For all your fancy-pants statistical needs.

Praise for The Basketball Distribution:

"...confusing." - CBS
"...quite the pun master." - ESPN

NBA Ratings as of 2/10/2014

Harrison Barnes is in last place in WARP82, which is my WARP metric extrapolated for a whole season's worth of games.

(Sorted by WARP82)
rtg rkPlayerTeamPS%minraw SPR(2.0) per 100+/- above teammate SPRTeam +/- WeightAdj RatingWARP82injury-adj-WARP82
1durant,kevinoklSF77%10.410.722%9.526.126.6
2curry,stephengswPG73%8.012.924%9.024.125.6
5james,lebronmiaSF75%9.88.731%7.321.622.1
3love,kevinminPF71%6.611.127%7.621.022.3
8wall,johnwasPG76%5.48.124%5.818.918.9
9anthony,carmelonykSF75%4.26.924%5.618.419.5
11george,paulindSG75%4.57.235%5.518.118.1
12griffin,blakelacPF75%5.56.724%5.217.517.5
7dragic,goranphoPG67%5.38.325%6.017.218.3
15lowry,kyletorPG75%4.55.830%5.017.117.1
10nowitzki,dirkdalPF65%4.87.825%5.615.816.5
16thomas,isaiahsacPG70%4.36.025%4.715.615.6
20aldridge,lamarcuporPF76%2.65.928%4.015.515.5
6cousins,demarcussacC58%7.58.325%6.415.417.9
17harden,jameshouSG67%4.66.324%4.514.517.1
14davis,anthonynorPF63%6.15.125%5.014.517.2
13conley,mikememPG61%4.46.823%5.114.216.5
21howard,dwighthouC71%4.54.924%3.914.214.2
19rubio,rickyminPG65%4.47.427%4.414.114.1
4paul,chrislacPG46%10.78.424%7.413.520.8
22millsap,paulatlPF67%4.85.227%3.913.413.6
23lawson,tydenPG67%4.33.925%3.813.214.6
30lillard,damianporPG75%2.34.428%2.912.912.9
27lee,davidgswPF67%1.67.824%3.112.012.7
28noah,joakimchiC67%3.13.824%3.111.812.3
44batum,nicolasporSF74%1.73.628%2.211.411.4
40jennings,brandondetPG72%2.43.819%2.311.311.8
25west,davidindPF62%0.95.635%3.211.311.3
32walker,kembachaPG64%1.84.426%2.911.012.7
38irving,kyrieclePG68%3.31.218%2.411.011.6
33hibbert,royindC63%-0.35.435%2.810.710.7
35bosh,chrismiaPF63%2.45.331%2.610.410.7
62ellis,montadalPG75%3.20.825%1.49.99.9
26iguodala,andregswSG53%1.011.024%3.29.712.6
47ariza,trevorwasSF65%2.04.724%1.99.710.7
52drummond,andredetC67%3.80.819%1.89.69.6
36varejao,andersonclePF58%1.46.818%2.59.510.1
68jordan,deandrelacC74%2.11.924%1.29.59.5
37jefferson,alchaC58%2.83.426%2.49.311.3
42frye,channingphoPF59%-0.36.425%2.39.39.3
63stephenson,lanceindSG70%1.32.735%1.49.29.5
46hill,georgeindPG61%0.14.135%2.09.19.6
45jackson,reggieoklPG59%1.24.622%2.29.09.0
67hayward,gordonutaSF68%1.70.725%1.38.99.9
61korver,kyleatlSG65%0.34.327%1.58.99.7
29wade,dwyanemiaSG50%5.74.831%2.98.812.0
41duncan,timsanPF56%3.40.920%2.38.89.5
84derozan,demartorSG75%0.71.230%0.88.69.0
18ginobili,manusanSG40%4.38.720%4.58.610.6
76matthews,wesleyporSG71%0.72.128%0.98.48.4
89smith,joshdetSF73%0.52.219%0.78.38.3
81parsons,chandlerhouSF71%1.51.624%0.88.29.1
54parker,tonysanPG58%2.50.920%1.78.19.0
80gortat,marcinwasC67%-0.34.224%0.87.97.9
34holiday,jruenorPG46%3.94.725%2.77.911.8
