Most QBs over 350 yards

In Sunday's (10/18/09) games six QBs threw for over 350 yards (Roethlisberger 417; Schaub 392; Flacco 385, Brady 380; Brees 369; Rogers 358...Garrard almost made it seven with 335). I can't imagine that has happened often, but I didn't hear any of the Sports Show talking heads mention this. Does anyone out there know how often this has happened before?

Ed Pandolfino

Bye Weeks

Do teams have an advantage after a bye week ?
by Denis O'Regan.

There's been some interest recently on various blogs concerning the performance of teams after their bye week.So here's some number crunching I did a few seasons ago,update to the present.

I looked at the record of teams coming off their bye week playing against teams who had played the previous week.I eliminated late season weeks,such as week 17 where teams are resting starters or perhaps not fully committed to winning in order to secure higher draft picks.And I also stuck to the regular season to avoid divisional games where the,usually inferior opponent has played in the wildcard round.

I used win percentage as one measure of a team's success and also average margin of victory (or defeat).The latter measurement can add a little more depth to the process of measuring a team's performance.For example if a team wins three games each by a single point,it is 3-0 from a win/loss point of view,but has in all probability put up a very similar performance to that of its opponents.

I initially looked at home teams alone and then away teams alone coming off a bye and then also at away teams who were favoured to win their post bye matchup.

I compared the results of each post bye group with a much larger,but similar group of teams who were playing having played the previous week.

Lastly I have a win probability model for games that I have used for the last 10 seasons.Over the close season I have taken the process back another decade.Therefore I have used this to determine which team is favoured to win any matchup.The regression used to produce the probabilities does not incorporate any perceived advantage from a bye week.The expected average margin of victory for any group of matches can be calculated and if this expected margin differs greatly from the actual margin over a large number of games,it could be reasonable to assume that the difference could be attributed to the missing ingredient from the regression.Namely the effect of a bye week.

A Game of Two Halves?

A Game of Two Halves ?

by Denis O'Regan.

One of the easiest traps to fall into when trying to predict the likely outcome of a sporting event,is to give far too much importance to the value of recent events.For example if a strong,pre game favourite is only narrowly leading a lower rated opponent at the half or is even trailing,it is tempting to assume that the remaining part of the game will be similarly fought out.

I therefore decided to look at the outcomes of games that had not appeared to have "followed the script" for all or part of their course based on pregame assumptions.

Firstly,I needed a robust model that did a good job of predicting the likely game result.This subject is extensively covered all over the net,so I'll simply give a broad outline of the parameters I used.The four main variables used in most models are the offensive rushing and passing capabilities of both team and the defensive rushing and passing counterparts.These factors are reasonably predictable from game to game and even with little or no adjustments for strength of schedule,they have quite an impressive predictive power for future match ups.I used data gathered from at least the previous four games for each team.

Alternatively,the against the spread quotes of the Vegas line are a reliable indicator of the likely outcome.

QB Rating

The Current QB Rating Formula Sucks
Luis DeLoureiro of www.nflstatanalysis.net


I did a little research this weekend.  I looked at the calculation for the current QB rating system and, you know what?  It kind of sucks.

Explanation of the Formula

Here's the formula – it's based on 4 general categories.  The specific category for each part of the calculation is in the brackets:
a = ((Comp/Att) * 100) -30) / 20  [Completion percentage]
b = ((TDs/Att) * 100) / 5  [Touchdown Pass pct]
c = (9.5 – (Int/Att) * 100))/4  [Interception pct]
d = ((Yards/Att) – 3) / 4  [Yards per attempt]

The final formula is (a + b + c + d)/.06
[source:  www.primecomputing.com]

So that you don't have to go too nuts digging into what the formula is doing, I'll try to explain as best I can.The intent of the formula is to give, essentially, equal weighting to each of these categories.

Since some of the numbers are percentages and others are integers, some data manipulation needs to take place (e.g., multiply the percentages by 100).

Also, not all stats are on the same scale – even if they are both percentages.  For example, 10% is a very good touchdown percentage, but it is a horrible completion percentage.  So, each of the categories is divided by a different amount.

The Worst Passing Teams in the NFL

By Doug of Football Burrito

(Edit: I think Doug deserves a plug simply due to the name of his site. Sweet.)

A couple of the worst teams in the NFL at rushing the ball had pretty good seasons. How did the worst teams at passing do?

#32 Oakland Raiders

Not a good start for the worst passing teams. Oakland will be drafting near the top of the draft as usual and will stay there until they get more balance on offense.

#31 Cleveland Browns

A QB controversy over the 31st ranked passing attack in the league? This isn't exactly Joe Montana vs. Steve Young, they should ship Brady Quin and Shaun Rogers off to Denver for Jay Cutler.

#30 Cincinnati Bengals

Without Carson Palmer behind center the Bengals went from 250 yards passing per game in '07 to 150 yards passing per game in '08 with a 4-11-1 season to show for it.

#29 Seattle Seahawks

A West Coast Offense is not suppose to finish at the bottom of the league in passing. Seattle's receiving core was decimated by injuries last season and they should be much better this year.

All of these teams finished with 5 wins or less and while running the ball is a good formula for winning you also better have some balance on your team.

Running Back Overuse II

by Delta Whiskey

INTRODUCTION

In the previous post, the notion that running backs are subject to "wear and
tear" as popularized by Football Outsiders "Curse of 370" was explored.
Brian Burke's critique of "the Curse" suggests that regression to the mean
better explains "The Curse." The following examines factors that may
explain or at least describe the processes associated with said regression.
Specifically, the study examines win differences (decline possibly due to
the fact that teams that are winning run more than those that are losing),
overall team offensive decline (running backs' performance may decline if
their own team in general declines) or tougher opposition in subsequent
years.

METHODOLOGY

As in the previous study, the primary sources of data for this study were
Pro-Football-Reference.com's list of "Single-Season Rushing Attempts
Leaders"
(http://www.pro-football-reference.com/leaders/rush_att_single_season.htm).

The data sets for testing the hypothesis were created in the same manner as
before. Again, two sets of statistical analyses were conducted. The first
utilized the full data set, while the second utilized Football Outsiders
measures to assess issues related to offensive strength and opponents'
strength. Again, 2x2 repeated measure factorial design was utilized to
analyze the data.

DATA ANALYSIS

WINs: The number of wins for each running back's team was examined. The
rationale for this analysis is that teams that are winning run the ball more
and therefore a difference in Year and Year+1 wins might indirectly explain
the differences noted in number of carries.

Wins were expressed as a percentage rather than raw totals due to the
progression from 12 to 14 and finally 16 games per year within the data set.

Group Year Mean Year+1 Mean
One 0.6114  0.4973
Two 0.5422  0.5536

Between subjects F =0 df (84,1), p <ns.
Within subjects F=2.2, df (84,1), p<ns
AxB F=3.4, df(84,1), p<ns

These results certainly do not support the hypothesis that running back
decline may be due to his team winning less.

DVOA Era Statistics
As in the previous study, this data set only includes players from 1996 and
beyond.

Wins: Again, analysis was conducted to assess for differences in Team Wins.

Group Year Mean Year+1 Mean
One 10.55  8
Two 8.35  7.55
 
ANOVA results yielded the following
Between subjects F =6, df (38,1), p < 0.05
Within subjects F=6.78, df (38,1), p < 0.01
AxB F=1.85, df(38,1), p

In contrast to the earlier analysis of wins, the within subjects results
appear to support the idea that a decrease in wins may explain in part of a
running backs decline, most likely in number of carries. Furthermore, the
between groups difference indirectly supports the notion that teams that are
winning run more. It should be noted the direction of this relationship, if
it exists is not determinate by this analysis. This also suggests that the
role of running the ball seems to have changed in the last twenty or so
years (i.e. DVOA data only goes back to 1996).

DVOA Statistics

Offensive DVOA: This analysis looked at the differences in offensive
performance, as measured by Offensive DVOA.

Group Year Mean Year+1 Mean
One .0943  .0131
Two -0.000  -0.03
 
ANOVA results yielded the following
Between subjects F =10, df (38,1), p < 0.01.
Within subjects F=6, df (38,1), p < 0.05
AxB F=1, df(38,1), p<ns

The within subjects results indicated that there is a significant offensive
decline from Year to Year+1. It is entirely possible that this decline is
mostly due to the decline in RB performance as the analysis does not control
for the RB's contribution to Offensive DVOA.

Opponent DVOA (x100): Next, the average overall DVOA of opponents was
examined. In order to facilitate analysis, the DVOA was returned to a
percentage.

Group Year Mean Year+1 Mean
One .9  1.365
Two -1.48  1.205
 
ANOVA results yielded the following
Between subjects F =1.5, df (38,1), p <ns.
Within subjects F=3.4, df (38,1), p<ns
AxB F=1.1, df(38,1), p<ns

There were no statistically differences in the quality of opponents between
groups or from year to year.

