511
Jared Abbrederis17623.057534.51957348.47147.50.430.310.3711
Tj Jones18921.457534.4818871.6343.21861420.350.390.3713
Quincy Enunwa20921.602744.452257474.736160.93205750.340.560.459
Michael Campanaro21822.78634.4619269.3843.0141610.450.460.4558
Jeremy Gallon24423.898634.4918567.531.4452157.72855460.390.290.343
Adrian FlemmingUDFA22.520554.40998589220074.1363.44647453163.85805230.100.050
Albert WilsonUDFA21.44.4320269.3852.4496160.50.40.30.355
Anthony DenhamUDFA22.35894.7723576.552.9396154.34854620.120.10.110
Bennie FowlerUDFA22.578084.5221773.2560.77461620.220.260.247
Bernard ReedyUDFA21.928774.52601319917467.6321.02930045148.03853810.360.430.39513
Brandon ColemanUDFA21.531514.562257871.7988155.34004510.20.20.211
Brandon WimberlyUDFA24.668494.47048053122574.1372.87357488160.34119780.340.430.3856
Brelan ChancellorUDFA21.419184.42579120218668.1340.13450354159.6476740.250.230.2410
Chandler JonesUDFA22.019184.3418368.548.0032152.70793230.330.360.34511
Cody HoffmanUDFA22.808224.6522375.8856.5952135.50.350.260.30515
Colin LockettUDFA22.728774.31107890418471.1357.28423293168.04086570.270.320.29512
Derel WalkerUDFA22.523294.47726606618573.7546.15115075142.03597620.20.190.1952
Dj BanksUDFA22.906854.46267956718268.6334.82893168158.2897050.1300.0651
Dj ColesUDFA24.271234.57006340823475.2570.53197264157.9027120.170.310.242
Eric ThomasUDFA22.065754.49691452121472.3859.43569426171.57080220.250.420.33513
Eric WardUDFA23.364384.59382871819971.1337.18122241156.96940080.210.340.2757
Isaiah BurseUDFA22.052054.5818870.3830.09161460.20.150.1753
Ja Mes LoganUDFA24.175344.36671200518773.6358.70946125158.91166130.180.080.131
Javontee HerndonUDFA22.353424.4420772.2560.6962150.5437580.30.140.223
Jerry RiceUDFA22.265754.62663528418571.2525.18908009148.70120420.0700.0350
Josh StewartUDFA21.21374.6917869.8811.22441520.220.090.1557
Julian HortonUDFA21.980824.6919772.1328.0094146.49137540.150.070.111
Kadron BooneUDFA22.17264.33831942820471.567.82885339153.08695080.110.170.144
Kain ColterUDFA21.495894.48953826319870.546.10346071147.27164710.030.250.142
Kenny ShawUDFA21.991784.28009069517071.1351.70312054164.41080860.220.120.174
Kofi HughesUDFA21.693154.53127437921773.1359.33940187155.76506490.230.20.2154
Kyle NunnUDFA21.75894.44005572820973.7565.16037527150.49340330.140.120.132
Ldamian WashingtonUDFA22.668494.4619575.8858.8141470.280.350.3158
Mike DavisUDFA21.657534.4575746721977252.02429529153.94513510.1200.060
Mike DavisUDFA21.652054.3929763981977258.77610693154.00126190.280.340.319
Quintin PaytonUDFA23.780824.50439325821175.3863.18401669163.13578610.20.230.2150
Ryan LankfordUDFA21.895894.38934759917571.6344.50358898157.94943270.210.170.194
Spencer HarrisUDFA22.112334.51681346520573.554.08265663155.32724910.130.050.092
Tevin ReeseUDFA23.01374.4616370.527.1408158.58687780.270.340.3056
Tracy MooreUDFA22.934254.43738360621573.1367.89286554168.68244850.220.180.22
Travis LabhartUDFA22.961644.44111633718268.6337.08272042148.43045260.190.190.190
Tyshon GoodeUDFA23.761644.54078562218371.6333.71528683155.719120.230.140.1859

This is obviously a very simplistic approach. Is it really better to be just above average on production and physique, than having extreme production or physique? Probably not. Weighting between the two PCs and their (non-)linear relationship should be investigated further, and anyone can create their own frontier to go with the PC graph.

Nevertheless, if round drafted and this graph was all your available information, you’d do better than random:

FPG Mean Max Min Mean Diff
Interior, Top 10 7.7 12.7 2.9 25.10%
Exterior, Top 10 6.1 8.4 3.2
Interior, 11-32 7.1 10.2 4.5 14.30%
Exterior, 11-32 6.2 9.9 2.6
Interior, 2nd round 4.3 9.6 1.4 1.20%
Exterior, 2nd round 4.2 10 0.6
Interior, 3rd round 5.5 9.9 1 37.90%
Exterior, 3rd round 4 9.3 0.5

Fantasy Points per Game

Lastly, looking at fantasy points per game (FPG) for those in my data set that were drafted in the first three rounds, it seems clear that people who struggled to produce in college will have a tough time producing in the pros, even if they have an intriguing physique.

FPG

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