Showing posts with label NFL. Show all posts
Showing posts with label NFL. Show all posts

Monday, December 30, 2013

Crude NFL Ratings, 2013

Since I have a crude rating system set up to evaluate MLB teams that relies on win ratio and identity of opponents and thus can be adapted to any number of sports, I see no reason not to apply it to the lesser NFL once a year. Since I am only a casual follower of the NFL, I will endeavor to avoid excessive comment on the results.

As a brief overview, the ratings are based on win ratio for the season, adjusted over the course of several iterations for opponent’s win ratio. They know nothing about injuries, about where games were played, about the distribution of points from game to game; nothing beyond the win ratio of all of the teams in the league and each team’s opponents. The final result is presented in a format that can be directly plugged into Log5. I call them “Crude Team Ratings” to avoid overselling them, but they tend to match the results from systems that are not undersold fairly decently.

First are ratings based on actual wins and losses. 12.2 games of regression are included when figuring the win ratios (this will apply to the point-based ratings as well). CTR is the bottom line rating, aW% converts it to an adjusted W%, and SOS is the average CTR of the team’s opponents:

I prefer to focus on the ratings based on points and points allowed, which are coupled with a Pythagorean approach published at Pro-Football Reference to generate the win ratios:

As you can see, the top five teams all hail from the NFC South and West, which unfortunately had a maximum of four playoff spots available, leaving Arizona as the odd team out. Note that despite going 10-6, a raw record that was bettered by nine NFL teams, the Cardinals ranked sixth in win-based rating, so this is not a Pythagorean fluke. Arizona was a legitimately outstanding team based on the actual on-field results in 2013, but will sit home as far lesser teams battle it out thanks to the vagaries of their micro-division.

The Browns are second-to-last either way you figure it; by W-L record the Redskins are worse, but rank 30th by points, and by points the Jaguars are worse, but rank 27th by W-L.

I use the geometric mean of the CTR of each team to calculate division and conference ratings:

The NFC West would rank fourth if it was a team--it was an absurdly strong division, with all of its teams among the top ten. The ratings imply that the composite NFC team would be expected to win about 55.2% of the time against its AFC counterpart.

The ratings can be used to feed playoff odds, naturally; here home field is assumed to be a 32.6% boost to CTR (equivalent to a .570 home W%). I’m not going to bother with the round-by-round breakout of potential matchups as I do for MLB, but here are the overall crude odds:

It’s worth acknowledging that each of the last two Super Bowl champs were longshots by this or any other estimate--last year’s Ravens were given only a 3% chance. Of course, I’d also point out that the probability of any longshot winning (let’s define that as 5% rounded probability or lower) is 20% and was 14% in 2012.

These odds imply a 60% chance that the NFC champ will win the Super Bowl, but also a 95% chance that the NFC champ will be favored by the odds to win the Super Bowl. The AFC’s best team, Denver, would be favored in only two potential Super Bowl matchups, as would...all five other AFC teams. The top four playoff teams in CTR hail from the NFC, the next six from the AFC, and then the winners of the micro-division lottery, Philadelphia and Green Bay. The NFL frequently provides examples of why I dislike tiny divisions, but never as clearly or as destructively as in 2013.

Tuesday, January 01, 2013

Crude NFL Ratings, 2012

Since I have a ranking system for teams and am somewhat interested in the NFL, I don’t see any reason not to take a once a year detour into ranking NFL teams (even if I’d much rather I have something useful to contribute regarding the second best pro sport, thoroughbred racing).

As a brief overview, the ratings are based on win ratio for the season, adjusted over the course of several iterations for opponent’s win ratio. They know nothing about injuries, about where games were played, about the distribution of points from game to game; nothing beyond the win ratio of all of the teams in the league and each team’s opponents. The final result is presented in a format that can be directly plugged into Log5. I call them “Crude Team Ratings” to avoid overselling them, but they tend to match the results from systems that are not undersold fairly decently.