DISCUSSION

Brian Burke has suggested that the decline in running back performance is primarily due to regression to the mean. This study examined whether other measurable group differences could be associated with and/or explain decline
in performance. The results indicated that at least since 1996 there is a difference in the number of wins from Year to Year+1. Additionally, there
is a decline in offensive performance (as measured by Offensive DVOA) from
Year to Year+1; however, as noted, the RB's individual contribution to
Offensive DVOA was not controlled for, and therefore it is difficult to
ascertain the robustness of overall offensive decline.

Next, regarding the first study, Derek asked "Question about the sampling
method:
A running back had 356+ carries in year Y and less than 290 in Y+1. Years Y
and Y+1 will show up in Group 1, but would Y+1 and Y+2 be in Group 2 as
well?" The answer is yes. He then asks "A thought stemming from that
question: Maybe it's not one year of overuse but multiple years of overuse
that kills a RB. Is there some threshold for the number of carries over 2 or
3 years that will cause a total break down the following year?" Football
Outsider's may thinks so, but I think the answer to this question is no.
Recall that the data analyzed is essentially the upper and lower bounds of
the "Top 250 Single-Season Rushing Attempts Leaders." The complete data set
of "Top 250 Single-Season Rushing Attempts Leaders," contains a total of 259
total data points, that is 259 RB seasons qualified. If overuse and decline
over one to two seasons is a real phenomena, then it is expected that there
would be somewhere between 129 (or 130) and 259 individual players on the
list. Instead, 103 individual players are on the list, meaning that each
player who makes the list, does so an average of 2.51 times. Moreover, of
those 103, 36 (35%) make the list (not necessarily consecutively) 3 or more
times. Wear and tear may be a real phenomena; however, it does not appear
as robust as Football Outsiders would like you to believe.

Follow on studies will attempt to isolate or model predictors of decline.

Home Field in Divisional Games.

by Denis O'Regan.

Home field advantage exists in every professional sport.For example in association football in the UK teams acquire upwards of 60% of their league points at home and on average win just under half of their home games.Home field is worth around 0.4 of a goal.

However,if you restrict the soccer samples to local derbies then the figures look significantly different.Local derbies are contested between very close geographical rivals (usually,but not always from the same city).The games therefore are of great importance to the fans,the players are familiar with their opponents and their surroundings and travel fatigue is eliminated.

In such games goals overall are less plentiful and home field advantage appears to be greatly reduced.Home sides now only win around 40% of the games (there are more draws) and the average margin of victory for the home side is nearer to 3 tenths of a goal.

Divisional games in the NFL appear to share many characteristics with local soccer derbies.Travel times are shorter,the away team is familiar with their opponents stadium and with their opponents and the game has heightened importance both to the fans and to the team.To get to the post season you first must top your division.

I therefore compared the scoring in divisional and non divisional games since the league went to 8 divisions of four teams.

Scoring is depressed in divisional games compared to non div ones,but the difference is small.Non divisional games averaged 42.9 points per game compared to 42.2 ppg for divisional ones.

It's when you start looking at the margin of victory for the home sides in the two types of matchups that potentially significant differences become apparent.The average scoreline in divisional games is 22.0-20.2 in favour of the home team for an average home field advantage of only 1.8 points.That compares to around 2.7 points for the league as a whole over the same timescale and 3.1 points for all non divisional games,again since 2002.

Wins and losses also confirm the depressed HFA in divisional games.Home teams win just 54% of divisional games (which tallies well with the 1.8 point average margin of victory),compared to 58% for the league overall and 59.5% for non divisional games.

Divisional games appear to be just as atypical when you look at how the HFA is distributed over the 4 quarters of the game.It's long been established that HFA appears to be at it's strongest in the first quarter and consistently declines to be at it's lowest in the 4th.This is evident in non divisional games.

In these type of games 39% of the HFA is gained on average in the first quarter,35% in the second,19% in the third and 6% in the 4th.

However the divisional games don't follow this pattern.Comprising 680+ games,40% of the HFA is accrued in the 1st Q,31% in the 2nd,ONLY 5% in the 3rd and 25% in the 4th.

The average points scored are

1st Q,home side 4.6 pts,away side 3.9 pts.
2nd Q,home side 6.7 pts,away side 6.1 pts.
3rd Q,home side 4.4 pts,away side 4.3 pts.
4th Q,home side 6.2pts,away side 5.7 pts.

and these numbers are reflected in the win/tie/loss figures for each quarter.

1st Q,home side "wins" 42% of the time,away side "wins" 35% of the time and 24% of games are tied after one quarter.

Re setting the game to 0-0 at the start of the 2nd Q,home sides "win" 46%,away sides 40% and 14% are tied.(The lower rate of ties reflects the higher scoring in this quarter).

3rd Q,home side "wins" 39%,away sides 38% and 23% ties.

4th Q,home side "win" 43%,away sides 39% and 17% are tied.

It's easy and probably dangerous to attribute reasons for the closeness of the third quarter and the surge of home field advantage in the fourth compared to other non divisional games.(The team trailing at the half is more likely to be the visitor,realising the importance of the game,they make considerable adjustment at half time and "up" their game to get back into contention.However,the effort takes it's toll in the 4th and increased crowd involvement sees the home side well back on top).

Plausible,but probably not even half the story.The numbers may just be a fluke of nature and they certainly aren't mirrored equally across every division. (For example visitors dominate the 4th Q in the AFC North and away sides "win" that quarter over 50% of the time).

Further superficial investigation suggests that visiting teams in divisional matchups are more efficient at throwing the ball than you would expected compared to visitors in non divisional matchups and the home side commits more penalties than is usual.

Whether these game stats cause the wins or the wins cause the games stats is,as ever open to debate.

Running Back Overuse

by 'DeltaWhiskey'

INTRODUCTION

The following explores the notion that running backs are subject to "wear and tear." Football Outsiders has popularized and continues to promulgate the notion that carrying the ball over 370 times a season places a running back at "greater risk for significant decline or injury the next season." A full explanation of the "Curse of 370" can be found here. Brian Burke, at Advanced NFL Stats, has suggested the "Curse" is more of a "Myth," noting that the Football Outsiders made several statistical errors in developing the theory and that regression to the mean better explains "The Curse." Mr. Burke's critique can be found here.

The following further examines the validity of the "Curse of 370" and the
possibility that "overuse" of running backs may be a real phenomenon that
results in a performance decline.

METHODOLOGY
The primary sources of data for this study were Pro-Football-Reference.com's
list of "Single-Season Rushing Attempts Leaders." This list contains the Top 250 single-season records for attempts. When accessed for this study, the number of attempts ranged 286 to 416, with a mean of 326 and SD of 30. To test the potential effects of overuse theory, two groups were identified; Group 1 consisted of players who were one or more SD above the mean (356 or more carries). Group 1 was compared to Group 2, which consisted of running backs who were more than one SD below the mean (295 carries). This break conveniently resulted in two groups with 43 members each. It should be noted that several running backs' data were discarded because they: a.) didn't play the following year (e.g. Ricky Williams) or made the list in 2008 (e.g. Michael Turner). Also, Quarterbacks that made the list, were discarded.

For each RB, the data from individual player "cards" at Pro-Football-Reference.com was utilized. Data was gathered for the relevant season (i.e. the year they rushed either 356 or more carries, or less than 295 carries = "Year") and the following season ("Year+1"). This design allowed for testing of the hypotheses via Repeated Measures 2x2 factorial designs.

Two sets of statistical analyses were conducted. The first looked at the issue of overuse utilizing readily available standard measures of running back performance utilizing data from the above described data source. The second set of analyses, utilized Football Outsiders measures to assess
running back. This second analysis required creating a subset of data from the first because Football Outsider's data extends only back to the 1995 season. Therefore, all running back performances prior to 1995 were discarded from these analyses (sorry Jim Brown fans). This conveniently left two groups of 20 each after one of Jamaal Anderson's season was
discarded because he did not have enough carries in Year+1 to generate Football Outsider statistics. Football Outsider data for each RB was "Year"
and "Year+1" included the following measures: individual DVOA and DYAR.

DATA ANALYSIS
Standard Statistics
# CARRIES: The first analyses simply addressed whether or not the two
groups being analyzed differed in the number of carries.

Group Means
Group Year Mean Year+1 Mean
One 377.16  282
Two 290.18  240.74

Note that the average number of carries for Group 1 is actually greater than
370.

ANOVA results yielded the following
Between subjects F =39.63, df (1,84), 0.0001
Within subjects F=46.28, df (1,84), 0.0001
AxB F=4.63, df(1,84), 0.05

These results indicate that in terms of number of carries, there is a statistical difference between the Groups, between years and a year by group interaction. These results suggest that not only is there a difference from "Year" to "Year +1," but that the magnitude of the decrease is significantly different between the groups.

