Saturday, 29 January 2011

Air Yard Adjusted Completions by Season.

In an earlier post on quarterback completions I introduced a correction which allowed for the average distance each quarterback threw the ball through the air.I used cumulative figures from the last five sasons to determine the most accurate QB over that period,in this post I've looked at individual seasons for each QB.As before the QB whose Completion Rate Above Baseline is the greatest is deemed to be the most accurate thrower over a single season.

Drew Brees wins with his Superbowl winnng 2009 season,his 70.6% conventional completion rate was a standout performance on it's own.His average air yards per attempt of 8.3 yards would have seen a regular,good QB completing something in the region of 64% of his passes,so to crack 70% was truely outstanding.Romo's 2006 was just as remarkable,he threw for over 10 air yards per attempt meaning a completion rate of 59% would have been considered par for a top QB.He hit 65.3% and all this in his first season.

Peyton Manning seasons heavily populate the top ten,confirming him the best and most consistent over the five season period.

Year CRAB Rank

Drew Brees
2009 6.7 1

Tony Romo
2006 6.7 2

Peyton Manning
2009 6.1 3

Tom Brady
2007 6.0 4
Ben Roethlisberger 2007 5.6 5

Philip Rivers
2009 5.3 6
Peyton Manning 2006 5.0 7
Ben Roethlisberger 2009 4.7 8
Aaron Rodgers 2010 4.5 9

Brett Favre
2009 4.1 10
Peyton Manning 2008 4.1 11
Peyton Manning 2007 3.8 12
Chad  Pennington 2008 3.7 13
Carson Palmer 2007 3.6 14
Peyton Manning 2010 3.5 15
Aaron Rodgers 2009 3.3 16
Philip Rivers 2008 3.2 17
Carson Palmer 2006 3.0 18
Drew Brees 2010 2.9 19
Chad  Pennington 2007 2.8 20

