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For more from Chase and Jason, check out their work at Football Perspective and The Big Lead.

Why do teams run the ball?

Posted by Chase Stuart on February 12, 2008

Note: It was pointed out in the comments that a similar discussion has been going on over at bbnflstats.com. Thanks to Brian, in comment 7, for pointing that out. His posts are well worth reading if you've got the time.

Everyone knows that teams average more yards per pass than per rush. In the 2007 season, NFL QBs averaged 6.85 yards per pass attempt, and NFL RBs averaged 4.17 yards per rush attempt. This past season wasn't an aberration.

YR 	RUSH	RYD	Y/R	PASS	PYD 	Y/P	Diff
2002	12,016	49,984	4.16	17,087	115,054	6.73	+62%
2003	12,698	53,345	4.20	16,330	108,403	6.64	+58%
2004	12,654	53,028	4.19	16,288	114,979	7.06	+68%
2005	12,726	51,822	4.07	16,411	111,468	6.79	+67%
2006	12,734	53,413	4.19	16,358	112,092	6.85	+63%
2007	12,414	51,786	4.17	17,018	116,580	6.85	+64%

So why do teams run the ball? The most common explanation I've heard is that rushing plays are more consistent, and the larger variance that comes with a passing play makes passing plays less attractive. I don't want to minimize the value of consistency. If a team could run for three yards every play (average yards per play = 3.0), that team would score a touchdown every drive. If a team passed for 10 yards on 50% of its plays, and 0 yards on the other half (average yards per play = 5.0), that offense would score less points; that team would have to punt a non-zero amount of times. The ability to consistently gain yardage is crucial in the NFL.

But I don't think that really explains why teams run as often as they do, considering that pass plays average over 60% more yards per play. After all, rushing plays are a lot less consistent and passing plays are more consistent in real life than in the hypothetical example given. A rush offense that goes for 2 yards, 3 yards and 4 yards a pop an equal number of times is a lot less valuable than the one in the previous paragraph, and more closely resembles the real world. Would you rather have rushing plays of 2, 4, 6 or passing plays of 10, 10, 0? The latter, of course. In the passing group, a team has just a one in twenty-seven chance of being forced into a fourth down situation; in the rushing group, a team has a four-in-twenty-seven chance of being in a fourth down situation (runs of 2, 2, 2; 2, 4, 2; 2, 2, 4; and 4, 2, 2). And of course, the passing group averages 6.7 yards per play while the rushing group averages just four yards per play.

So there has to be more to this run-calling business than consistency. It turns out, there is.

Let's start with yards per pass -- what are we forgetting to calculate? QBs throws interceptions (which are bad) and touchdowns (which are good). Well, adjusted yards per pass solves that. We subtract 45 yards for every interception and add 10 yards for every TD thrown. Here's a table of the league average adjusted yards per attempt by QBs for every year since the merger:

2007	5.85
2006	5.85
2005	5.79
2004	6.07
2003	5.57
2002	5.75
2001	5.65
2000	5.68
1999	5.63
1998	5.79
1997	5.71
1996	5.54
1995	5.79
1994	5.74
1993	5.59
1992	5.51
1991	5.69
1990	5.83
1989	5.81
1988	5.54
1987	5.73
1986	5.59
1985	5.58
1984	5.73
1983	5.64
1982	5.47
1981	5.51
1980	5.38
1979	5.20
1978	4.69
1977	4.31
1976	4.86
1975	4.69
1974	4.52
1973	4.59
1972	4.85
1971	4.51
1970	4.81

That brings things a bit closer together, but we're still pretty far off. After factoring in interceptions (and touchdowns) thrown, passing plays still average in the high fives and rushing plays in the low fours. What else are we missing? When you pass the ball, you can get sacked. That doesn't happen on running plays. If we add sack yards lost to the numerator and sacks to the denominator, we get adjusted net yards, and adjusted net yards per attempt can be calculated. This closes the gap considerably.

Last season was the second best passing season ever. QBs attempted 17,009 passes and were sacked 1,096 times (18,105 plays), and recorded 116,490 passing yards, 715 TDs, 534 interceptions and lost 7,133 yards due to sacks (92,477 adjusted, net yards). That 5.11 yards per pass play by QBs trailed only 2004 as the most prolific passing season ever.