# of GAMES: A central component of "The Curse" proposes that more carries (specifically greater than 370) will result in a decline in the number of games a running back will play the following year (Year+1). The following analysis compared the two groups' number of games played in Year and Year +1.

Group Year Mean Year+1 Mean
One 15.674  13.534
Two 14.953  13.116

ANOVA results yielded the following
Between subjects F =1.95, df (1,84), p <ns.
Within subjects F=27.99, df (1,84), p<0.0001
AxB F=, df(1,84), p<ns.

These results indicate that high use, whether above or below 370 carries results in a decline. This is most consistent with Mr. Burke's findings. There is no statistical difference between the groups, nor is the magnitude of decline between the groups different. If a "Curse" exists, the bar is much lower than 370.

Y/A: Next, yards per attempt were assessed. Yards per attempt provide an indicator of a RB's effectiveness on a carry per carry basis.

Group Year Mean Year+1 Mean
One 4.3419  4.086
Two 4.3163  4.093

As pointless as it seems, here are the results of the analysis.
Between subjects F =0 df (1,84).
Within subjects F=10.74, df (1,84),0.01
AxB F=0.04, df(1,84),

In sum, a running back that carries a lot, on average, will experience a decline the following year - again, there is nothing magic about 370.

"DVOA Era Statistics"
Perhaps the measures utilized above are simply too crude to properly detect the effects of "370." To address this possibility, similar analyses were conducted utilizing Football Outsiders stats. First a series of analyses utilizing "Standard Statistics" were conducted to ensure that the sub-groups being analyzed were relatively the same as the original groups.

Standard Statistics
#Carries:  
Group Year Mean Year+1 Mean
One 375.5  291.4
Two 291.65  242.7

ANOVA results yielded the following
Between subjects F =19.83, df (1,38), p <0.0001
Within subjects F=17.11, df (1,38), p<0.001
AxB F=, df(1,38), p<ns.

These results suggest the groups are different in the number of carries. The nonsignificance of the interaction effect is the only difference and suggests that the previously detected difference may be due to a larger sample size.

#Games

Group Year Mean Year+1 Mean
One 15.5  13.85
Two 15.4  14.2

ANOVA results yielded the following
Between subjects F =.04, df (1,38).
Within subjects F=6.89, df (1,38), 0.01
AxB F=.17, df(1,38), p<ns.

These results are similar to those found above.

Y/A (Yards/Attempt)
Group Year Mean Year+1 Mean
One 4.355 3.94
Two 4.165 3.89

ANOVA results yielded the following
Between subjects F =.52, df (1,38),.
Within subjects F=11.33, df (1,38), p<0.01
AxB F=0.48, df(1,38), p<ns.

Results are again similar to above. These results then suggest that the sub-group of players, post 1995, are statistically, fairly similar to the group as a whole.

DVOA Statistics
To test validity of Football Outsider's "Curse of 370," it seems appropriate to utilize some of Football Outsider metrics. For an explanation of these metrics - http://www.footballoutsiders.com/info/methods.

Individual DVOA: This analysis tests the difference in DVOA between running backs in Group 1 and Group 2 based on Year and Year+1. DVOA is usually expressed as percent, in the following, it is expressed in decimal fashion.

Group Year Mean Year+1 Mean
One 0.0755  -0.026
Two -0.000  -0.062

ANOVA results yielded the following
Between subjects F =6, df (38,1), p <.05.
Within subjects F=13, df (38,1), p<0.001
AxB F=1.0, df(38,1), p<ns

These results suggest that there is a difference in Year and Year+1 (wear and tear or regression) and a difference between Group 1 and Group 2; however, the ns interaction effect indicates that the magnitude of the wear and tear is nonsignificant between groups. That is, the 0.1015 drop between Year and Year+1 observed in Group 1 is not significantly greater in magnitude than the approximately 0.062 drop observed in Group 2.

DYAR

Group Year Mean Year+1 Mean
One 260.1  93.05
Two 105.95 55.45

ANOVA results yielded the following
Between subjects F =7.06, df (38,1), p <.01.
Within subjects F=10.46, df (38,1), p<0.01
AxB F=3, df(38,1), p<ns

These results are similar to those for DVOA.

DISCUSSION

This study analyzed "the Curse of 370" by comparing two groups comprised of RBs who accumulated enough carries to be ranked in the top 250 single-season attempts list. The first group consisted of 43 running backs that were at least one SD above the mean in number of carries. The second group consisted of 43 running backs who were one SD below the mean. This process yielded two groups that had a high likelihood of being significantly different regarding the number of carries in a season, and if a high-number of carries is the cause for decline in subsequent seasons, then there should be significant detectable differences in the magnitude of decline. None of the results suggested this to be the case. Simply stated, this study did not detect any evidence to support "the Curse of 370." The study did find that a large number of carries are associated with decline the following year; however, that decline does not become magnified as the number of carries increases - at least not in this data set.

Mr. Burke has asserted that the decline is probably due to regression to the mean; however, further analyses utilizing this data set suggest other factors may be associated with the decline and will be examined in future posts.

Rating Quarterbacks

by Jason Winter of Defensive Indifference

There’s no really good existing way to rate quarterbacks, from a statistical standpoint. Most people understand the flaws with the widely known statistic, though there are alternatives. Adjusted Yards Per Attempt is one of the simpler ones. To review, that’s:

AYA = (Passing Yards + 10*TD passes - 45*Interceptions)/(Pass Attempts)

It is, essentially, a QB’s “yards” (counting TD passes as 10 yards and interceptions as -45 yards) divided by his attempts. Seems logical enough, and fits with other generally accepted “average” stats (like yards per carry for running backs or yards per reception for wide receivers).

But it’s always bugged me how pretty much every stat ever used to rate quarterbacks only accounts for their passing numbers. Since the days of Fran Tarkenton, carrying forth into the days of Randall Cunningham, and, more recently, with Michael Vick and Vince Young, people have argued that rushing stats should play a role in whatever system exists to rate quarterbacks. It makes sense; how can you say a QB with a 6.5 AYA (or 88.7 passer rating) for the season who runs 40 times for 40 yards is the same, statistically as one with a 6.5 AYA who runs 40 times for 200 yards? Isn’t the second guy better?

But if we get into adding rushing yards to a quarterback’s numbers, why shouldn’t we add other things, as well? Isn’t it better if a QB takes 20 sacks instead of 50, or if he fumbles five times instead of nine (assuming identical attempts)?

Ah, but now that opens up another can of worms. Many people would argue that some sacks – not all, but a fair number – are the fault of the offensive line and not the quarterback. You could make similar arguments regarding fumbles, many of which occur as the result of sacks. Why should those numbers be counted against a quarterback in any “comprehensive” statistic?

My response is: Why should passing yards be counted? Or touchdown passes? If we’re going to credit the QB for a completed pass, and assign him positive stats based on his good play, why shouldn’t we blame him for a bad play, like a sack or fumble? True, the negative play might not have been his fault entirely. But no completed pass is ever completely due to his efforts – the receiver and offensive line likely had a role in it, as well – and nobody would suggest we not include passing yards in our rating of a quarterback. If we can’t determine what percentage of a quarterback’s “good stats” are due solely to his efforts and adjust his numbers downward as a result, there’s no reason we should exclude his “bad” stats just because some part of them wasn’t his fault. Just as it’s clear that some QBs are better at running than others, it’s clear that some QBs are better at not taking sacks or not fumbling than others? Why shouldn’t the QBs who are good at this be rewarded and the ones who are bad at it penalized?

Even if we accept that some guys are “just playing on a bad team” or behind a bad offensive line and want to make adjustments for that, why shouldn’t we make adjustments for players with good offensive lines or receivers? Would Tom Brady have thrown 50 TD passes in 2007 if he’d been playing for San Francisco instead of New England and been throwing to Arnaz Battle and Darrell Jackson instead of Randy Moss and Wes Welker? Of course not.

That comes to the heart of this system, however. It’s not meant to show who the “better” QB is, not from a strict interpretation of the word. Tom Brady would have been the exact same person and same player in San Francisco, but his stats would have been lower, due to having worse teammates and coaching. A quarterback who takes a lot of sacks puts up worse numbers than one who doesn’t, all other things being equal. He may or may not actually be worse, but his stats should suffer, just as a quarterback who has Randy Moss and Wes Welker to throw to should have better numbers than one who didn’t (and we might get a chance to see how Matt Cassel does when he doesn’t have those two to throw to). Rather, this system is meant to show which quarterback had the best statistical year, taking all available statistics into account and not biasing the results with any judgments based on credit or blame. If it’s on the player’s stat line, it counts, whether for good or bad.

We can use AYA as a baseline for our “new” stat, which I like to call Total Yards per Attempt (TYA). We can stick with the basic premise of Yards/Attempts, but we’ll need to add a few things to each side. Our numerator has to include:

Passing yards
Rushing yards *
Passing touchdowns
Rushing touchdowns *
Interceptions (negative)
Sack yardage (negative) *
Fumbles (negative) *

And the denominator includes:

Pass attempts
Rush attempts *
Sacks *

(* indicates new statistic. And yes, I know I could add receiving stats, but those are so rare for QBs that I think we don't lose much by leaving them out.)