Tony Romo
2010 2.8 21
David Garrard 2007 2.7 22
Philip Rivers 2010 2.7 23
Tom Brady 2009 2.7 24
Matt Schaub 2007 2.5 25
Matt Schaub 2009 2.5 26
Tony Romo 2007 2.2 27
Aaron Rodgers 2008 2.0 28
Michael Vick 2010 1.9 29
Ben Roethlisberger 2010 1.6 30
Eli Manning 2010 1.5 31
David Garrard 2010 1.5 32
Brett Favre 2007 1.2 33
Marc Bulger 2006 1.2 34
Jon Kitna 2007 1.1 35
Sage Rosenfels 2007 1.1 36
Tom Brady 2010 0.9 37
Jay Cutler 2008 0.7 38
Drew Brees 2008 0.6 39
Vince Young 2007 0.6 40
Kurt Warner 2009 0.5 41
Brett Favre 2008 0.5 42
JP Losman 2006 0.4 43
Joe Flacco 2009 0.4 44
Joe Flacco 2010 0.3 45
Kurt Warner 2008 0.3 46
Tony Romo 2008 0.3 47
Drew Brees 2007 0.2 48
Eli Manning 2009 0.1 49
Matt Schaub 2008 0,1 50
Jay Cutler 2007 0 51
Kyle Boller 2007 0 52
Philip Rivers 2006 -0.1 53
Matt Ryan 2008 -0.3 54
David Garrard 2008 -0.3 55
Jon Kitna 2006 -0.3 56
David Garrard 2006 -0.4 57
Jay Cutler 2010 -0.7 58
Jake Delhomme 2008 -0.8 59
Kurt Warner 2007 -0.8 60
Jeff Garcia 2008 -1.0 61
Josh Freeman 2010 -1.1 62
Trent Edwards 2008 -1.2 63
Matt Ryan 2010 -1.2 64
Ben Roethlisberger 2006 -1.3 65
Matt Hasselbeck 2007 -1.3 66
Shaun Hill 2008 -1.4 67
Eli Manning 2008 -1.6 68
Ben Roethlisberger 2008 -1.6 69
Damon Huard 2007 -1.6 70
Vince Young 2009 -1.8 71
Chad Pennington 2006 -1.8 72
Jeff Garcia 2007 -1.9 73
Charlie Frye 2006 -2.0 74
Donovan McNabb 2009 -2.0 75
Carson Palmer 2010 -2.0 76
Michael Vick 2006 -2.1 77
Tarvaris Jackson 2007 -2.1 78
Joe Flacco 2008 -2.2 79
Matt Hasselbeck 2006 -2.2 80
Tony Romo 2009 -2.3 81
Chad Henne 2010 -2.4 82
Tom Brady 2006 -2.6 83
Jason Campbell 2007 -2.6 84
Dan Orlovsky 2008 -2.6 85
Brett Favre 2010 -2.6 86
Matt Cassel 2008 -2.6 87
David Garrard 2009 -2.7 88
Donovan McNabb 2008 -2.8 89
Philip Rivers 2007 -2.8 90
Chad Henne 2009 -2.8 91
Matt Hasselbeck 2010 -2.9 92
Kyle Orton 2010 -2.9 93
Jon Kitna 2010 -2.9 94
Carson Palmer 2009 -2.9 95
Matt Schaub 2010 -3.0 96
Steve McNair 2006 -3.1 97
Drew Brees 2006 -3.1 98
David Carr 2006 -3.1 99
Damon Huard 2006 -3.1 100
Marc Bulger 2007 -3.2 101
Brad Johnson 2006 -3.2 102
Kerry Collins 2010 -3.3 103
Jason Campbell 2009 -3.6 104
Jake Delhomme 2006 -3.7 105
Jay Cutler 2009 -3.7 106
Donovan McNabb 2007 -3.8 107
Donovan McNabb 2006 -3.8 108
Ryan Fitzpatrick 2010 -4.1 109
Matt Cassel 2010 -4.3 110
Kerry Collins 2008 -4.3 111
Ryan Fitzpatrick 2009 -4.5 112
Brian Griese 2007 -4.6 113
Jason Campbell 2010 -4.7 114
Kyle Orton 2009 -4.9 115
Donovan McNabb 2010 -5.0 116
Gus Frerotte 2008 -5.0 117
Matt Ryan 2009 -5.1 118
Jake Delhomme 2009 -5.2 119
Jason Campbell 2008 -5.6 120
Eli Manning 2006 -5.6 121
Mark Brunell 2006 -5.6 122
Jake Plummer 2006 -5.6 123
Shaun Hill 2010 -5.7 124
Kyle Orton 2008 -5.8 125
Andrew Walter 2006 -5.8 126
JaMarcus Russell 2008 -5.9 127
Joey Harrington 2007 -6.1 128
Mark Bulger 2008 -6.1 129
Seneca Wallace 2008 -6.2 130
Ryan Fitzpatrick 2008 -6.4 131
Eli Manning 2007 -6.6 132
Brett Favre 2006 -6.6 133
Derek Anderson 2007 -6.8 134
Alex  Smith 2009 -6.9 135
Josh Freeman 2009 -7.0 136
Mark Sanchez 2009 -7.0 137
Alex Smith 2006 -7.0 138
Mark Sanchez 2010 -7.1 139
Matt Leinart 2006 -7.2 140
Rex Grossman 2006 -7.3 141
Alex Smith 2010 -7.4 142
Matt Hasselbeck 2009 -7.4 143
Tyler Thigpen 2008 -7.5 144
Derek Anderson 2010 -7.6 145
Rex Grossman 2007 -7.7 146
Vince Young 2006 -7.7 147
Cleo Lemon 2007 -8.1 148
Sam Bradford 2010 -8.2 149
Joey Harrington 2006 -8.3 150
Marc Bulger 2009 -8.5 151
Matt Cassel 2009 -8.9 152
Bady Quinn 2009 -9.7 153
Brodie Croyle 2007 -10.1 154
JaMarcus Russell 2009 -10.3 155
Kellen Clemens 2007 -10.5 156
Trent Edwards 2007 -10.8 157
Matt Stafford 2009 -11.1 158
Derek Anderson 2008 -13.1 159
Bruce Gradkowski 2006 -13.5 160
Jimmy Clausen 2010 -16.8 161

 Overtime .....Not Just a 50/50 Coin Toss (Mark 2).

Conventional wisdom appears to suggest that after two teams have played a stalemate after 4 quarters,any pre game advantage enjoyed by the better side has vanished.It's assumed that before the overtime coin toss the game is considered a 50/50 proposition and after the coin toss the team electing to receive the ball now has around a 60% chance of winning and that increased chance of winning is solely as a result of receiving the ball first.