First, I’ll offer ratings based on actual wins and losses, but I would caution against putting too much stock in them given the nature of the NFL. Ratios of win-loss records like 2-14 and 15-1 which pop up in the NFL are not easily handled by the system. In order to ensure that there are no divide by zero errors, I add half a win and half a loss to each team’s record. This is not an attempt at regression, which would require much more than one game of ballast. This year the most extreme records were 2-14 and 13-3, so the system produced fairly reasonable results:

In the table, aW% is an adjusted W% based on CTR. The rank order will be exactly the same, but I prefer the CTR form due to its Log5 compatibility. SOS is the average CTR of a team’s opponents, rk is the CTR tank of each team, and s rk is each team’s SOS rank.

The rankings that I actually use are based on a Pythagorean estimated win ratio from points and points allowed:

Seattle’s #1 ranking was certainly a surprise, but last year Seattle’s 92 CTR ranked 13th in the league, reflecting a little better than their 7-9 record. When I have posted weekly updates on Twitter, I’ve gotten a few comments on the high ranking of the Bears. CTR may like Chicago more than some systems, but comparable systems with comparable inputs also hold them in high regard. Wayne Winston ranks them #5; Andy Dolphin #7; Jeff Sagarin #7; and Football-Reference #6. Chicago ranked sixth in the NFL in P/PA ratio, which is the primary determinant of CTR, and played an above-average schedule (they rank 10th in SOS at 116, which means that their average opponent was roughly as good as the Vikings). The NFC North was the second-strongest division in the league, with Green Bay ranking #6, Minnesota #9, and Detroit #17. They played the AFC South, which didn’t help, although it was marginally better for SOS than playing the West. Their interdivisional NFC foes were Arizona (#24), Carolina (#16), Dallas (#19), Seattle (#1), San Francisco (#3), and St. Louis (#13) which is a pretty strong slate.

Obviously the Bears did not close the season strong, but the system doesn’t know the sequence of games and weights everything equally. Still, their losses came to #1 Seattle, #3 San Francisco, twice to #6 Green Bay, #7 Houston, and #9 Minnesota. I didn’t check thoroughly, but I believe that no other team save Denver was undefeated against the bottom two-thirds of the league (the Broncos’ losses came to #2 New England, #7 Houston, and #8 Atlanta). Even the other top teams had worse losses--for instance, Seattle and New England both lost to #24 Arizona, San Francisco lost to #13 St. Louis, Green Bay and Houston lost to #23 Indianapolis, and Atlanta lost to #20 Tampa Bay.

Last year I figured the CTR for each division and conference as the arithmetic average of the CTRs of each member team, but that approach is flawed. Since the ratings are designed to be used multiplicatively, the geometric average provides a better means of averaging. However, given the properties of the geometric average, the arithmetic average of the geometric averages does not work out to the nice result of 100:

The NFC’s edge here is huge--it implies that the average NFC team should win 64% of the time against an average AFC team. The actual interconference record was 39-25 in favor of the NFC (.609). The NFC’s edge is naturally reflected in the team rankings; 7 of the top 10 teams are from the NFC with 7 of the bottom 8 and 10 of the bottom 12 from the AFC.

This exercise wouldn’t be a lot of fun if I didn’t use it to estimate playoff probabilities. First, though, we need regressed CTRs. This year, I’ve added 12.2 game of .500 to each team’s raw win ratio based on the approach outlined here. That produces this set of ratings, which naturally result in a compression of the range between the top and bottom of the league, and a few teams shuffling positions:

The rank orders differ not because the regression changes the order of the estimated win ratios fed into the system (it doesn’t), but because the magnitude of the strength of schedule adjustment is reduced.

Last year I included tables listing probabilities for each round of the playoffs, but I will limit my presentation here to the first round and the probabilities of advancement. After each round of the playoffs, the CTRs should be updated to reflect the additional data on each team, and thus the extensive tables will be obsolete (although I will share a few nuggets). This updating might not be particularly important for MLB, since a five or seven game series adds little information when we already have a 162 game sample on which to evaluate a team. But for the more limited sample available for the NFL, each new data point helps.