Rushing yardage can be added easily enough. Rush TDs can have the same weight as passing TDs, 10 per. Sack yardage can simply be negative yardage. Pass attempts, rush attempts, and sacks present no problems, either.

What to do about fumbles, though? Not every fumble results in a turnover, so they should be weighed less than an interception (which is always a turnover). Yet I don't know of any easy place to find the stats on individual quarterbacks' lost fumbles, and I can't assign a -45 per lost fumble for each quarterback, some of which are recovered by the offensive team.

Looking at the last few years, I find that, overall, fumbles (by any player) are recovered by the defense about 2/3 of the time (usually 65-70% per season). That's a convenient enough result, since 2/3 of 45 is an even 30. Works for me. Thus, fumbles are worth -30 to a quarterback.

(I realize, too, that fumbles by a quarterback are generally worse than an interception, since they often occur on or behind the line of scrimmage, as opposed to downfield, but unless there’s something in The Hidden Game of Football (which I haven’t read) or anyone else has any other data out there to assign better values to fumbles, I’ll go with what I’ve got.)

So, putting it all together, we get the following formula:

TYA = (Passing Yards + Rushing Yards - Sack Yards + 10*TD passes + 10*Rushing TDs - 45*Interceptions - 30*Fumbles)/(Pass Attempts + Rush Attempts + Sacks)

Which appears to take pretty much every QB stat into account.

To close, here’s the leaders in TYA for 2008, along with their rank in passer rating. The average among these quarterbacks was 5.04; figuring the average for the entire league is difficult because it requires individually looking up rushing numbers for every quarterback, as well as excluding players who threw passes and whose rushing numbers would skew the results (like running backs).

Rank	Quarterback	TYA	PR Rank
1	Philip Rivers	6.6	1
2	Drew Brees	6.52	4
3	Chad Pennington	6.39	2
4	Peyton Manning	6.19	5
5	Jake Delhomme	5.86	18
6	Kurt Warner	5.82	3
7	Matt Ryan	5.8	11
8	Jay Cutler	5.8	16
9	Jeff Garcia	5.55	9
10	Aaron Rodgers	5.51	6
11	Matt Schaub	5.49	7
12	Donovan McNabb	5.46	14
13	Tony Romo	5.23	8
14	Matt Cassel	5.19	10
15	Kerry Collins	5.18	23
16	Seneca Wallace	5.11	13
17	Eli Manning	5.1	15
18	Jason Campbell	4.9	19
19	Trent Edwards	4.83	17
20	Shaun Hill	4.76	12
21	David Garrard	4.66	20
22	Tyler Thigpen	4.57	27
23	Kyle Orton	4.56	25
24	Dan Orlovsky	4.28	30
25	JaMarcus Russell	4.23	26
26	Joe Flacco	4.17	22
27	Ben Roethlisberger	4.03	24
28	Brett Favre	3.91	21
29	Gus Frerotte	3.83	28
30	Marc Bulger	3.81	31
31	Derek Anderson	3.24	33
32	JT O'Sullivan	3.12	29
33	Ryan Fitzpatrick	2.94	32

Breaking Down the Superbowl.

by Denis O'Regan

With the Superbowl over and every conceivable statistic from the game duly recorded,I though it would be a good time to try to develop a measurement of individual contribution to the game.

I've had an idea about the methodology to use for a couple of seasons,but the appearance on this site of Brian's win probability calculator has made the application much more feasible.

Basically,every point on the field has an average value in terms of the number of points a team can expect to score.Therefore,the point of the snap will be worth say X points and the end of the play will be worth Y.The difference between the two,be it positive or negative will be the 'worth' of the play in terms of increased or decreased expected points.

Passing plays are potentially more interesting than running plays because they can be further broken down into their component parts by taking yards after the catch into account.You could think of the points difference from the point of the snap to the point of the catch being attributed to the passer (with the assistance of the catcher) and those from the point of the catch to the end of the play as belonging to the receiver (with the assistance of the passer).

Overall it's a way of defining individual plays,and therefore individual players contributions to a game in the more readily recognizable currency of game points.It also puts into context plays for big yardage gains on third and long that don't get to the first down marker.

Here's how these calculations look for the two outstanding performers from this month's Superbowl.

Larry Fitzgerald caught 7 passes,his yards after the catch numbers changed the points expectancy for his team by a cumulative 7.7 points.Kurt Warner's contribution on those completions came to a cumulative 3.9 points and incompletions reduced the team's expected points by 0.6.

Combined,the Warner/Fitzgerald duet altered Arizona's points expectation by 11 points.That's 1.4 points per pass attempt.

Pittsburgh's SB MVP Santonio Holmes only combined with Ben Roethlisberger to advance the Steelers expected points by 8 points.Those 8 points were made up from 9.6 yac points,3.1 QB yards points and minus 4.7 points from incompletions and interceptions.Overall Holmes averaged 0.6 points per pass attempt.

Miller contribute a net gain of 3.7 points,Ward 3.1 points,Breaston 4.7 and Boldin(as a result of being the intended recepient of Warner's 100 yard interception return) minus 6.9 points.

Neither side's primary running back contributed positive points to their respective teams points expectation when they ran the ball,although they fared better as pass receivers.

The method can be expanded at look at how whole units perform and looks especially attractive as a way of quantifying the punting unit.

How Teams Try To Win

by Denis O'Regan

One of the more obvious ultimate aims of a NFL team is to score enough points to try to guarantee victory over it's opponents.However,it is equally apparent that at certain times during a game teams have other objectives that take preference over maximizing the score.Running the ball to run out the clock when they already have a large lead,for example.

What follows tries to identify the different stages in a game and tries to pinpoint the tactics used by teams when they are actively trying to score points.

There's a multitude of factors that determine a team's approach during a game,but I'll concentrate on ones I consider most influential.

Firstly,down and distance.These two factors can be reasonably broken down into predominately passing or running plays.To try to eliminate any in built play calling bias as a result of down and distance I decided to look exclusively at 1st and 10 plays.It's not an obvious running or passing down/distance and it also provides a hefty sample size for each team.Everyone gets a first and 10 sooner or later.

Next the current score.It's well documented that teams favour the run when well ahead and the pass when well behind.So I further broke the first and 10 plays down by the current score.I looked at the ratio of runs to passes when teams trailed by 2 or more scores,trailed by 1 score,where tied,led by one score and finally when they led by 2 or more scores.

And lastly I decided to include a teams offensive strength.Even poor offensive teams are likely to be better at running the ball compared to passing it or vice versa.I was simply interested in which offensive skill a team did better at and by how much compared to their weaker discipline.

I firstly compiled a run attempt/pass attempt ratio for all 32 teams from the 2007 season,to confirm that teams favour the run when well ahead and the pass when well behind.

And they do.

On average teams throw around two passes for every one run when they trail by 2 or more scores on 1st and 10.

When down by 1 score the ratio has moved closer to parity,but on average 1.2 throws are still made for every one run.

Running is favoured when teams are tied.1.2 runs for every one pass.

That increases to 1.5 runs to 1 pass if teams lead by a score.

Lead by 2 or more scores and runs start to outweigh passes by almost 3:1.

This progression from throwing when behind to running when in front is mirrored by all 32 teams.

However,this carn't be the whole story.There must be periods of the game where teams are trying to maximize the points they score and they must be trying to do this by a combination of maximizing their yards per play and increasing their chances of continuing drives.It further seems reasonable that they attempt to do this by playing to their offensive strengths.Playcalling when trailing or winning big,seems to be dictate more by the state of the game than a team's offensive strength.So the next step was to see if a team's offensive strength dictated how a team played when the game was close,say within a score either way.

Initially,I chose two teams with widely differing offensive styles.Minnesota ran the ball extremely well and passed it relatively poorly,while the reverse was true for Indianapolis.

If offensive strength did play a part in playcalling as well as the state of the scoreboard,then it seemed likely that as these two teams went from trailing to winning,you would see Minnesota committed earlier to the run (their relative offensive strength) ,while Indy would stay with the pass (their strength) for longer.

And that's what happens.

Minnesota are already running more than they pass when they still trail by 1 score (the league as a whole are still passing more than they run) and Indy are still passing almost as often as the run even when they lead by 1 score (the league as a whole become more frequent runners around when the scores are tied).

Having seen that two teams with polar opposite approaches to offense tend to go to their strengths in close games the last step is to see if there's a general league wide tendency for teams to rely on what they do best.To do this I calculated the strength of the correlation between what a team does best on offense and how often they attempt to do it split by current score.