However,in a previous Overtime post I presented figures which showed that the better side from a pregame perspective still wins more often in overtime.In this post I hope to show that there can be little doubt that pre game favouritism does indeed carry over into overtime.Results used were from the 1995 season onwards because the kickoff was moved to the 30 yardline from this season onwards.Pregame favourites were determined by a regression model based on passing and rushing efficiency on both sides of the ball.

The earlier post used results stretching back to1989,so to firstly ensure that only games since the latest kickoff rule change were included I repeated the analysis using post 1994 games.

The sample size comprised just over 250 games and once again the pre game favourite did better in overtime,winning 58% of the overtime contests.(Non playoff games that ended scoreless after one period of overtime were credited as half a win to each team).
However,this opened up the possibility that pregame favourites were merely being lucky at guessing the coin toss and their winning percentage was down to them receiving the overtime ball first more often.

So the next step was to see how teams fared when they received the kick off in OT.In this instance pregame favourites were indeed slightly more luckier than their underdog counterparts.Just over 51% of the coin tosses were won by the pregame favourite.

Now if overtime should be considered a 50/50 proposition between the two teams prior to the overtime coin toss,there should be little or no difference between the winning percentages of favourites who receive the ball first in overtime and underdogs who also get the ball first.Every receiving team in overtime should just have the advantage of having the ball first,their pregame chances should count for nothing.

However the results don't support this view.

When the pre game favourite receives the kickoff in overtime they go onto win over 66% of the time.When the underdog receives they win just 50% of the time.

So it would seem that favourites win significantly more overtime games than do underdogs,even when you correct for favourites having a slightly better record at guessing the coin toss.Pre game match probabilities are  better indicators of what will happen in overtime compared to using what has already occurred.Favourites who are tied at the half still go onto win that tied game much more often than do their underdog opponents.Therefore it would be surprising if favs didn't continue the trend when they are taken to OT.

To summarise.
The receiving team has won 58% of overtime games since 1994.
When the receiving team is also the pregame favourite,they win 66% of the games.
When the receiving team is also the pregame underdog,they win 50% of the games.

Friday, 28 January 2011

Overtime .....Not Just a 50/50 Coin Toss.

With nine seconds remaining in the 4th during week 14 Washington were a point adrift of Tampa Bay with the extra point to come. Redskins had two options.They could kick the extra point and take their chances in almost certain overtime or go for the 2 point conversion and try to win the game there and then.

In researching the post "A Game of two Halves",posted last year,I looked at how teams fared in overtime.I specifically looked to see if the pregame chances of the teams carried over into overtime.This involved producing pre game probabilties for over 300 games that have gone to overtime since 1989.I then grouped the games into batches where the home team had a similar probability of winning the game at the outset.

For example there were 42 OT games where the home side had about a 59% chance of winning the game before a ball was kicked.Of those 42 games the pre game favourite went on to win the game in overtime on 23 occasions.Just under 55%.Similarly,home teams having a pregame win probability of just 25% who managed to take the game to OT went on to win 33% of the time in sudden death.

I repeated the process over a wide range of pre game probabilities and plotted pregame probability against overtime winning percentage to see if there was a correlation.

There appears to be a positive,moderate to strong correlation between a team's pre game chances and their chance of winning that game should it go to overtime.
If P is the pregame probability of the home side winning,then the probability of that team winning should the game go to overtime is given by

OT win probability =(P multiplied by 0.732) + 0.124

To summarise, favourites are still favoured in overtime,but not by as much.Underdogs are still more likely to lose,but they do see their chances increase in OT compared to pre game.

So returning to Washngton's game at Tampa.Pregame estimates of Washington's chances of winning the game varied.Efficiency based models had the Redskins as narrow favourites,the model I used gave the Redskins a 0.56 probability of winning the game.

The probabilty of Washington winning in OT becomes.

(0.56*0.732)+0.124 = 0.53

The success rates for 2 point conversions is in the region of 48%.Therefore given the almost automatic outcome for a extra point kick and assuming the accuracy of the pre game probabilty,Washington made the correct decision in attempting the kick,even though they missed it!