2007	5.11
2006	5.02
2005	4.98
2004	5.23
2003	4.83
2002	4.97
2001	4.82
2000	4.85
1999	4.81
1998	4.91
1997	4.79
1996	4.77
1995	5.04
1994	5.02
1993	4.78
1992	4.53
1991	4.86
1990	4.89
1989	4.88
1988	4.69
1987	4.71
1986	4.59
1985	4.47
1984	4.63
1983	4.56
1982	4.38
1981	4.58
1980	4.45
1979	4.20
1978	3.66
1977	3.17
1976	3.74
1975	3.58
1974	3.55
1973	3.41
1972	3.78
1971	3.47
1970	3.76

Quarterbacks also fumble the ball, but I'm going to put the discussion of fumbles off for another day (hopefully one day soon). For reasons to be explained later, I think it's in our best interest to ignore them.

So now we have a true measure of what happens on a pass. We don't just look at the yards, we look at the interceptions (and touchdowns), the sacks, and the sack yardage lost. But we can't compare that to rushing yards just yet -- because on a running play, you can score a TD, too. Since we looked at passing touchdowns, we can't ignore rushing touchdowns. (Since we ignored QB fumbles, we will ignore RB fumbles as well. It turns out, the rates are pretty similar.)

So if we really want to compare what happens every time a QB goes back to pass to what happens every time a QB hands the ball off to a RB, we need to add in rushing touchdowns to yards per rush. If we add ten yards to each RB's rushing yards total for every rushing TD, we'll get adjusted yards per rush. Here's a look at the historical numbers:

year	rb rsh	rb ryd 	rb ypc	rb td	rb aypc
2007	12012	50153	4.18	328	4.45
2006	12236	51464	4.21	365	4.50
2005	12407	50507	4.07	372	4.37
2004	12287	51637	4.20	370	4.50
2003	12219	51340	4.20	345	4.48
2002	11746	49044	4.18	360	4.48
2001	11242	45698	4.06	275	4.31
2000	11059	44302	4.01	325	4.30
1999	11405	44489	3.90	289	4.15
1998	11669	46546	3.99	314	4.26
1997	11535	46480	4.03	318	4.31
1996	11539	45117	3.91	302	4.17
1995	11282	44886	3.98	318	4.26
1994	10293	38759	3.77	267	4.02
1993	10344	40195	3.89	246	4.12
1992	10083	40698	4.04	280	4.31
1991	10104	39679	3.93	293	4.22
1990	10249	41586	4.06	313	4.36
1989	10866	42423	3.90	315	4.19
1988	11291	45090	3.99	339	4.29
1987	11057	43173	3.90	285	4.16
1986	11435	44996	3.93	343	4.23
1985	11767	49017	4.17	374	4.48
1984	12242	49712	4.06	351	4.35
1983	12553	51373	4.09	380	4.40
1982	 6866	26348	3.84	200	4.13
1981	12798	51628	4.03	377	4.33
1980	12565	49785	3.96	357	4.25
1979	13414	53755	4.01	423	4.32
1978	14596	57859	3.96	404	4.24
1977	13147	50448	3.84	287	4.06
1976	13115	53004	4.04	342	4.30
1975	12022	47265	3.93	361	4.23
1974	11062	42423	3.84	300	4.11
1973	11156	45045	4.04	261	4.27
1972	10758	43721	4.06	290	4.33
1971	10015	39698	3.96	263	4.23
1970	 9618	35852	3.73	250	3.99

The first thing that jumps off to me is that 1985 was a highwater mark for RBs -- the 4.17 ypc average was higher than any season from 1970-2001, and the same is true for the league-wide adjusted yards per rush. Gerald Riggs had a huge year, and Marcus Allen, Walter Payton, Tony Dorsett and Earl Campbell were all running strong. James Wilder, Freeman McNeil, Joe Morris and Curt Warner all had big seasons, too. It just seemed to be a perfect storm of young and old RBs playing at elite levels.