When the 32 teams trail by 2 or more scores there is no correlation between the two conditions. There appears to be no evidence that teams that run better than they pass run more often in these situations(correlation of 0.01).The same applies to better passing than running teams (correlation of -0.04).It appears that the situation of being 2 scores or more adrift,strongly dictates play calling,everyone has to pass whether it's their most potent attacking force or not and it appears to be a haphazard process.

However,when down by just 1 score teams are able to start to go to their strengths.Teams that pass much better than they run,tend to pass more often than other teams in this situation.When teams trail by a score the correlation between passing well and passing often is 0.35.

The correlation is similar when scores are tied and peaks at 0.47 when teams lead by a score.(Presumably they recognise that one score isn't a decisive lead and they need to press home their advantage and the best way to achieve this is to do what they do best and do it more often than league average).

Once teams lead by 2 or more scores the correlation becomes entirely random again and playcalling mirrors what happens when teams are trailing by 2 scores.Running becomes predominant and teams effectively forget where their strengths lie.Their gameplan is no longer focussed on increasing their score,it's more about shortening the game by keeping the clock running.

The situation for running the ball is identical.The better a team is at running the ball compared to passing it,the more they pound the ball when the scoreboard is within a score either way.Once the lead or deficit becomes larger,they randomly apply the doctrine of pass if you're behind and run if you're ahead and the reasonably strong correlation disappears.

Superbowl Matchups

by Denis O'Regan

Here's a breakdown of the main offensive and defensive stats for Sunday's Superbowl teams.Inevitably the post's heavy on numbers,so a brief summary may be in order.

The most useful and relevant stat to future performance is a team's yards per carry/attempt on offense or defense compared to those of the opponents they've faced throughout the season. A team that gets 4.5 yards per carry and does it over the season against defenses that only allow 4 yards per carry, can confidently be assumed to be above average when it comes to moving the ball on the ground.

These numbers are the first ones quoted in the subsequent post.

The supplementary stats that breakdown the numbers by play direction and field depth merely add colour. Sample sizes on these plays are so much smaller, so any conclusions drawn will inevitably come with a degree of caution.They can,however highlight where a team has had considerable success or major problems during the season.

Matching each team's respective offensive stats against their opponents defensive stats shows areas where each team may be successful or not on Sunday.Judging by the matchups,both teams look like having difficulty moving the ball on the ground.Pittsburgh should pass the ball well,whilst Arizona,despite good passing figures will struggle because they match up badly with Pittsburgh's excellent pass defense.

The primary stats also form the basis for a prediction model that has consistently outperformed the Vegas benchmark over multiple seasons and on this occasion predicts Pittsburgh having a 67% winning chance on Sunday.Various subsets for example using matchups involving playoff calibre teams only increase Arizona's chances by a percentage point or so.So,not surprisingly the game appears to be Pittsurgh's to lose,although Arizona should stay within a touchdown.

The model predicts around 40 points to be scored,but the one off nature of this game can see predictions made to look rather silly very quickly.

Enjoy the game.

Pittsburgh's Run Defense.

Pittsburgh allowed only 3.3 yards per carry through the regular season.Their opponents over that period played a combined 256 games,they made over 7,000 rushing plays and gained a average of 4.12 yards per carry.If we assume that Pittsburgh's opponents opponents represent a broad cross section of the NFL that allows us to put the Steelers raw 3.3 ypc figure into some sort of context.They allow 0.82 ypc less than their opponents habitually gained.

If we further breakdown the Pittsburgh run defense by looking at yards allowed depending on which direction the play was run we find that they excel all the way along the line.

When opponents ran behind their own right end they averaged 5 ypc.When they ran in that direction against Pittsburgh they gained jut 3.4 ypc.

Running behind right tackle opponents gained 4.15 ypc on average,but just 3.28 to Pittsburgh.

Right guard figures were 4.06 ypc overall compared to 3 ypc against Pittsburgh.

Runs up the middle were 4.1 to 3.24 ypc.
Runs to left guard were 4.2 to 3.45 ypc.
Runs behind left tackle were the only direction where opponents did better against Pittsburgh compared to their league average.They gained 4 ypc overall and 4.21 ypc against Pittsburgh.
Opponents averaged 5.3 ypc on runs deignated as left end,but just 3.79 ypc against Pittsburgh.

Arizona's Run Offense.

NFL games are all about matchups and Arizona look like struggling badly if they try to move the ball on the ground.

They gain 3.46 ypc against teams that allowed 4.11 ypc.So already they are gaining just 84% of their opponents average rushing yardage allowed per play.When you match those numbers up against a Pittsburgh run defense that has allowed teams just 80% of their usual yards per carry yardage it begins to look likely that Arizona will struggle to get even 3 yards per carry.

Split by direction the Cardinals are strongest running to their right side.They gain 4.23 ypc against defenses that allow 3.82 ypc when running behind their right guard.They're around average running to right end (gain 4.6 ypc against 4.8 ypc defenses),but tail off at right tackle (gain 3.8ypc against 4.32 ypc defenses).

Running up the middle is a real struggle ( gain 2.6 ypc against 4.14 ypc defenses),as is left guard (2.44 ypc verses 3.72 ypc).There's an improved,but still below average effort behind left tackle (gain 4 ypc against 4.25 ypc defenses) and they're around league average when stretching it out to the left end (5.06 ypc against 5.07 ypc defense).

Arizona's Run Defense.

Overall Arizona allow teams that average 4.34 ypc overall to get just 3.96 ypc.So they're good,but not in the same league as the Steelers.They are also patchy along the line.

Teams running behind their own right end gain 5.76 ypc against Arizona compared to an overall,combined season long figure of just 5.1 ypc.
Behind right tackle they gain just 2.33 ypc against Arizona compared to 4.49 ypc overall.
Behind right guard they gain 4.23 ypc against Arizona compared to 4.11 ypc.
Up the middle they gain 4.4 ypc against Arizona compared to 4.5 ypc.
Behind left guard they gain 5.2ypc against Arizona compared to 3.93 ypc.
Behind left tackle they gain 4.02 ypc against Arizona compared to 4.42 ypc.
Behind left end opponents gain 5.3ypc against Arizona compared to 5.3 ypc overall.

So unlike Pittsburgh's run defense which is virtually bombproof where ever you try to attack it,Arizona does have areas of vulnerability that doesn't show up in the fairly impressive average yards per carry number.

Pittsburgh's Run Offense.

Overall Pittsburgh gain 3.68 yards per carry against opponents who allow on average 4.03 ypc.That makes them below average,but not to the same extent as Arizona.They're struggle most running the ball up the middle,but progressively improve when running out towards the edges and are actually above average when running in the direction of left end.

Running behind right end they gain 4.27 ypc against defenses who allow 4.8 ypc.
Behind right tackle they gain 3.62 ypc against 4.03 defenses.
Behind right guard they gain 3.84 ypc against 4.24 ypc defenses.
Up the middle they gain 3.2 ypc against 3.73 ypc defenses.
Behind left guard they gain 3.34 ypc against 4 0 ypc defenses.
Behind left tackle they gain 3.84 ypc against 3.92 ypc defenses.
Behind left end they gain 5.97 ypc against 5.15 ypc defenses.

Again we have a below average running attack matched up with an above averge run defense,however Pittsburgh should be able to run the ball better than Arizona on the day.We've already seen that there are areas of weakness in the Arizona defensive line that can be exploited.Around 3.5 ypc looks a reasonable upside for the Steelers on Sunday.

Now for the aerial matchups.

Pittsburgh's pass Defense.

The Steelers are a very,very good pass defense.They allow teams who averaged 6.18 yards per pass attempt to only pass for 4.6 yards per attempt.Those are exceptional figures.

I further break these numbers down by looking at which areas of the field are best defended.Passes that are caught within twenty yards of the line of scrimmage are designed as short,anything longer is deep.Passes are further split as being caught to the right side of the field from the offenses viewpoint,middle or left.Again a team's raw yards per attempt figure is compared to the average ypa allowed or gained by their seasonal opponents when defending or attacking these same areas.

As with their run defense,the Steelers do not have to hide any of their players and they defend all parts of the field equally well.

They allow 4.9ypa on short left passes against teams who average 6.11ypa over the season.
They allow 5.4 ypa on short middle passes against teams who average 6.32 ypa.
They allow 4.8 ypa on short right passes against teams who average 5.39ypa.

Deeper passes are defended even better.

They allow 6.87 ypa on deep left passes against teams who average 10.24 ypa.
They allow 9.38 ypa on deep middle passes against teams who average 11.44 ypa.
They allow 8.71 ypa on deep right passes against teams who average 9.94 ypa.

Well above average right across the board.

Arizona's pass Offense.

The Cardinals pass the ball very well,they gain 7.38 ypa against defenses who allow just 6.54 ypa.However,that still compares unfavourably with the Pittsburgh defense.Overall Pittsburgh's pass defense allows 1.6 ypa less than their opponents gain over the season,whilst Arizona only gain 0.8 ypa more than their opponents allow.That still gives Pittsburgh's pass defense the upper hand by a fairly large margin.