As an aside,the Vegas line made Tampa the 2 point favourites.If we instead use this figure as a reflection of the pre game odds,we find now that Washington should have gone for 2.Their pregame win probability would have been about 0.46.This would increase by a very small amount if they took the game to OT,but not by enough to pass the 48% chance they probably had to make the two point conversion.
A Game of Two Halves ?

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.

Next I needed to ensure that game situation was not unduly influencing the points scored in the remainder of the game.Passing sides inevitably run the ball when they have a large lead and running sides are forced away from their core values if they trail.So it was decided to chose games that were tied at the interval (or within a point either way in some cases to increases sample size).This ensured that we still had a contest where both teams were playing to their strengths and trying to maximize any points they scored.

Lastly,I needed to know how the pregame expected supremacy of the favoured team would decay over the course of the game.In sports such as soccer the scoring rates of each team in a game decays as a factor of initial expected scoring rate and time remaining in such a way as there is slightly more scoring activity in the second half compared to the first.Unfortunately,the scoring in the NFL is much more messy.A score can amount to either 2,3,6,7 or 8 points and time outs and 2 two minute warnings can prolong quarters.I decided against incorporating an extensive study into how teams scoring rates decay and instead used the broadly correct assumption that by half time a favourites pre game expected points supremacy has decayed to half it's initial value.

In short,a team with a win probability at kick off of 0.78 which would expect on average to win such match up by 10 points would expect to win the second half alone by,on average 5 points.

Games tied at halftime.

In order to obtain a reasonably large number of games I was forced to go back into the '80's and I looked at all games from the view point of the team who were favoured to win,be they the home or away side.It wasn't possible to eliminate any games where a team had lost a significant player such as the quarterback during the first two quarters,but these matchups would most likely be small in number.

Almost 450 games over the 20+ year period saw a favoured team tied at half time and the average pre game expected margin of victory for those favourites was around 5.5 points.If the previous 30 minutes of action was a better indicator of the relative strengths of both teams then we would expect that the ultimate game winners would be split almost equally between the pre game favorites and the pre game underdogs.However,if the pregame model,based on at least four previous games was a better predictor we would expect the pre game favourite to win more of the half time stalemated games.

And it's the latter that occurs.

All favourites that are tied at halftime go on to win about 64% of those games and their average margin of victory in these games is around 2.5 points,about half of their predicted pre game supremacy.
If you slice and dice the sample the effect remains.Teams favoured by a field goal or more should win by an average of six points,but if they are tied at the half they still win more than half the games (66%) and the margin of victory is around a field goal.
Strong favourites win 84% of games in which they are held at the break and their margin of victory is 7 points compared to the pre game predicted 13.

However you look at things,judging a game solely on what has happened in the first 30 minutes is flawed,pre game esimates derived from a robust model is much the better indicator of what will happen in the third and fourth quarters.

Overtime Games.
If tied games after two quarters resulting in the favourite eventually winning the larger share isn't perhaps too surprising,what about overtime games,where teams appear to be equally matched over 4 quarters.Again sample sizes are small so we need to go back 20+ years,but the results are very similar.

We now have a sample size of around 300 and in almost 57% of the games the pregame favourite wins in OT,by an average margin of victory of 0.5 of a point compared to a pre game predicted margin of victory of 6.The effect is smaller because the game is often decided in just a few drives and any score,as opposed to a maximized score is all that is required (extra points aren't kicked either).The coin toss advantage should even out (unless better teams are also lucky ones).

Again if you group the games from weak favourites to stronger favourites the effect of the better pre game side winning more than a 50% split outright remains in each and every group.For example teams favoured to win by a touchdown or more won over 60% of their games when they were taken to overtime.


Very recent,but low sample size evidence is a poor indicator of future events compared to larger sample size,but older data.

Generally speaking the best indicator of what will occur in the second half of a game is what we would have forecast before the match began, before we had watched the first half.Predictions based on probabilities describe the most likely outcome,but that outcome is not exclusive. Favourites can easily trail at the half (it's just one of the less probable outcomes),but that is not inconsistent with the pre game prediction that they are the superior side.And results suggest that on average in the second half they demonstrate their superiority regardless of what occurred in the first half.

Thursday, 27 January 2011

How Teams Try To Win

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.

  From This...............To This


Initially,I chose two teams with widely differing offensive styles.In 2008 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 apply the doctrine of pass if you're behind and run if you're ahead and the reasonably strong correlation disappears.