60pekovic,nikolaminC57%1.24.927%1.57.89.2
55sullinger,jaredbosPF55%-0.24.423%1.77.88.1
50bogut,andrewgswC53%2.44.824%1.87.78.3
70middleton,khrismilSF60%-0.44.015%1.07.67.6
85ibaka,sergeoklPF66%1.51.122%0.87.67.7
92randolph,zachmemPF68%0.20.523%0.67.67.9
71crawford,jamallacSG63%1.11.924%1.07.67.6
90monroe,gregdetC66%1.21.719%0.77.47.4
56chalmers,mariomiaPG52%3.43.431%1.77.38.4
39leonard,kawhisanSF47%2.81.420%2.37.39.3
64pierce,paulbroSF54%1.92.625%1.47.17.9
98oladipo,victororlSG66%1.6-1.321%0.47.07.0
140thompson,klaygswSG78%-1.42.924%-0.27.07.0
115afflalo,arronorlSG70%0.5-0.721%0.16.97.4
96teague,jeffatlPG64%2.20.727%0.46.87.1
young,thaddeusphiSF65%1.6-1.017%0.26.77.1
93nelson,jameerorlPG61%0.70.721%0.56.77.4
86johnson,amirtorPF58%0.01.530%0.76.76.8
43williams,deronbroPG43%3.56.325%2.26.69.6
82carter-williamsphiPG55%2.61.817%0.86.68.5
103martin,kevinminSG62%0.12.927%0.36.57.0
65collison,darrenlacPG49%2.40.024%1.46.46.4
105mcroberts,joshchaPF61%-0.61.226%0.36.36.5
31mills,pattysanPG36%2.55.020%2.96.36.3
94favors,derrickutaPF57%1.7-0.425%0.56.27.0
101knight,brandonmilPG55%1.2-0.915%0.46.07.2
87hilario,nenewasC53%1.63.724%0.76.07.0
24westbrook,russeloklPG32%5.91.322%3.46.012.7
141brewer,coreyminSF65%-1.53.027%-0.25.85.9
74diaw,borissanPF48%0.21.220%0.95.86.1
53horford,alatlPF40%4.34.427%1.75.79.7
114gasol,paulalPF57%1.6-1.825%0.15.76.6
127dunleavy,mikechiSG60%-1.21.824%0.05.65.6
170turner,evanphiSG71%-1.10.317%-0.75.65.7
48gay,rudysacSF37%4.64.725%1.95.510.5
113butler,jimmychiSG56%-0.42.024%0.15.57.5
131carroll,demarreatlSF59%0.31.427%-0.15.55.9
95belinelli,marcosanSG51%0.2-0.320%0.55.45.5
young,nicklalSG56%-1.61.525%0.05.45.7
139gibson,tajchiPF59%-0.60.824%-0.25.35.3
104livingston,shaunbroPG51%0.41.825%0.35.35.3
106lin,jeremyhouPG52%1.4-0.524%0.35.36.6
173green,jeffbosPF70%-1.4-1.623%-0.75.35.3
100faried,kennethdenSF50%0.70.425%0.45.35.5
99carter,vincedalSG49%0.40.425%0.45.25.3
158calderon,josedalPG64%0.9-1.525%-0.55.25.3
163lopez,robinporC65%-1.10.728%-0.65.15.1
145green,geraldphoSG58%-0.20.125%-0.35.05.0
169hawes,spencerphiC62%0.7-1.617%-0.75.05.2
79mozgov,timofeydenC42%0.13.925%0.95.05.0
118morris,markieffphoPF50%0.9-0.625%0.14.95.0
49bledsoe,ericphoPG33%5.01.125%1.94.910.2
147foye,randydenPG57%-1.00.325%-0.34.95.0
135jones,terrencehouPF53%0.6-0.524%-0.14.85.3
151burks,alecutaPG57%-0.6-0.125%-0.44.84.8
91evans,tyrekenorPG43%2.2-0.525%0.64.85.7
69blair,dejuandalC38%2.4-0.925%1.14.74.8
73green,dannysanSG39%-0.41.920%0.94.75.7
184johnson,joebroSG65%-1.3-0.225%-0.94.64.8
57redick,j.j.lacSG33%0.85.424%1.64.68.3
102vucevic,nikolaorlC43%1.92.521%0.34.56.9
111lamb,jeremyoklSG46%-1.10.622%0.24.54.5
122crawford,jordanbosSG47%1.0-1.423%0.04.56.1
88blatche,andraybroPF39%2.81.425%0.74.55.1