Broken down by field position.

Arizona gain 6.52 ypa on short left passes against defenses who allow 5.94 ypa.
They gain 6.34 ypa on short midde passes against defenses who allow 6.8 ypa.
They gain 5.68 ypa on short right passes against defenses who allow 5.43 ypa.

These short passes match up particularly badly for Arizona against Pittsburgh's short range passing defense.If they are going to have any success aerially it's going to come on the deep ball where they potentially have the upper hand when throwing deep middle and deep right.But these are high risk/high reward plays.

Arizona gain 13.5 ypa on deep left passes against defenses who allow 11.24 ypa.
They gain 22.4 ypa on deep middle passes against defenses who allow 13.39 ypa.
They gain 17.07 ypa on deep right passes against defenses who allow 11.64 ypa.

These are great figures,but bear in mind in a normal game plan the Cardinals will only be throwing around half a dozen such passes.That will make the yardage susceptible to small sample errors and also limit their impact on the game compared to the more numerous shorter passes.

Arizona's pass Defense.

Arizona's pass defense is almost as bad as their passing offense is good.They allow team's who average 6.29 ypa to get 6.77 ypa when they play Arizona.

They allow 7.83 ypa on short left passes against teams who average 6.01ypa over the season.
They allow 7.38 ypa on short middle passes against teams who average 6.79 ypa.
They allow 5.09 ypa on short right passes against teams who average 5.38ypa.

They're above average defending short right passes,but well below par elsewhere.

They allow 12.19 ypa on deep left passes against teams who average 10.91 ypa.
They allow 12.1 ypa on deep middle passes against teams who average 12.6 ypa.
They allow 7.99 ypa on deep right passes against teams who average 9.84 ypa.

Pittsburgh's pass Offense.

The Steelers are marginally above average passing the ball.They gain 6.48 ypa against defenses who allow 6.31 ypa.The bulk of their gains come when they're connecting with short passes and they match up well against Arizona's pass defense in this area.They project to have success where ever they throw the ball short and in a game that could see offenses struggling this will be the key area.

They gain 5.41 ypa on short left passes against defenses who allow 5.67 ypa.
They gain 7.80 ypa on short midde passes against defenses who allow 6.53 ypa.
They gain 6.26 ypa on short right passes against defenses who allow 5.38 ypa.

Pittsburgh gain 10.8 ypa on deep left passes against defenses who allow 11.34 ypa.
They gain 10.45 ypa on deep middle passes against defenses who allow 12.29 ypa.
They gain 11.40 ypa on deep right passes against defenses who allow 10.91 ypa.

Even though Arizona passes the ball better than Pittsburgh the offensive/defensive matchups make it likely that it will be Pittsburgh will have greater success through the air on Sunday.

Super Bowl XLIII- Some Food for Statistical Thought

by Josh Fryman

Instead of draw up an entire thesis or go into a detailed analysis of Sunday’s Super matchup, I decided to take the lazy way out. Below are four statistical insights that may shed some light on what will unfold in Super Bowl XLIII.

1. Blitz Kurt Warner at your own risk- Warner had a very impressive QB rating of 96.9 during the regular season, but in blitz situations, his rating rose to 103.8. Blitzes are gambles, and it is normal to expect a QB’s rating to increase in such situations, but Warner’s rating in these situations is quite high. This year, the Cardinals faced 197 blitzes on pass plays, so for some reason, teams seem to believe that the Cardinals offense is susceptible to them. Not a good idea. Not only does Warner’s QB rating improve, but when blitzed, his yards per attempt increase to 7.86.

A lot of Warner’s success comes from his quick release, but the plethora of options is a tremendous factor, as well. In the playoffs, the Cardinals have moved Larry Fitzgerald onto both sides of the field and also into the slot, which gives Warner his favorite target anywhere he wants him in case of a secondary mismatch. Much speculation has said that the Steelers will blitz a lot in order to diminish Warner’s opportunity to throw to his deep targets.

2. There’s a Hole in the Pittsburgh O-Line- And it’s at the center and left guard positions. Justin Hartwig and Chris Kemeoatu have not been doing Ben Roethlisberger many favors this year. Whereas most quarterbacks improve their passer rating during blitzes, Roethlisberger’s dropped this year from 80.3 in normal situations to 70.3 in blitzes. Considering that the average quarterback improves 5.6 ratings points with a standard deviation of 4.4, Roethlisberger’s drop during blitzes is alarming. When you watch the film, you see that teams send blitzing defenders primarily into the gap between Hartwig and Kemeoatu. As if allowing sacks weren’t enough, Steeler’s running backs’ yards per carry drop from 3.7 overall to 3.3 when running through the left side of the offensive line.

3. The Arizona DB’s can be exploited- A lot has been made of the breakout performances of Antrel Rolle and Dominique Rogers-Cromartie this postseason, especially given some of the interceptions that the secondary has come up with. Don’t be fooled by interceptions. As discussed before on this site and at my own blog, takeaways have as much to do with chance and rely far more on an offense’s propensity to make turnovers as it is on a defense’s ability to create them.

Furthermore, when one looks beyond the takeaways, one will see that wide receivers have had field days against Arizona of late. In the postseason alone, DeSean Jackson, Muhsin Muhammed, and Roddy White all had better statistical days (receptions, yards) than was the average for the season. Only Steve Smith had a subpar performance. During their current 4-game win streak, the Cardinals have allowed 275.5 yards passing per game. Super Bowl XL MVP Hines Ward should be licking his chops.

4. Big Ben will need to get into the shotgun- Aside from the O-Line woes, Roethlisberger has turnover problems in the form of both fumbles and interceptions. Furthermore, possibly the best linebacker in the Super Bowl will be lining up for Arizona. Karlos Dansby finished the season with 119 tackles and 9 stuffs behind the line. When the quarterback is under center with only a lone back, Dansby’s tackles per play nearly double. Furthermore, Arizona has registered 7 sacks and 9 stuffs in the postseason so far. Without a serious deep threat, Pittsburgh cannot afford to leave two men in the backfield to guard against these threats. Big Ben, however, cannot be trusted under center against a reinvigorated pass rush. Therefore, the gun may be the best call.

Scoring environment

Recently, Brian has made his win probability (WinEx) calculator available for all to use. This is a really powerful toy, and I plan on using it for some stuff I'll post about later. For now, however, I want to point out a flaw.

One of the first things one notices when looking at NFL stats is that they lack context. How valuable is a 3 yard run? Is it a three yard run on third and two? Is it from the 2 yard line, when down by 6 with 20 seconds left? Is it in the middle of the field, as time expires, down by 27? Obviously, context is important. It only gets worse as the stats get bigger. How valuable is a 1000 yard rushing season? Well, if that's 15 rushes with 13 touchdowns, it's the best season by anyone, ever (and the question is "why did he not get more touches?"). If it's 400 rushes with 2 TDs, the question is "why is he not on the practice squad?" It's all about context -- in this case, the context of the event: what were you trying to achieve?

This extends further, however. How good is throwing for 6000 yards in a season? Well, it'd set a lot of records. Unless, of course, defensive players are on strike and teams are running amateurs out there every weekend, causing 12 quarterbacks to throw for 6000 yards. How about scoring 200 points across the regular season? Kinda crap...unless you have the best defense of the last decade, and are 14-2 when the dust settles. Again, it's all about context -- this time about the context of the achievement: how did everyone else do?

WinEx calculations are an attempt to solve the first series of questions I posed. The second is a little trickier. How does the system know that being up by 12 with 5 minutes left is good? Because those teams usually win. Note, however, that this is "those teams," not that team. In this case, the league scoring context is being used to determine how often teams tend to score.

The question is, is there another context each game is played in? I wouldn't have written all this unless the answer is "yes," of course. There are actually a couple different contexts: team-level and game-level.

A team-level context is simply which teams are playing. Let's say the Steelers and Raiders are playing. Just before the opening kick-off, you're asked who's going to win. If you're looking at things in the "NFL" context, it's 50/50. But if you know who the teams are, it's certainly not. This becomes less and less true over the course of a game -- if the Raiders are up by 14 with 20 seconds left, they've probably won, whether or not they're the Raiders -- but before the opening kickoff, it is not "anybody's ballgame".

There's another context which is important for calculating WinEx, though, and that's game context. Let's say your team is up by 10 with 8 minutes remaining. That's a pretty good lead, right? Well, if it's a 13-3 game, it's a VERY good lead -- if their poor opponents couldn't muster more than a field goal in 52 minutes, they're unlikely to close a 10 point gap now. On the other hand, if it's a 42-32 shoot-out, it's still anybody's ballgame -- the hometown heros haven't stopped them yet, and they're unlikely to start now. One piece of good fortune on an onside kick, and you could be drinking away the evening, trying to forget how the WinEx calculator told you the game was in the bag.