In figuring playoff odds, I assume that having home field advantage increases a team’s CTR by 32.6% (this is equivalent to assuming that the average home W% is .570). Here is what the system thinks about the wildcard round:

The home team is a solid favorite in each game except for Washington, which faces the top-ranked team in the league. Houston is the weakest favorite; the Texans would be estimated to have a 54% chance on a neutral field and 47% at Cincinnati.

The overall estimated probabilities for teams to advance to each round are as follows:

San Francisco, Denver, and New England are all virtually even at 20% to win the Super Bowl. The Patriots are the highest ranked of the three, but San Francisco benefits from the weak NFC and Denver from home field advantage. CTR would naturally pick Seattle to win it all if they weren’t at a seeding disadvantage; however, their probability of winning the Super Bowl given surviving the first round is 14%, greater than Atlanta’s 12%.

The most likely AFC title game is Denver/New England (48% chance), with Denver given a 54% chance to win (it would be 47% on a neutral field and 40% at New England); the least likely AFC title game is Indianpolis/Cincinnati (1% chance). The most likely NFC title game is Atlanta/San Francisco (34%), with a 53% chance of a 49ers road win; the least likely matchup is Washington/Minnesota (2%). The most likely Super Bowl matchup is Denver/San Francisco (14% likelihood and 54% chance of a 49er win); the least likely is Indianapolis/Washington (.1%). The NFC is estimated to have a 51% chance of winning the Super Bowl, lower than one might expect given the NFC’s dominance in the overall rankings. However, the NFC’s best team has to win three games on the road (barring a title game against Minnesota) while the probability of New England or Denver carrying the banner for the AFC is estimated to be 77%.

Of course, all of these probabilities are just estimates based on a fairly crude rating system, and last year the Giants were considered quite unlikely to win the Super Bowl (although I didn’t regress enough in calculating the playoff probabilities last year, resulting in overstating the degree of that unlikelihood).

Wednesday, January 04, 2012

Crude NFL Ratings, 2011

The NFL is a distant third on my list of pro sports interests (baseball is #1, of course, and horse racing ranks #2), but I’m interested enough to run the teams through my crude rating system (see explanation here) and figure I might post the ratings here. They are based on points/points allowed, adjusted for strength of schedule. 100 represents a win/loss ratio of 1, and so the resulting ratings are adjusted win ratios and can very easily be used to estimate the probability of a team winning a particular game. A team with a rating of 100 should beat a team with a rating of 50 2/3 of the time (100/(100 + 50)).

Actually, let me first run a list based on actual wins and losses. I’ve actually calculated W/L ratio as (W + .5)/(L + .5) here just to avoid the (real in the NFL) possibility of a 16-0 team crashing the system:

In the chart, aW% is an adjusted W%; it averages to .500 for the NFL and will produce the same list in rank order as the CTR; I prefer the latter because of its Log5 readiness, but aW% is a more meaningful unit. SOS is the weighted average of opponent’s strength of schedule. “rk” is the team’s rank in CTR, while “s rk” is the team’s rank in the SOS estimate.

I really do not care for the actual W% presentation for the NFL due to the short season magnifying differences in the teams. The Packers tower over the league here, which is appropriate given a 15-1 record against a decent schedule, but it doesn’t have any predictive value. You will notice in the table above that the NFC does quite well, which will be carry through to the points-based ratings:

Green Bay does not even rank #1 in the league; both New Orleans and San Francisco rank ahead of them. The top nine and eleven of the top fourteen teams made the playoffs, which is pretty good I think.

The aggregate ratings for the divisions (simply the average rating of the four teams) illustrates the superiority of the NFC and why I don’t care for micro-divisions:

Last year, the NFC West in turned in a ghastly 29 rating. Led by San Francisco, they were from the worst in the league, a distinction that went to their AFC brethren.