When looking at the RB data, there's a general increase in rushing efficiency each year. The correlation coefficient between "year" and "rb ypc" is very close to 0.50, so we can feel comfortable in noting that running games are improving slightly each season. The addition of the touchdown bonus to the numerator boosts up league-wide running back yards per rush by about seven percent. But now, let's compare the RB adjusted rushing yards per rush to QB adjusting passing yards per play:

year	rb aypc	qb nay/a diff	
2007	4.45	5.11	 0.66
2006	4.50	5.02	 0.51
2005	4.37	4.98	 0.60
2004	4.50	5.23	 0.72
2003	4.48	4.83	 0.35
2002	4.48	4.97	 0.49
2001	4.31	4.82	 0.52
2000	4.30	4.85	 0.55
1999	4.15	4.81	 0.65
1998	4.26	4.91	 0.66
1997	4.31	4.79	 0.49
1996	4.17	4.77	 0.60
1995	4.26	5.04	 0.78
1994	4.02	5.02	 0.99
1993	4.12	4.78	 0.66
1992	4.31	4.53	 0.22
1991	4.22	4.86	 0.64
1990	4.36	4.89	 0.53
1989	4.19	4.88	 0.69
1988	4.29	4.69	 0.40
1987	4.16	4.71	 0.55
1986	4.23	4.59	 0.36
1985	4.48	4.47	-0.01
1984	4.35	4.63	 0.28
1983	4.40	4.56	 0.16
1982	4.13	4.38	 0.25
1981	4.33	4.58	 0.25
1980	4.25	4.45	 0.20
1979	4.32	4.20	-0.12
1978	4.24	3.66	-0.58
1977	4.06	3.17	-0.88
1976	4.30	3.74	-0.56
1975	4.23	3.58	-0.66
1974	4.11	3.55	-0.55
1973	4.27	3.41	-0.86
1972	4.33	3.78	-0.56
1971	4.23	3.47	-0.76
1970	3.99	3.76	-0.22

As you can see, for most of the '70s, running the ball actually was superior to passing the ball. Had you just compared yards per pass to yards per rush, here's what you would have seen:

year	rb ypc	qb ypa	diff
2007	4.45	6.85	2.40
2006	4.50	6.85	2.35
2005	4.37	6.79	2.42
2004	4.50	7.06	2.55
2003	4.48	6.63	2.15
2002	4.48	6.72	2.24
2001	4.31	6.76	2.46
2000	4.30	6.74	2.44
1999	4.15	6.75	2.60
1998	4.26	6.85	2.59
1997	4.31	6.68	2.38
1996	4.17	6.68	2.51
1995	4.26	6.77	2.51
1994	4.02	6.77	2.74
1993	4.12	6.69	2.56
1992	4.31	6.86	2.55
1991	4.22	6.89	2.68
1990	4.36	7.00	2.64
1989	4.19	7.14	2.95
1988	4.29	6.94	2.64
1987	4.16	6.99	2.83
1986	4.23	7.02	2.78
1985	4.48	7.06	2.58
1984	4.35	7.12	2.77
1983	4.40	7.15	2.76
1982	4.13	6.98	2.85
1981	4.33	7.00	2.67
1980	4.25	6.98	2.74
1979	4.32	6.84	2.51
1978	4.24	6.70	2.46
1977	4.06	6.51	2.45
1976	4.30	6.67	2.37
1975	4.23	6.67	2.44
1974	4.11	6.48	2.37
1973	4.27	6.51	2.24
1972	4.33	6.76	2.43
1971	4.23	6.69	2.46
1970	3.99	6.71	2.72

Pretty interesting, eh? The difference in yards per rush and yards per pass was the exact same in the early '70s as it is now! Yet take a look at pass attempts and rush attempts in the modern era:

year	pass 	rush	ratio
2007	17009	12012	1.42
2006	16355	12236	1.34
2005	16429	12407	1.32
2004	16299	12287	1.33
2003	16438	12219	1.35
2002	17239	11746	1.47
2001	16137	11242	1.44
2000	16294	11059	1.47
1999	16726	11405	1.47
1998	15453	11669	1.32
1997	15708	11535	1.36
1996	15939	11539	1.38
1995	16667	11282	1.48
1994	15032	10293	1.46
1993	14384	10344	1.39
1992	13341	10083	1.32
1991	13602	10104	1.35
1990	13481	10249	1.32
1989	14176	10866	1.30
1988	13773	11291	1.22
1987	12747	11057	1.15
1986	13835	11435	1.21
1985	13687	11767	1.16
1984	13753	12242	1.12
1983	13422	12553	1.07
1982	7595	 6866	1.11
1981	13643	12798	1.07
1980	13218	12565	1.05
1979	12765	13414	0.95
1978	11594	14596	0.79
1977	 9412	13147	0.72
1976	 9602	13115	0.73
1975	 9359	12022	0.78
1974	 9159	11062	0.83
1973	 8200	11156	0.74
1972	 8450	10758	0.79
1971	 8944	10015	0.89
1970	 9415	 9618	0.98

In the early '70s, teams passed about 80% as often as they ran the ball. Now, the average team passes about 40% more often than they run the ball. Meanwhile, yards per attempt and yards per rush haven't changed very much. But considering how the adjusted numbers show the pass/run effectiveness gap increase significantly is very strong evidence that the adjusted data is what matters.

In the early '70s, rushing was indeed superior to throwing. Teams averaged about two feet more per rush than per pass, when factoring in sacks and interceptions. That's why the Dolphins with Larry Csonka, Mercury Morris and Jim Kiick were able to dominate the early '70s, and the Steelers with Franco Harris and Rocky Bleier were dominant in the mid '70s. The running game was paramount then, because passing wasn't a very attractive option. If you could run and stop the run, you could win. And that's why we probably still hear that phrase today.

But then the rule changes of 1978 kicked in. Defenders were no longer allowed to mug receivers. The Mel Blount rule prevented defenders from making contact with receivers once the offensive player was five yards past the line of scrimmage. Of equal importance, offensive lineman were now allowed to extend their arms and open their hands to pass block. Can you imagine what passing offenses would look like today if those rule changes never happened? We could certainly imagine a large bump in sacks allowed and interceptions. Take a look:

year	sk/att	int/att
2007	 6.4	3.1
2006	 7.1	3.2
2005	 7.2	3.1
2004	 7.3	3.2
2003	 6.6	3.2
2002	 6.8	3.0
2001	 7.4	3.3
2000	 7.6	3.2
1999	 7.4	3.4
1998	 7.8	3.3
1997	 8.0	3.0
1996	 6.9	3.4
1995	 6.4	3.0
1994	 6.2	3.1
1993	 7.3	3.2
1992	 8.5	3.9
1991	 7.1	3.5
1990	 7.9	3.5
1989	 7.6	3.9
1988	 7.4	3.9
1987	 8.1	3.9
1986	 8.4	4.0
1985	 9.2	4.2
1984	 9.1	4.0
1983	 8.7	4.4
1982	 8.4	4.3
1981	 7.2	4.3
1980	 7.5	4.5
1979	 8.1	4.6
1978	 8.6	5.4
1977	 9.7	5.8
1976	10.0	4.8
1975	 9.3	5.4
1974	 8.4	5.2
1973	 9.8	5.4
1972	 8.7	5.3
1971	 8.2	5.9
1970	 8.9	5.1

As recently as 1985, rushing the ball was more effective than passing the ball. As recently as 2003, the difference in true yards per rush and pass was just 0.35 per attempt. The two rules enacted in 1978 severely diminished the impact on the two biggest negatives associated with passing the ball -- sacks and interceptions. In 1978, the average pass play netted just 3.66 yards per pass; three years later, the average pass play was worth 4.58 yards per pass. Teams passed 80% as often in 1978 as they ran; by '81, teams passed 7% more often than they ran.

The rule changes of 1978 answered the question: Why do teams pass the ball? There's a lot of game theory involved in the decision to run or pass, but it's clear that running was a more efficient option and had a lower variance. Now, running is less efficient (but with still a lower variance). Looking at true yards per pass overstates the passing option by about 55% from 1970-2007, and by about 37% over the past ten years. Combined with how not counting rushing touchdowns in yards per rush (understating the average run play by about 7%), and you can see, finally, why teams run the ball. Once you include the lower variance, the only question left is why don't teams run the ball more often?

This entry was posted on Tuesday, February 12th, 2008 at 4:50 am and is filed under General. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.