I know that Brian's WinEx calculator doesn't take these things into account -- it doesn't ask what teams are playing, and it asks for score differential, not current scores. It may never take them into account, and that won't stop it from being a useful tool. But there's more to think about when analyzing in-game scenarios: that 3 yard rush is meaningless without context.

In running model for the NFL.

by Denis O'Regan

(Before I start this can I just say that Brian's online "in running" calculator is a fantastic bit of kit and I want to thank him for making it available to everyone.My approach is going to be different to Brian's.....my calculator wouldn't know a first down if it got blindsided by one.....)

Modeling in running soccer matches is a relatively easy undertaking and usually involves estimating in game scoring rates for both teams and using these averages to calculate the probability of individual scoring events occurring in the remainder of the game by way of the Poisson distribution.

I decided to try to apply the approach to the NFL by following the methods I use for soccer games and trying to work around problems caused by the differences of the two sports when they arose.

At first glance American football is a much higher scoring sport than soccer.The average total goals in a soccer game hovers somewhere around 2.7 goals compared to 40 points in gridiron.However,the 40 NFL points are scored as a result of only 8 or 9 scoring events broken down as touchdowns,field goals with the odd safety thrown in.

Therefore I used scoring events instead of points to create a scoring expectancy for the NFL teams. For example,Team A's offense averages A scoring events per game in a league where the league average is L scoring events per game.They play Team B,whose defense allows B scoring events per game.It should be possible to work out how many scoring events Team A should be able to manage on average when they host Team B.

Team A scores at A/L times the league average.
Team B concedes at B/L times the league average.

Multiply these two rates together gives you a good idea of the scoring rate Team A will achieve against Team B's defense at a neutral venue.If we want to make Team A the home side we further need to divide the average scoring rate of all home teams (call this H) by the league average and incorporate this.

The scoring rate for Team A at home to Team B can be calculated as

Team A = A/L * B/L * H/L

Lastly,to convert this scoring rate to actual scoring events we multiply this rate by the league's average scoring events per game,namely L.

If we repeat this process for Team B,using the average scoring rate for away sides this time,we now have a scoring expectancy for each team.If you'd gone through this process for the NFC Championship game,you would have had Philly in for just over 5 scoring events and Arizona in for just over 4.

Armed with these team averages we can now use the Poisson distribution to calculate the probability that each team will achieve exactly zero scoring events,1,2,3 etc.
That further allows us to calculate the probability that,for example the game will end with Team A scoring twice and Team B scoring just once...and here's where the problems start.

In soccer winning 2-1 is definitive,you win the game,in the NFL it merely gives you a very good chance to win the game.Even if we throw out safeties as a rarity and assume all touchdowns are single point conversions,you can still score two field goals and lose to one touchdown.Whereas in soccer you could safely add the probability of a team winning the whole game 2-1 to it's overall win probability you have to keep some back in the NFL.

Breaking down the 2-1 scoring events into different combinations of TDs and FGs quickly become unwieldy if you include 2 point conversions,safeties,missed extra points,as do more common,higher scoring combinations.So I've tried various fudges.These include,do nothing (what you gain in terms of win probability on the 2-1 you lose when it comes to a 1-2 scoreline) to incorporating a points per score factor and using real life data based on scoring events.

Putting aside these problems for a moment,we do now have a way to attach a probability to every scoring event combination from say 0-0 all the way to 12-12.Which should cover most eventualities in the NFL.

So far all we've got is a clunky pre match predictor.To turn it into a serviceable "in play" predictor we need firstly to predict how each team's pre game scoring expectancy decays with time.Again soccer is quite easy.Scoring rate increases as the game goes on and you can calculate a team's remaining goal expectancy by multiplying the pre game number by the proportion of time remaining raised to the power of 0.84.The NFL also looks straightforward.After an initial lull due to kick off field position,the scoring rate remains relatively steady,until peaking inside each two minute warning.
For example 10 minutes into a game a team will still have 88% of it's pregame scoring expectancy "left".By half time it's declined so that only 47% remains.

We can now see what each team's pre game scoring expectation has decayed to at any point in a game.By entering these revised numbers into a Poisson calculation we can calculate scoring event combinations and their probabilities for the remainder of any game.Together with the current score and the average points per score for each team,this is valuable information as to determining the final outcome of the game.

A team that currently leads by 7 can now be assured of winning if they "win" the remaining mini match 2 scores to one.So for this particular combination of current score and predicted outcome the team can be assigned the full probability.Other combinations still require "interpretation".

Here's the current version in action.I've stuck to win probability updates after each score,firstly to keep it brief,but also to avoid the need to add much of an additional field position correction.

I've also added the in running probabilities from a UK betting site for comparison.

Philly@ Arizona.

Pre game Philly were favoured at most places by about 4 points.To make Arizona the favourites I think you had to take a very positive view about their home field advantage.The in running model favoured Philly pre game.I'll list the win probability of the current favourite and suffix it with a letter to denote who that fav was.

Score (Philly first) Model UK betting site.
Pre game 60%(P) 62%(P)
0-7 53%(A) 54%(A)
3-7 51%(A) 53%(A)
3-14 72%(A) 67%(A)
6-14 60%(A) 62%(A)
6-21 79%(A) 80%(A)
6-24 91%(A) 87%(A)
13-24 89%(A) 87%(A)
19-24 67%(A) 65%(A)
25-24 69%(P) 62%(P)
25-32 93%(A) 85%(A).

and now for Baltimore@Pittsburgh.

Pregame the UK were very bullish about Pittsburgh's chances and they were favoured by around 6 points.The model also favoured the Steelers,but only by about 4.5 points.

Score (Balti first) Model UK betting site.
Pre game 65%(P) 69%(P)
0-3 74%(P) 73%(P)
0-6 81%(P) 78%(P)
0-13 95%(P) 89%(P)
7-13 83%(P) 81%(P)
7-16 93%(P) 89%(P)
14-16 74%(P) 77%(P)
14-23 99%(P) 98%(P).

The fascinating game for me is the Ravens/Steelers one.Despite getting within 2 points,once the scoring started,the Ravens were still only a 26% chance to win immediately after that score.One of the strengths of this type of model is that it takes your pre game,long-term opinion of each team and sticks with it regardless.By the time they made it 14-16 just ten minutes remained.Baltimore's pre game scoring expectation had decayed to around half a score,Pittsburgh's was about a tenth higher.Plugging these new expectations into a Poisson you find that the chances of Baltimore scoring and Pittsbugh not in what remained of the game was around 17%.Both teams scoring once each was about a 20% chance,but most "one score each" permutations still gave the Steelers an overall win.Most betting men seemed to agree that,despite the closeness of the scores,Pittsburgh were still big favourites .....although I'll bet both sets of fans didn't feel quite so sure.

A Scoring Efficiency Model v.2

By Cyril Smith

Last week I described a simple scoring efficiency model based on points per minute. As is not unusual in the financial modeling world it promptly went 0 for 4 on the divisional playoff round games. Other models - the Las Vegas line for example - were better in getting at least one game right.
In reviewing the model (which itself was based on data from the 2005-07 regular season and playoff games) it seemed that the weak point was the assumption that each team was roughly equal and that its scoring potential was based on 30 minutes of possession. While this approach had worked reasonably well on past data as well as the wild card round, it did not perform well in the divisional round. There is in fact a great deal of volatility in each team's points per minute and time of possession - volatility which is obscured by using averages. I therefore looked for a way to incorporate this volatility into the model.

At first blush it is apparent that volatility is inversely related to wins. Teams that showed greater volatility in points per minute and time of possession tended to do worse in results. A reasonable hypothesis is that volatility represents weaknesses which a team may not be able to overcome in the playoffs because the opposing team will zero in on those weaknesses. According I took a first cut at combining volatility of points per minute and time of possession, in each case measured by the standard deviation of the series, into the model. The preliminary results look promising. Using the additional input resulted in two changes for the divisional round: Pittsburgh was now favored over San Diego and Baltimore over Tennessee.

Looking ahead the revised model has Philadelphia over Arizona by a point and Pittsburgh over Baltimore by 4 points.