This whole exercise would be devoid of a great deal of entertainment value if I did not use the results to estimate Super Bowl probabilities. The disclaimer list here is lengthy enough that I will skip it less I leave anything out. A credibility adjustment would be pretty simple to implement (adding 12 games of a 100 rating would do the trick), but this is just NFL stats, not something important. The playoff odds do consider home field advantage; the home team’s rating is multiplied by 57/43 to reflect a fairly average NFL home field advantage. I feel bad about listing the probabilities to the thousandth place, but there are so many possible combinations for the championship games and Super Bowl that those tables would look silly without it:

Two road favorites on the first weekend is probably pretty typical given the quality of teams that often win micro-divisions (particularly those like the AFC West). The Denver Broncos simply aren’t a very good football team (it is tough for me to leave it at that, but piling on more snark re: you-know-who is beyond excessive at this point).

I like reseeding in theory, but when your initial seeding insists that Denver ranks #4 in the AFC because they are the sharpest scissors in the kindergarten classroom, it loses some of its luster.

Life is tough enough as a Browns fan without having to worry about horrors like a Denver/Cincinnati AFC title game, but thankfully there’s a 99.8% chance that will not come to pass. Pittsburgh/Baltimore, on the other hand, is the most likely championship game scenario that doesn’t involve either conference’s #1 seed.

Combining all of these, here are the playoff probabilities for each team:

The system still considers Green Bay the Super Bowl favorites even though they rank below New Orleans and San Francisco, thanks to favorable second round matchups and home field advantage, which is much more significant in the NFL playoffs than in MLB. Ratings and home field aside, if the NFC title game turns out to be Packers/Saints, I’m picking the latter to win it all. These probabilities add up to a 57% chance of the NFC representative winning the Super Bowl.

Thursday, April 21, 2011

Wayne Winston's Mathletics

The "book reviews" on this blog are almost always a day late and a dollar short. They are written and published long after the book, and my comments about them usually don't amount to a review but rather as a springboard from which to discuss other topics. This one is no different.

Wayne Winston is a professor of Decision Sciences at Indiana University's business school and a former consultant to the NBA's Dallas Mavericks. He published Mathletics in 2009 with the tagline "How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football."

If you are a regular reader of this blog or similar material, do not buy this book expecting to learn a lot of new things about sabermetrics. The sabermetric material is fairly standard, rudimentary type material--introductory-level discussion of run estimators, park factors, replacement level, the base/out table, win expectancy, and the like. I would also not recommend it to a novice, not because it is poor (there are elements I like and dislike, as I'll discuss below), but because there are better resources out there--internet primers, Bennett and Fluck's Curve Ball, and Lee Panas' Beyond Batting Average among others.

I am not particularly well-read on either football or basketball quantitative analysis, so I cannot definitively state the level of Winston's discussion on those topics. My guess is that the football discussion is fairly basic (with the caveat that football analysis as a field lags behind apbrmetrics), but that the basketball material is much stronger. It is certainly obvious from the writing that basketball is Winston's passion, and that the adjusted plus/minus ratings are a particular favorite.

Winston's writing is not particularly strong--he writes like someone whose favorite class was math (as do I). There are some minor slip-ups in the baseball discussion; these won't mislead the reader, but they also reflect the pedestrian nature of the material:

* Winston includes a formula for estimating batting outs that accounts for ROE by putting a multiplier on at bats. But this applies the adjustment to all at bats, including those in which we know a batter did not reach on an error (hits) and those in which the likelihood was very small (strikeouts).

* He refers to Keith Woolner's statistic as VORPP--Value Over Replacement Player Points. This makes sense in that he applies the replacement level concept to WPA points, but he also refers to Woolner's run based version as VORPP. Additionally, he credits the concept of replacement level to Woolner. In reality, Woolner did much to popularize replacement level, but the concept did not originate with him.

