Superbowl XLVII Projection, Week 3, Sunday

Houston over Atlanta

Houston remains the strongest team, but Atlanta moves right up behind them, and has the greatest chance among NFC teams of making the Superbowl.

I've added the strength column thanks to a question by Josh from Royals and Randoms. The strength is the Pythagorean Winning Percentage expectation, found from a statistic called PythagenPat, originating in Baseball Prospectus

Each time I run my simulations, the total number of points and games played thus far are used to find the points-per-game (ppg). An exponent, X, is defined as ppg^0.287. The 0.287 is actually used for baseball, but I've yet to find a "better" value for football. Then, a team's Pythagorean Winning Percentage expectation is found using their Points For and Points Against, as PF^X/(PF^X + PA^X). A team that has shut out every opponent will have a winning expection of 1.000, and a team with the same number of points for and against will have an expectation of .500, which makes sense.

Finally, I use a tactic from SportsClubStats.com, which is regressing the expectation to the mean. I do this by first subtracting .500, making all values between .500 and -0.500. Then I multiply by the percentage of the season passed so far, 3/16 for most of the teams below. Then the .500 is added back. This means that a team who has had nothing but shutouts for 3 games of the 16 game season would have a strength of .59375, and a team that has scored no points would have .40625. This keeps crazy results early in the season from showing a team with a huge chance of being the champion after 1 dominant game.

Denver has the same Points For and Points Against so far, and so are at exactly .500.

The strengths are used to simulate the games. If team x has strength xp, and team y has strength yp, team x's chances of beating team y are:
xp(1-yp) / (xp(1-yp) + yp(1-xp))
and vice versa for team y beating team x, and it can be seen this will sum to 1.

Then a random number is generated between 0 and 1 and used to determine the winner of the simulated game in a weighted fashion.  I run it at least 100,000,000 times, and The result is the lovely table of percentages below.

TEAM	Record	Strength	Div	Plyff	WC	Qtr	Semi	Champ
HOU	3-0	0.576	79.234	88.536	75.505	43.098	24.293	13.103
ATL	3-0	0.572	78.630	84.601	68.263	37.634	20.472	11.157
ARI	3-0	0.561	57.848	76.198	58.897	31.626	16.763	8.956
CHI	2-1	0.550	36.818	54.555	37.797	19.620	10.095	5.279
BAL	2-1	0.549	51.602	68.129	50.415	26.876	14.081	7.212
NYG	2-1	0.548	40.103	57.002	39.649	20.402	10.429	5.427
SEA	1-1	0.538	17.278	40.745	25.975	13.046	6.561	3.352
NE	1-2	0.534	22.815	37.990	24.573	12.509	6.348	3.156
SD	2-1	0.529	52.260	65.615	46.818	23.816	11.917	5.867
MIN	2-1	0.524	30.595	47.266	31.191	15.286	7.441	3.696
BUF	2-1	0.514	28.414	49.059	32.331	15.841	7.702	3.674
GB	1-1	0.511	22.217	35.308	21.822	10.389	4.925	2.383
NYJ	2-1	0.511	35.526	51.934	34.326	16.746	8.087	3.837
SF	2-1	0.511	19.480	40.048	24.856	11.799	5.611	2.712
PIT	1-2	0.504	18.983	31.747	19.268	9.207	4.385	2.048
DEN	1-2	0.500	23.061	35.233	21.352	10.093	4.758	2.205
MIA	1-2	0.498	13.244	26.226	15.288	7.181	3.374	1.557
WAS	1-2	0.497	15.042	24.528	14.247	6.531	2.997	1.410
DET	1-2	0.489	10.370	18.671	10.499	4.756	2.157	0.996
TB	1-2	0.484	11.623	21.112	11.495	5.160	2.326	1.063
DAL	2-1	0.481	25.964	38.800	22.971	10.157	4.485	2.035
CIN	2-1	0.475	24.593	41.722	25.121	11.250	5.014	2.199
NO	0-3	0.472	3.551	7.628	3.884	1.691	0.741	0.329
STL	1-2	0.464	5.395	12.753	6.663	2.849	1.227	0.537
CLE	0-3	0.463	4.823	9.236	4.834	2.099	0.919	0.392
JAC	1-2	0.460	7.004	21.042	11.124	4.771	2.085	0.885
IND	1-2	0.459	7.553	19.180	10.310	4.439	1.938	0.820
PHI	2-1	0.456	18.891	28.227	15.528	6.472	2.700	1.157
OAK	1-2	0.453	11.152	19.876	10.596	4.487	1.904	0.792
KC	1-2	0.452	13.528	20.952	11.285	4.772	2.023	0.841
CAR	1-2	0.447	6.196	12.559	6.263	2.581	1.069	0.450
TEN	1-2	0.438	6.209	13.523	6.855	2.814	1.173	0.472

First to 10% Chance of Superbowl win: Houston (Week 2, Sunday)

First to 80% Chance of Playoffs: Houston (Week 2, Sunday)

[Week 1]
[Week 2, Thursday]
[Week 2, Sunday]
[Week 2, Final]
[Week 3, Thursday]