Punting and Field Goals

by Dean Jens

Field Goals

One of the things I often wondered before discovering The Football Project was how the probability of a kicker making a field goal varied as a function of distance. After eyeballing the distributions for a few kickers for the 2005 season, I figured I could try raising a logistic function to some power. For the first several kickers I tried, I found that that power was statistically indistinguishable from 1, so I set about fitting the probabilities to a simple logistic function, i.e. (1/2)(1+tanh((m-x)/w)).†

I had imagined, in the absence of data, that w might be independent of the kicker, and that kickers could be characterized by m, i.e. how far away they are when their percentages drop. This is not the case; w depends on the kicker, with larger values to kickers who tend to miss easy ones and make longer ones, with lower values to more consistent kickers. Olindo Mare missed a few short ones, so his percentages didn't drop off very quickly. Matt Bryant actually had a slight improvement as distances got longer; this would surely change if more statistics were taken at a normal range of distances. On the other hand, John Kasay had a much higher tendency to hit field goals shorter than 50 than if they were longer than 50; of the 8 he missed, the shortest was 42 (he made 24 shorter than that). Jeff Reed had an even sharper drop around 45 yards, missing nothing shorter than 41 and making nothing longer than 47. While I was unable to fairly characterize the best kicker in terms of a drop-off length, I was able to generate a different metric that adjusts for length. By using my logistic fits, I predicted the percentage of field goals a kicker would make if they kicked from a given distance; I then took the 1006 field goal attempts for the season and calculated the percentage of those 1006 field goals that each kicker would have made. I've only included those kickers who attempted more than 4 kicks; the kickers who were dropped were all notably worse than the ones listed.

kicker	normalized score	percentage	number of kicks
racken001	0.963	0.952	42
nednej001	0.917	0.9	30
wilkij001	0.889	0.871	31
dawsop001	0.889	0.933	30
kaedin001	0.866	0.875	24
kasayj001	0.86	0.805	41
vandem003	0.857	0.889	27
stovem001	0.851	0.882	34
grahas002	0.837	0.879	33
hansoj001	0.836	0.792	24
bryanm001	0.836	0.846	26
bironr001	0.835	0.793	29
feelyj001	0.832	0.833	42
linder001	0.819	0.829	35
mareo001	0.815	0.833	30
hallj006	0.81	0.824	17
elamj001	0.806	0.771	35
tynesl001	0.803	0.818	33
akersd001	0.802	0.727	22
brownj018	0.796	0.697	33
petert005	0.794	0.885	26
reedj005	0.785	0.844	32
nugenm001	0.773	0.786	28
vinata001	0.773	0.786	28
carnej001	0.762	0.781	32
longwr001	0.751	0.741	27
gouldr001	0.749	0.786	28
brownk008	0.745	0.765	34
scobej001	0.743	0.75	32
edingp001	0.736	0.735	34
janiks001	0.704	0.667	30
franct001	0.686	0.778	9
cortej002	0.671	0.706	17
novakn001	0.608	0.8	10
cundib001	0.541	0.556	9

This obviously does not adjust for wind, and the linemen on both the kicking and defending sides will have some influence on these statistics, but this at least tells which unit is doing better than which other with the confounding variable of distance removed. The average length for a field goal attempt was 36.3 yards; the average for Nick Novak was 33.7, while for Josh Brown it was 41.2. Accordingly the "scores" for these kickers find themselves lower and higher, respectively, than the raw percentage. The scores and the actual percentages have a corelation of 0.8. The means and variances are very similar, though the variance of the raw percentages is a little bit smaller; while the difference isn't statistically significant*, it is what would be expected from coaches deciding to attempt longer field goals with better kickers, and punting or going for the first down with worse kickers. Perhaps looking at all fourth down plays from around the thirty yard line would be a good step for further research.

† This isn't a least-squares fit; I try to maximize the sum of the logarithm of the fitted probability of the actual outcome: for kicks that the kicker makes, P is the fitted probability that the kicker would make the kick, while for those the kicker missed (or were blocked or whatever), it is the fitted probability that the kicker would miss the kick.

* It would be significant at the 25% confidence level on a two-tailed test; arguably a one-tailed test could be used here, but even that isn't going to pass a common significance test. When a team prepares to punt, the punter's statistics are often cited, typically the average length of his punts and the number of times he has left teams behind their own 20 yard line. These seem like kind of strange statistics to me; if I were to take the line of scrimmage and the end position of the ball and plot one against the other, what I would likely expect to see, as a first approximation, would be a 45 degree line† up to a point, and then a horizontal line from there on out. Behind a certain point on the field, a punter would be expected to net a certain length; ahead of that, he would be expected to average a certain level of field position. Grabbing every punt the Packers made that year, I found that the break-point from a least squares fit was very near midfield. Accordingly, it seems to me we ought to characterize the net length of punts from one's own half of the field, and the average final field position for punts from the fifty yard line and beyond.

Punting

Taking the data from The Football Project for 2005, I calculated these statistics for each player who punted. Every player who punted more than twice had at least one punt from each half of the field, so the figures for them are well defined. Remember, the "length" is only calculated for those punts from the punter's own end of the field; the "depth", the name of which is probably more poetically than logically motivated, is the average ensuing field position of the receiving team after punts from the fifty and beyond. I use results net of the return, though using results before the return leaves a lot of what follows more or less unchanged. The players are ordered by length-depth/4, due to the fact that about 4/5 of punts originated from the punting team's side of the fifty.

punter	length	depth	number of punts
moormb001	41.51	13.85	74
jonesd018	41.04	13.35	88
johnsd022	39.78	10.5	42
bergem001	39.69	10.88	75
sauert001	39.38	11.05	83
grahab001	38.84	9.82	75
scifrm001	39.76	14	74
bakerj001	39.55	14.18	88
hentrc001	39.48	14.22	79
mcbrim001	39.16	13.09	85
bidwej001	39.45	15.68	97
hansoc001	38.72	14.52	92
koenem001	38.8	14.84	78
feaglj001	38.02	13.35	78
frostd001	38.21	14.71	91
grooma001	38.89	17.67	12
playes001	36.95	10.5	76
colqud001	37.8	14.14	66
harrin002	36.05	9.71	89
landes001	38.41	20	34
edingp001	35	7	2
maynab001	37.78	18.48	106
leea003	36.44	13.11	110
barkeb001	36.7	14.27	51
gardoc001	36.48	13.95	86
aragul001	37.08	16.4	18
lechls001	36.18	13.08	84
smithh009	35.28	11.08	59
larsok002	36.47	17.73	66
stanlc002	34.81	11.5	79
benned001	34.57	11	8
millej012	36.46	19.1	88
kluwec001	35.21	14.43	75
richak003	34.81	13.17	81
rouent001	34.96	14	76
murphn001	33.5	15	7
sandeb002	33.37	15.4	64
hodger001	32.31	13.92	44
flinnr001	31	23	6
brownj018	NA	11.5	2
cundib001	NA	20	1
dawsop001	NA	6.5	2
ellina001	NA	2	1
gouldr001	NA	24	1
kasayj001	NA	20	1
mareo001	NA	27	1
nugenm001	NA	17	1
roethb001	NA	10.5	2
vinata001	NA	4	1
wilkij001	NA	20	1

Number one is Brian Moorman, of the Buffalo Bills; second is Donnie Jones. They are the only two punters to average more than 40 net yards from their own end of the field; of punters who punted more than twice, the two who left the ball inside the ten yard line when they punted from midfield or closer were Ben Graham, who had pretty good length as well, and Nick Harris, whose length was more mediocre.

Adding the length and depth for each player with more than two punts, I get a surprisingly narrow distribution. It is centered around 51.4 or 51.5 — 50.5 would be ideal for the use of these statistics — and has a standard deviation of only 3.5 yards. Most punters, then, seem to punt for distance behind their own 49 or so, and for field position beyond there. If I exclude Ryan Flinn, who had six punts (the fewest among those with more than two) for the worst result in both statistics (among those with more than two punts), the correlation between length and depth is 0 to two decimals.* Accordingly, a punter with better length will tend to be affected by the endzone further into his own territory, while a punter who is particularly good at pinning the opposing team against its goal line is more likely to still be punting for length a bit beyond the fifty; there is no unambiguous connection, independent of one's measure of "skill", between a punter's "breakpoint" and the skill of the punter.

It won't come as a great surprise that the length as I measure it and the average length of all punts has a correlation greater than 0.9. It might not be a big surprise either that the percentage of punts to end up inside the twenty has a correlation of -0.4 with "depth", but, interestingly, either length measurement has a correlation of 0.4 with the inside-the-twenty statistic. From a linear regression standpoint, it looks as though the inside-the-twenty statistic is including some length information; 1/3 of the variance can be explained from the two numbers in my table. The median punt to end up inside the 20 starts from 2 yards behind midfield, but 20% come from behind the punter's own 40; some of what is being recorded in that figure is not any deftness in terms of avoiding the touchback or letting one's teammates get downfield, but is simply the ability to kick to the red zone from farther away. This is a nice skill, of course, but it is fully incorporated into the length statistic; the frequency of leaving a punt inside the twenty is a hybrid of skills, and is not the best measure for any of them.

† There is some attempt here to keep the statistics simple. In fact, this line is slightly flatter than 45 degrees because the endpoint is bounded both above and below; punts from behind midfield give a slope of 0.95 that is statistically distinct from 1 at the 5% confidence level.

* This actually is less true without the return; punters who punt the ball farther before the return also tend to punt it closer to the endzone, but not dramatically so. The distribution of punters' depth+length is similar to the results with the return, with several yards simply moved from depth to length.