* Similarly, he credits the concept of park factors to Bill James. James had much to do with popularizing the notion that statistics could be corrected for park effect, but if any single person is to be credited with the concept, Pete Palmer would be an easy choice.

* There is a chapter that discusses player improvement over time by comparing annual performance, but it does so without even really addressing aging and survivor bias.

* The discussion of strategy is fairly bare-bones and deals only with basic estimates based on a standard run expectancy table.

There are positive things of similar magnitude to the list of negatives--for example, while he uses Runs Created, he explains that a theoretical team construct is necessary to make accurate player comparisons. As a whole, the baseball portion of the book is adequate without being excellent for a novice and a yawn for those well-versed in sabermetrics.

Being a novice myself when it comes to football and basketball analysis, I found the discussion in those chapters much more interesting. Focusing on a couple interesting football tidbits, Winston offers a version of the famed two-point conversion chart that incorporates the expected number of possessions remaining in the game. There is also a formula for the probability of a successful field goal in the NFL based on distance that I found interesting, although the model produces results that are clearly too high for very long kicks.

There is also a discussion of quarterback ratings, which have always interested me. Like every other sane person, Winston has little use for the NFL system, focusing his discussion on Berri's rating from Wages of Wins and his own adaptation of Brian Burke's regression of team categories against team wins. Isolating the categories from Burke's equation that can be related directly to individual quarterbacks, Winston offers the following as a quarterback rating:

1.543*(Yards - Sack Yards)/(Attempts + Sacks) - 50.0957*(Interceptions/Attempts)

If you factor out and ignore the 1.543 coefficient, and change the second quantity's denominator to (Attempts + Sacks), this can be rewritten as:

(Yards - Sack Yards - 32.47*Interceptions)/(Attempts + Sacks)

In this form, Winston's rating is very similar to a number of rating formulas, including the NEWS rating published by Bob Carroll, John Thorn, and Pete Palmer in The Hidden Game of Football:

NEWS = (Yards - Sack Yards - 45*Interceptions + 10*Touchdowns)/(Attempts + Sacks)

Breaking into editorial mode and stepping away from Mathletics for a moment, the treatment of a touchdown pass can be thought of as somewhat analogous to the sacrifice fly in baseball. The comparison is strained as touchdown pass is always a positive play from any perspective, while a sacrifice fly might actually reduce run expectancy.

A fairly large number of touchdown passes occur on short passes. Suppose a quarterback completes a three-yard touchdown pass. This will actually reduce his rating in Winston's ranking, as the quarterback's rating prior to the touchdown will be higher than three. By giving a positive weight to all passing touchdowns, one could ensure that a touchdown pass always increases ranking.

However, in doing so, one gives special treatment to the touchdown because it is a tracked category (like sacrifice flies). However, one could also track "sacrifice grounders" or "first down completions". These theoretical categories would also be cases in which a positive or somewhat positive outcome was achieved, but the statistics treat it as a negative (a batting out or a reduction of the passer's rating, assuming the completion was short). Giving special treatment to the recorded categories can thus be seen as unhelpful and biased by particular types of players that might be predisposed to one or the other.

Moving back to the book, most of my comments to this point have focused on the negatives. However, there are three things that Winston does really well:

1. Winston provides downloadable spreadsheets for many of the examples. This allows the reader to follow along with the work and to learn how to carry it out in Excel. Many of the Excel steps are explained in the text as well.

The drawback to this is that some of the why behind the math is glossed over in favor of a quick Excel solution. Winston's rating system for NBA and NFL teams basically boil down to finding the best-fitting solution for a system of linear equations to predict the point margin in each game. Winston doesn't explain the math in that manner, though, instead just explaining that the Excel solver is used to minimize error. While this gives the reader enough detail to produce their own ratings, and no one is actually going to solve hundreds of equations, I personally prefer a stronger emphasis on the underlying math.