78gasol,marcmemC37%1.01.923%0.94.48.2
112beverley,patrickhouPG44%-1.53.624%0.24.46.4
120morris,marcusphoPF46%0.00.225%0.04.44.4
159shumpert,imannykSG54%-1.91.824%-0.54.34.5
72collison,nickoklPF36%-2.36.222%0.94.34.3
83robinson,natedenPG36%0.25.225%0.84.24.8
58allen,tonymemSG30%2.63.823%1.64.17.6
128williams,marvinutaPF43%0.13.125%0.04.15.2
97crowder,jaedalSF38%-1.94.725%0.44.14.1
183plumlee,milesphoPF57%-0.7-0.825%-0.94.04.0
107casspi,omrihouSF39%-0.92.424%0.34.04.1
182boozer,carloschiPF55%-0.3-1.124%-0.93.94.4
119dalembert,samueldalC40%0.8-2.325%0.13.94.0
59patterson,patrictorPF27%1.36.730%1.53.86.4
225tucker,p.j.phoSG63%-1.5-0.625%-1.33.83.8
121miles,c.j.cleSG38%1.17.018%0.03.74.0
161felton,raymondnykPG46%-0.51.224%-0.63.75.4
205valanciunas,jonatorC58%-1.0-1.730%-1.23.73.7
176sessions,ramonchaPG49%-1.00.026%-0.83.63.6
194waiters,dioncleSG53%-1.72.518%-1.03.64.0
178hinrich,kirkchiSG49%-1.41.124%-0.83.64.4
51johnson,jamesmemPF25%3.94.923%1.83.66.6
198ross,terrencetorSG53%-2.5-0.730%-1.13.53.5
226hickson,j.j.denPF58%0.1-3.425%-1.33.53.5
77splitter,tiagosanPF29%0.1-0.220%0.93.45.2
181williams,moporPG47%-0.7-1.628%-0.93.43.6
250meeks,jodielalSG64%-0.2-4.125%-1.63.33.5
197henson,johnmilPF45%1.7-6.015%-1.13.24.1
126humphries,krisbosPF34%0.32.323%0.03.23.8
143deng,luolchiSF35%1.8-0.124%-0.23.16.8
259gordon,ericnorSG63%0.2-3.925%-1.73.13.3
109davis,edmemPF30%-1.03.423%0.33.13.6
138andersen,chrismiaC34%1.10.831%-0.13.13.6
129fisher,derekoklPG33%-3.21.922%-0.13.03.1
156watson,c.j.indPG38%-1.3-3.235%-0.53.03.0
165augustin,d.j.chiPG38%2.8-5.024%-0.63.05.0
166koufos,kostamemC38%-0.7-3.423%-0.63.03.0
116marshall,kendalllalPG30%1.92.925%0.13.06.3
150mack,shelvinatlPG34%0.71.827%-0.42.93.4
233burke,treyutaPG49%-1.60.025%-1.42.93.8
246chandler,wilsondenSG54%-1.1-2.625%-1.62.93.4
144anderson,ryannorPF32%-0.23.825%-0.32.86.6
wright,brandandalC21%3.75.625%1.42.85.2
305henderson,geraldchaSG69%-2.0-2.526%-2.02.82.8
75lee,courtneymemSG23%1.28.423%0.92.88.2
265johnson,wesleylalSG57%-1.9-2.625%-1.72.82.8
260bradley,averybosPG55%-2.2-2.423%-1.72.73.1
191hill,jordanlalC40%0.6-3.625%-1.02.72.8
242sefolosha,thabooklSG52%-1.8-2.922%-1.52.72.9
134prigioni,pablonykPG28%1.03.724%-0.12.63.8
168blake,stevelalPG33%1.4-1.525%-0.62.65.3
258davis,glenorlPF51%-1.6-0.621%-1.72.63.2
117gay,rudytorSF26%0.8-0.230%0.12.57.1
160chandler,tysonnykC31%1.20.324%-0.52.54.7
203garnett,kevinbroPF39%-0.70.025%-1.12.52.9
251wallace,geraldbosSF48%-0.7-4.723%-1.62.52.5
154adams,stevenoklC30%-1.5-7.022%-0.52.52.5
124ayres,jeffsanPF26%-2.61.420%0.02.42.6
210roberts,briannorPG38%-0.8-2.425%-1.22.42.7
190scola,luisindPF37%-1.9-4.935%-1.02.42.4
306smith,j.r.nykSG58%-1.7-2.324%-2.02.42.7
108lopez,brookbroC22%4.91.525%0.32.36.7
294thompson,jasonsacPF53%-3.2-0.325%-1.92.32.3
132granger,dannyindSF24%-4.32.035%-0.12.14.2
315cole,norrismiaPG53%-0.7-1.931%-2.12.12.1
327jefferson,richarutaSF56%-1.6-3.425%-2.22.02.0
130leuer,jonmemPF21%0.1-2.323%-0.12.03.0
171plumlee,masonbroPF26%2.4-4.025%-0.72.02.5
269green,draymondgswSF41%-1.6-2.124%-1.72.02.0
136joseph,corysanPG22%-1.3-5.820%-0.12.02.6
172calathes,nickmemSG25%-0.6-7.223%-0.71.92.5
125farmar,jordanlalPG20%1.86.725%0.01.94.2
185bayless,jerrydmemPG27%-3.32.023%-0.91.93.1
219olynyk,kellybosPF31%-1.4-0.923%-1.21.92.3
227barnes,mattlacSF32%-3.0-4.324%-1.31.92.9
326antetokounmpo,gimilSG45%-1.7-0.415%-2.21.92.1
193henry,xavierlalSG27%-1.43.625%-1.01.93.1
209morrow,anthonynorSG29%-2.52.025%-1.21.92.1
206salmons,johntorSF29%-3.5-1.230%-1.21.83.1
199brooks,aaronhouPG28%-1.3-5.924%-1.11.82.3
157hansbrough,tylertorPF22%-2.0-1.030%-0.51.82.7
344beal,bradleywasSG55%-1.1-1.324%-2.31.82.2
367thompson,tristanclePF67%-2.7-3.118%-2.51.81.8
275battier,shanemiaSF38%-3.60.831%-1.81.82.0
347anderson,alanbroSG52%-3.1-1.225%-2.31.71.7
152lee,courtneybosSG20%-0.78.423%-0.41.73.0
202martin,kenyonnykPF26%-1.23.024%-1.11.72.7
228evans,jeremyutaSF28%0.00.325%-1.31.72.4
186miller,andredenPG24%-1.40.625%-0.91.72.8
272teletovic,mirzabroPF35%-1.3-1.725%-1.71.71.9
153bonner,mattsanPF20%-3.84.020%-0.41.62.0
195vasquez,greivistorPG23%-3.3-1.930%-1.01.62.7
253mahinmi,ianindC33%-3.6-7.135%-1.61.61.6
331harkless,mauriceorlSF42%-1.3-2.721%-2.21.51.6
313perkins,kendrickoklC40%-4.1-5.022%-2.01.51.6
363bass,brandonbosPF57%-1.3-6.323%-2.51.51.5
339stuckey,rodneydetPG45%-0.8-2.419%-2.31.51.8
164kaman,chrislalC19%1.00.725%-0.61.52.9
357dudley,jaredlacSG55%-3.9-1.624%-2.51.51.5
273lewis,rashardmiaPF31%-1.6-2.831%-1.71.51.7
249williams,shawnelalSF28%-3.54.925%-1.61.52.2
301williams,louisatlSG35%-0.5-3.927%-2.01.52.0
252freeland,joelporPF29%-4.0-3.828%-1.61.41.5
356allen,raymiaSG50%-0.9-3.031%-2.41.41.6
274fournier,evandenSG29%-4.21.325%-1.81.41.6
189jones,perryoklSF21%-4.3-2.922%-1.01.41.7
295garcia,franciscohouSG33%-3.7-3.724%-2.01.41.7
371aminu,al-farouqnorSF54%-0.9-5.925%-2.61.31.4
325tolliver,anthonychaPF36%-4.11.526%-2.21.31.6
267pressey,philbosPG26%-3.10.223%-1.71.31.4
309arthur,darrelldenPF30%-5.22.425%-2.01.21.4
wolters,natemilPG34%-2.36.315%-2.51.21.5
241beasley,michaelmiaSF22%0.9-8.131%-1.51.21.7
213vasquez,greivissacPG19%-0.82.725%-1.21.23.4
180larkin,shanedalPG16%-2.74.725%-0.91.21.8
280rivers,austinnorSG25%-3.91.525%-1.81.21.5
394marion,shawndalSF58%-0.2-6.325%-2.81.11.3
232antic,peroatlPF19%-2.07.027%-1.41.11.9
300brand,eltonatlPF27%-0.9-5.327%-2.01.11.3
283kelly,ryanlalSF24%-2.90.825%-1.81.11.9
222fredette,jimmersacPG17%0.3-7.225%-1.31.11.4
304hamilton,jordandenSG25%-2.2-7.625%-2.01.01.4
292udrih,benonykPG24%-0.5-8.224%-1.91.01.7
