Applying Pythagorean Expectation to Fantasy Football

With only 16 games in a season of the National Football League, every game is vital to a team's success. When compared to the MLB's 162 game season, or the NBA's 82 game season, variance plays a much larger role in final win-loss totals. A typical Fantasy Football Regular season typically runs for 14 games, give or take depending on league conditions. Although MIT researchers proved that skill is a vital component in Daily Fantasy Sports gambling, Luck and variance and inexorably intertwined with regular Fantasy Football. Crucial injuries can sink an aspiring manager's season, and just a few unlucky losses can be insurmountable. This random nature is what makes fantasy sports exciting and engaging, it's also what makes real sports exciting and engaging. The human element carries over from real life sports to their digital approximation.

A popular method of better representing a team's true performance is Pythagorean Expectation, developed by sabermetrician Bill James. The formula is shown below, and if you're wondering what the relationship between the pythagorean theorem and Bill James' Pythagorean Expectation is, there is none, he just thought it looked like the pythagorean formula and named it that way.

Under Pythagorean Expectation, a team that scores as many runs as they allow would be expected to win 50% of their games. While the original formula does a decent job of predicting team success, future efforts to refine it place the exponents not at two, but roughly around 1.8. The formula I will be using for this exercise is the Pythagenpat formula, which was developed by David Smyth. Pythagenpat, as shown below, has a distinct advantage in use for football due to the variable Games Played being endogenized within the model. I believe this makes porting the equation from baseball to fantasy football much more sensible.  

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Fantasy Football Teams Sorted by Pythagenpat Expected Wins, 2016-2018

Final Rank	Manager	Wins	Year	PythagoreanWR	PythagoreanEW	PythagenpatWR	PythagenpatEW	Difference B/W	Points/G
1	Todd Scales	11	2017	0.59	8.25	0.70	9.78	1.22	114.39
2	Nathan Kelley	9	2017	0.57	7.93	0.65	9.09	-0.09	110.82
3	Connor Crook	9	2016	0.56	7.79	0.63	8.76	0.24	104.50
1	Nathan Kelley	8	2018	0.55	7.66	0.61	8.58	-0.58	128.21
2	Josh Patterson	9	2016	0.55	7.64	0.60	8.45	0.55	102.86
5	Todd Scales	8	2016	0.54	7.56	0.59	8.24	-0.24	95.93
1	Nathan Kelley	8	2016	0.54	7.54	0.59	8.22	-0.22	101.43
2	Conner Brown	7	2018	0.53	7.46	0.58	8.13	-1.13	134.86
4	Richard Francais	10	2016	0.53	7.37	0.56	7.84	2.16	97.79
3	Max Leibl	8	2018	0.51	7.21	0.54	7.50	0.50	128.07
7	james kepler	7	2016	0.51	7.21	0.53	7.45	-0.45	91.50
9	Todd Scales	7	2018	0.51	7.17	0.53	7.41	-0.41	118.07
6	Richard Francais	6	2017	0.51	7.17	0.53	7.40	-1.40	102.32
6	Tom Glines	7	2018	0.51	7.16	0.53	7.38	-0.38	124.79
4	Josh Patterson	10	2018	0.51	7.07	0.51	7.18	2.82	125.21
8	Jack Healy	7	2018	0.50	7.00	0.50	7.01	-0.01	132.00
3	Tom Glines	7	2017	0.49	6.90	0.48	6.77	0.23	101.21
4	Max Leibl	8	2017	0.49	6.90	0.48	6.77	1.23	99.25
8	Connor Crook	7	2017	0.48	6.75	0.46	6.44	0.56	94.25
5	Conner Brown	7	2017	0.48	6.74	0.46	6.40	0.60	98.25
5	Richard Francais	6	2018	0.48	6.73	0.45	6.34	-0.34	131.86
7	james kepler	5	2017	0.47	6.52	0.42	5.91	-0.91	93.82
6	Matthew Patz	5	2016	0.46	6.47	0.41	5.81	-0.81	92.21
10	Noah Dellenbach	6	2017	0.46	6.41	0.41	5.69	0.31	85.54
10	Max Leibl	6	2016	0.45	6.28	0.39	5.45	0.55	81.36
7	james kepler	5	2018	0.45	6.34	0.39	5.42	-0.42	115.86
9	Jack Healy	4	2017	0.45	6.24	0.38	5.28	-1.28	94.11
10	Connor Crook	5	2018	0.44	6.20	0.36	5.10	-0.10	118.14
8	Tom Glines	4	2016	0.43	6.03	0.35	4.93	-0.93	80.93
9	Conner Brown	4	2016	0.42	5.92	0.33	4.65	-0.65	87.79