2. The bibliography is excellent, as it includes not just a list of sources but descriptions of what they offer. For example, this is the description of Phil Birnbaum's Sabermetric Research blog:

This is perhaps the best mathletics blog on the Internet. Sabermetrician Phil Birnbaum gives his cogent review and analysis of the latest mathletics research in hockey, baseball, football, and basketball. This is a must-read that often gives you clear and accurate summaries of complex and long research papers.

3. Winston's description of Birnbaum's blog provides a nice transition into discussing the best thing about his approach. While Winston has excellent academic credentials (he is a professor of Decisions Sciences at Indiana and earned a PhD at Yale in Operations Research), but he does not beat you over the head with it. In fact, I don't think that his doctorate is ever explicitly referenced.

In any event, Winston mixes the research of other academics into his text, but he gives plenty of space to amateurs as well. Some academics that enter the sports arena seem to thumb their nose down at anyone who doesn't hold an advanced degree or a teaching position. Winston is not one of them. He even used one of Birnbaum's posts to offer a counterpoint to an academic paper on the NFL draft.

Winston's book provides a great example of how sabermetric knowledge generated by academics, amateurs, and everyone in between can be integrated, and how all parties can respect and learn from each other. It also gives analysts specializing in each sport a window into the work being done on other sports. Thanks to those attributes, Mathletics is a worthwhile read.

Monday, January 03, 2011

Crude NFL Ratings

I feel bad about starting 2011 with a post about the third-best professional sport, but the material is time-sensitive. I came up with a crude rating system for baseball teams last year, and it is equally applicable to teams from other sports. So I've been tracking NFL ratings throughout the season, and since the playoffs are about to start I figured that I would share them here.

(*) "came up" is a big stretch, actually, since while I'm not aware of anyone doing it in exactly the manner I did, that's mostly because the way I did it is not the best way to do it and because a lot of similarly-designed systems have worked with point differentials rather than estimated win ratios. "Implemented" would be a more appropriate and honest description.

I do not have a full write-up ready for the system yet; it's actually fairly simple (part of the reason why I'm only confident describing the results as "crude"), but I am going to do a full explanation that tries to express every thing in incomprehensible math formulas rather than words. It's backwards to post results before methodology, but results of an NFL ranking system aren't very interesting after the season unless you are a huge NFL fan, and I am not.

The gist of the system is that you start by calculating each team's estimated win ratio, based on points/points allowed ratio (I used this formula from Zach Fein for the NFL). Then, you figure the average win ratio of their opponents and the average win ratio for all 32 teams in the NFL. To adjust for strength of schedule, you take (team's win ratio)*(opponents' win ratio)/(average win ratio). Now you have a new set of ratings for each team, and so you repeat the process, and you keep repeating until the values stabilize.

At that point, I take each team's adjusted win ratio/average win ratio and multiply by 100. This is the Crude Team Rating. Similarly, I figure the strength of schedule for each team. The nice thing about these ratings is that they are Log5-ready. If a team with a rating of 140 plays a team with a rating of 80 on a neutral field, they can be expected to win 140/(140 + 80) = 63.6% of the time.

Since the system is crude, there are a number of things it doesn't account for: the field on which the game is actually played, the effect that a team has on its opponents' estimated win ratio (losing 31-7 reduces your expected win ratio, but it also makes your opponent look like a stronger team), any changes in team composition due to injuries and the like, regression, and this is by no means a comprehensive list.

The ratings are based solely on aggregate points and points allowed. Even if you restrict the inputs to aggregate season data, there are a number of possible other inputs that you could use--actual win/loss record, predicted win loss record based on total yards, turnovers, and other inputs (akin to using Runs Created rather than actual runs scored for a baseball rating), or some combination thereof. I have not done that here (I'm not sufficiently motivated when it comes to NFL ratings, and I will offer a set of ratings based only on W/L with a slight adjustment), but have done some of that for MLB ratings.