243robinson,thomasporPF20%-2.8-11.128%-1.51.01.2
298garrett,dianteutaSG23%-2.73.125%-2.01.01.3
284o'quinn,kyleorlPF21%-0.50.021%-1.81.01.3
342stoudemire,amarenykPF29%-0.2-9.924%-2.31.01.3
336pachulia,zazamilC22%0.00.215%-2.31.02.3
354scott,mikeatlPF33%0.1-8.627%-2.41.01.0
381thornton,marcussacSG44%-4.5-0.425%-2.71.01.1
279smith,ishphoPG21%-3.1-9.225%-1.81.01.3
405webster,martellwasSF59%-1.8-2.224%-2.91.01.0
380hardaway,timnykSG42%-2.0-5.124%-2.71.01.0
230ajinca,alexisnorC16%-1.4-2.925%-1.30.91.8
146decolo,nandosanPG11%0.1-4.420%-0.30.92.0
208hollins,ryanlacC15%-3.1-6.924%-1.20.91.1
289green,willielacSG22%-5.4-6.524%-1.90.91.4
220kirilenko,andreibroSF15%-0.83.325%-1.20.92.3
wright,dorellporSF20%-4.6-7.128%-1.80.91.2
360smith,jasonnorPF33%-3.2-3.925%-2.50.91.5
296raduljica,miroslmilC16%-0.62.115%-2.00.91.3
177hayes,chucktorPF12%-3.55.530%-0.80.92.1
187bayless,jerrydbosPG13%-1.64.723%-0.90.93.2
282faverani,vitorbosC19%-2.1-8.823%-1.80.91.3
392miller,mikememSF44%-2.8-7.423%-2.80.90.9
137rondo,rajonbosPG9%2.6-2.823%-0.10.95.2
240artest,ronnykSF15%-1.90.024%-1.50.81.5
268patterson,patricsacPF17%-3.89.025%-1.70.82.5
270motiejunas,donathouPF17%-4.2-3.924%-1.70.81.3
317stiemsma,gregnorC21%-2.7-6.825%-2.10.81.4
211barbosa,leandrophoPG13%-3.49.125%-1.20.82.7
375kidd-gilchrist,mchaSF32%-2.8-3.326%-2.60.81.3
201randolph,anthonydenPF12%-0.2-13.725%-1.10.81.6
263ayon,gustavoatlPF16%-0.8-2.227%-1.70.81.6
155johnson,chrisbosSF9%-0.712.823%-0.50.83.7
237novak,stevetorSF13%-5.7-1.530%-1.50.71.3
334deng,luolcleSF20%-0.52.418%-2.20.72.5
174harris,mikeutaSF9%0.77.525%-0.70.71.8
244asik,omerhouC13%-3.1-2.124%-1.50.71.9
352shved,alexeyminPG22%-3.7-6.727%-2.40.70.8
withey,jeffnorC11%-2.35.425%-1.20.71.2
302o'neal,jermainegswC16%-2.9-5.824%-2.00.71.7
264gobert,rudyutaC13%-2.62.225%-1.70.61.3
148bryant,kobelalSG7%2.4-4.225%-0.40.65.4
382biyombo,bismackchaPF29%-2.7-6.326%-2.70.60.7
328turiaf,ronnyminC17%-2.8-7.327%-2.20.61.6
221adrien,jeffchaSF10%-2.1-0.526%-1.20.61.4
224murry,toure'nykSG10%-1.4-2.724%-1.30.61.0
346salmons,johnsacSF18%-4.62.425%-2.30.61.7
133pargo,jannerochaPG6%4.0-13.426%-0.10.61.8
285miller,quincydenSF13%-3.6-9.925%-1.80.61.1
366sacre,robertlalC22%-4.0-5.125%-2.50.60.8
410sanders,larrymilC24%-1.5-2.115%-3.00.61.3
162tyler,jeremynykPF7%1.111.424%-0.60.51.7
196harris,devindalPG8%-0.85.125%-1.10.52.6
377bynum,willdetPG23%-0.3-8.619%-2.60.50.9
422bargnani,andreanykPF51%-2.4-4.824%-3.10.50.7
293miller,dariusnorSF12%-5.56.325%-1.90.51.1
278johnson,orlandoindSG14%-8.0-9.835%-1.80.50.7
254baynes,aronsanPF11%-5.3-4.820%-1.60.50.9
365martin,cartieratlPF19%-2.5-8.127%-2.50.50.9
311rose,derrickchiPG13%-3.1-4.324%-2.00.52.5
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O Flappy Bird, The Pipes, The Pipes Are Calling

OK. So I love this game, Flappy Bird.
It's insanely stupid.
But my friends and I are playing it and competing over our best scores.





A couple of us started running stats on the game (of course), and I noticed some trends.

First of all, that my expected high score was much lower than my talent suggests! I get extremely nervous as I get nearer to high scores (among my friends' is currently 61) and end up dying shortly beforehand. So I wanted to quantify this.

First, the most basic principle for Flappy Birds - math (yes, you are still reading this...) is the following:


Where p represents the probability of dying on any given score.

For example: if my average score is 2, I am making it through 66% of all the pipes (2 successfully, failing on the 3rd. 2/3 = 66%). This is fairly straightforward.

Next I wanted to figure out my expected # of rounds by which I successfully get to each score. Couple of steps are required.

1) As of this writing, my (p) value is 94.0527% - (my average score is 15.8.) So I made a chart of probabilities. Probability of getting at least 0 points? 100%. Probability of getting at least 1 point? 94% of course. Probability of getting at least 2 means I've made it through the 94% twice, so 0.94^2 or 88.4%. And so on and so forth. So we now know that the inherent probability of making it to a certain number of points in the game is p^number of points. 

2) By multiplying this probability by the number of trials I have completed, we have determined the number of expected times I should have reached at least __ number of points. I then compare this with the actual number of times I reached that number of points. The resultant chart is what I like to call my FBNG or "Flappy Bird Nervousness Graph":



As you can see I tend to do much better than expected in rounds 10-25, after which I taper off heavily to average/below average # of games finished with said score. So one could justifiably argue that I do fine until I hit 25. I honestly do start nervously looking at the score whereupon it gets into larger figures.

So from this graph I can see how I'm doing versus expected. But I want to know something simpler: what should my high score be? Currently mine is 57, but according to my 94% pipe clearance I can tell that I should be able to do better. In fact, my little chart of numbers shows that I should have at least 1* game of all the way up to around 74 according to the math! But I don't want to use a chart to guess and check. I want a formula.

So I can see that around (p of 0.94) ^ (74 games) is roughly 1. I want to see at what game # my (p) should hit EXACTLY 1.

I derived it like so:
(p^exp high score) * #GamesPlayed = 1
1/GamesPlayed = p^score
therefore
log with base (p) of 1/GamesPlayed = expected high score
or


When you plug this in, you'll see that 74 is close. Plugging in 94.0527% and 97 games gives you 74.61.
My high score is 57, so I've got to get over some nervousness so I can achieve my true high score.



* I thought about using 0.5, but 1.5 is just as relevant, so I settled on 1 which is in the middle.

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About Me

I wish my heart were as often large as my hands.