To account for home field in making game predictions, I've assumed that the home field advantage is a flat multiplier to win ratio. Since the average NFL home-field record is a round .570 (a 1.326 win ratio), the expected win ratio of the matchup is multiplied by 1.326 (or divided if it is the road team). For example, in the 140 v. 80 matchup, the expected win ratio is 140/80 = 1.75. If the 140 team is at home, this becomes 140/80*1.326 = 2.321, and if they are on the road it becomes 140/80/1.326 = 1.320. So the expected winning percentage for the 140 team is 1.75/2.75 = 63.6% on a neutral field, 2.321/3.321 = 69.9% on their home field, and 1.320/2.320 = 56.9% on the opponents' field.

In this table with the 2010 rankings, aW% is the estimated "true" winning percentage for the team against a league-average schedule; "SOS" is strength of schedule; and "s rk" is the team's SOS rank.

The next chart gives ratings for each division, which is simply the average CTR of the four teams that comprise the division:

The NFC West was truly a dreadful division, with an average CTR of just 29. If you treat the division ratings as team ratings, that implies that the W% for a NFC West team against an average NFL team should have been 22.5%. The NFC West teams combined for an actual record of 25-39, which is 13-27 (32.5%) when you remove intra-divisional games. Of course, thanks to the unbalanced schedule, their average opponent is not an average NFL team.

With the playoff picture now being locked in, one can use the ratings to estimate the probability of the various playoff outcomes. I offer these as very crude probabilities based on crude ratings, and as nothing more serious. For these playoff probabilities, I assumed that each team's effective winning percentage should be 3/4 of its actual rating plus 1/4 of .500, and converted this to a win ratio. I have no idea if this is a proper amount of regression or not; I would guess it's probably not aggressive enough in drawing teams towards the center, but I really don't know. The key word is "crude", remember. That results in the following rankings for the playoff teams (this won't change the order in which they rank from the original CTR, but it will reduce the magnitude of the differences):

This chart illustrates why I don't like the NFL playoff seeding system, although this year is worse than most. In both conferences, the wildcard teams are estimated to be better than the lesser two division winners. In the case of Seattle this is completely uncontroversial, but Indianapolis was not a particularly impressive team and Kansas City played the estimated weakest schedule in the NFL. When your divisions are as small as four teams, a crazy year like this is bound to happen eventually. At the very least, I would suggest that the NFL allow wildcard teams to host playoff games if they have a better record than the division winner they are slated to play. When an 11-5 team like the Saints to have to go on the road to play the 7-9 Seahawks, I suggest that your playoff structure is too deferential to your micro-divisions.

With those ratings, we can walk through each weekend of the playoffs. P(H) is the probability that the home team wins; P(A) is the probability that the away team wins. For later rounds, P is the probability that the matchup occurs (except for the divisional round, in which case P is the probability that the designated set of two matchups occurs):

According to the ratings, the road teams should be favored in each game this weekend. They suggest there's about a 16% chance that they all win, but only a 2% chance that all of the home team wins.

It's necessary to look at the possible division matchups together by conference thanks to reseeding. The most likely scenarios result in teams from just four of the eight divisions making it to the round of eight, with the AFC featuring divisional rematches (allowing the "Divisional" round to truly live up to its name) but a inter-divisional matchup in the NFC.

Once you get to the championship game level there are so many possibilities that there isn't much to say, so I'll move right on to the Super Bowl:

There are two potential Super Bowl matchups that come out at .1%; the least likely is considered to be Kansas City/Seattle (.013%, or about 7700-1).

Combining those tables, one can look at the advancement odds for each team:

Again, I need to issue the standard disclaimer--these are very crude odds based on a crude rating system.

Finally, here are ratings based on the actual W-L record rather than points/points allowed. I did cheat and add a half a win and half a loss to each team; as the Patriots and Lions have shown us in recent years, 16-0 and 0-16 are not impossible in the NFL, and either would break a ratio-based ranking system: