Regression to the mean and Team Wins

The two Texas teams had much better seasons in 2014 than they did in 2013. Houston jumps from 2 to 9 wins, while Dallas improved from 8 to 12 wins. Which season was more impressive as far as team improvement?

If you like math, you probably are thinking that improving by 7 wins is more impressive than improving by 4 wins. But if you love math, you are probably thinking about regression to the mean. After all, sure, Houston won only 2 games in 2013, but nobody expected them to be that bad last year. In fact, the Texans were arguably projected to be the best team in the state last year!1

But instead of using Vegas odds, I thought it would be interesting to take a quick look at the effects of regression to the mean on team wins. I looked at every team season from 2003 to 2014, and noted how many wins each team won in the prior year and in the current year. I then ran a linear regression using prior year (Year N-1) wins to create a best-fit formula for current (Year N) wins. That formula was:

5.51 + 0.31 * Year N-1 Wins

What this means is that to predict future wins, start with a constant for all teams (5.51 wins), and then add only 0.31 wins for every prior win. In other words, three additional wins in Year N-1 aren’t even enough to project one full extra win in Year N! That’s a remarkable amount of regression to the mean, even if not necessarily surprising.2 For those curious, the R^2 was just 0.094, another sign of how not valuable it is to just know how many games a team won in the prior year.

As a basic matter, no team in 2014 exceeded prior wins like Houston did. But with 2 wins in 2013, Houston would have been expected to win 6.1 wins last year; that means the Texans “only” exceeded expectations by 2.9 wins after we account for regression to the mean. Dallas, meanwhile, was expected to win 8 games for the 33rd year in a row; by winning 12, the Cowboys exceeded expectations by 4 wins.

The table below shows each team from 2003 to 2014; for each team, I have listed their wins in the prior season (Year N-1), their expected number of wins in Year N based on the above regression formula, their actual Year N wins, the raw difference between Year N and Year N-1 wins, and the difference between Year N actual wins and Year N expected wins. The table is fully searchable and sortable, so type in “NYJ” to see all Jets seasons since ’03.

YearTmN-1 WinsExp N WinsYear N WinsRaw DiffExp Diff
2014DAL881244
2014GNB8.58.2123.53.8
2014DET77.71143.3
2014PIT881133
2014HOU26.1972.9
2014NWE129.21202.8
2014DEN139.612-12.4
2014SEA139.612-12.4
2014ARI108.61112.4
2014IND118.91102.1
2014BAL881022
2014BUF67.4931.6
2014CIN118.910.5-0.51.6
2014PHI108.61001.4
2014SDG98.3900.7
2014CLE46.8730.2
2014KAN118.99-20.1
2014MIA88800
2014MIN5.57.271.5-0.2
2014ATL46.862-0.8
2014SFO129.28-4-1.2
2014NYG77.76-1-1.7
2014STL77.76-1-1.7
2014CAR129.27.5-4.5-1.7
2014NOR118.97-4-1.9
2014WAS36.441-2.4
2014CHI885-3-3
2014JAX46.83-1-3.8
2014OAK46.83-1-3.8
2014NYJ884-4-4
2014TAM46.82-2-4.8
2014TEN77.72-5-5.7
2013KAN26.11194.9
2013CAR77.71254.3
2013SEA118.91324.1
2013DEN139.61303.4
2013NOR77.71143.3
2013PHI46.81063.2
2013ARI57.11052.9
2013SFO11.59.1120.52.9
2013NWE129.21202.8
2013CIN108.61112.4
2013IND118.91102.1
2013SDG77.7921.3
2013NYJ67.4820.6
2013MIA77.7810.3
2013DET46.8730.2
2013DAL88800
2013PIT88800
2013TEN67.471-0.4
2013GNB118.98.5-2.5-0.4
2013CHI108.68-2-0.6
2013BAL108.68-2-0.6
2013STL7.57.87-0.5-0.8
2013NYG98.37-2-1.3
2013BUF67.460-1.4
2013JAX26.142-2.1
2013OAK46.840-2.8
2013CLE57.14-1-3.1
2013MIN108.65.5-4.5-3.1
2013TAM77.74-3-3.7
2013ATL139.64-9-5.6
2013WAS108.63-7-5.6
2013HOU129.22-10-7.2
2012DEN881355
2012IND26.11194.9
2012ATL108.61334.4
2012MIN36.41073.6
2012HOU108.61223.4
2012SEA77.71143.3
2012WAS57.11052.9
2012NWE139.612-12.4
2012CHI881022
2012SFO139.611.5-1.51.9
2012CIN98.31011.7
2012STL26.17.55.51.4
2012GNB1510.211-40.8
2012BAL129.210-20.8
2012NYG98.3900.7
2012TAM46.8730.2
2012DAL88800
2012CAR67.471-0.4
2012MIA67.471-0.4
2012SDG887-1-1
2012PIT129.28-4-1.2
2012BUF67.460-1.4
2012CLE46.851-1.8
2012NYJ886-2-2
2012TEN98.36-3-2.3
2012NOR139.67-6-2.6
2012ARI885-3-3
2012PHI884-4-4
2012OAK884-4-4
2012DET108.64-6-4.6
2012JAX57.12-3-5.1
2012KAN77.72-5-5.7
2011GNB108.61556.4
2011SFO67.41375.6
2011NOR118.91324.1
2011NWE149.913-13.1
2011PIT129.21202.8
2011BAL129.21202.8
2011DET67.41042.6
2011HOU67.41042.6
2011CIN46.8952.2
2011TEN67.4931.6
2011DEN46.8841.2
2011ARI57.1830.9
2011DAL67.4820.6
2011ATL139.610-30.4
2011NYG108.69-10.4
2011OAK88800
2011CAR26.164-0.1
2011SDG98.38-1-0.3
2011PHI108.68-2-0.6
2011SEA77.770-0.7
2011BUF46.862-0.8
2011CHI118.98-3-0.9
2011NYJ118.98-3-0.9
2011KAN108.67-3-1.6
2011MIA77.76-1-1.7
2011WAS67.45-1-2.4
2011JAX885-3-3
2011CLE57.14-1-3.1
2011MIN67.43-3-4.4
2011TAM108.64-6-4.6
2011STL77.72-5-5.7
2011IND108.62-8-6.6
2010NWE108.61445.4
2010ATL98.31344.7
2010PIT98.31233.7
2010BAL98.31233.7
2010TAM36.41073.6
2010CHI77.71143.3
2010KAN46.81063.2
2010NYJ98.31122.7
2010NYG881022
2010NOR139.611-21.4
2010STL15.8761.2
2010GNB118.910-11.1
2010PHI118.910-11.1
2010OAK57.1830.9
2010JAX77.7810.3
2010IND149.910-40.1
2010SEA57.172-0.1
2010DET26.164-0.1
2010SDG139.69-4-0.6
2010MIA77.770-0.7
2010WAS46.862-0.8
2010TEN886-2-2
2010SFO886-2-2
2010CLE57.150-2.1
2010HOU98.36-3-2.3
2010DAL118.96-5-2.9
2010MIN129.26-6-3.2
2010BUF67.44-2-3.4
2010ARI108.65-5-3.6
2010DEN884-4-4
2010CIN108.64-6-4.6
2010CAR882-6-6
2009NOR881355
2009SDG881355
2009IND129.21424.8
2009GNB67.41153.6
2009MIN108.61223.4
2009CIN4.56.9105.53.1
2009DAL98.31122.7
2009PHI9.58.5111.52.5
2009ARI98.31011.7
2009NWE118.910-11.1
2009HOU88911
2009NYJ98.3900.7
2009SFO77.7810.3
2009ATL118.99-20.1
2009BAL118.99-20.1
2009DEN88800
2009JAX57.172-0.1
2009PIT129.29-3-0.2
2009CAR129.28-4-1.2
2009NYG129.28-4-1.2
2009CHI98.37-2-1.3
2009TEN139.68-5-1.6
2009BUF77.76-1-1.7
2009CLE46.851-1.8
2009SEA46.851-1.8
2009MIA118.97-4-1.9
2009OAK57.150-2.1
2009KAN26.142-2.1
2009DET05.522-3.5
2009WAS884-4-4
2009STL26.11-1-5.1
2009TAM98.33-6-5.3
2008MIA15.811105.2
2008TEN108.61334.4
2008CAR77.71254.3
2008ATL46.81174.2
2008BAL57.11163.9
2008NYG108.61223.4
2008PIT108.61223.4
2008IND139.612-12.4
2008NYJ46.8952.2
2008MIN881022
2008PHI889.51.51.5
2008CHI77.7921.3
2008ARI88911
2008TAM98.3900.7
2008NWE1610.511-50.5
2008DEN77.7810.3
2008NOR77.7810.3
2008HOU88800
2008SFO57.172-0.1
2008WAS98.38-1-0.3
2008DAL139.69-4-0.6
2008BUF77.770-0.7
2008SDG118.98-3-0.9
2008OAK46.851-1.8
2008CIN77.74.5-2.5-3.2
2008GNB139.66-7-3.6
2008JAX118.95-6-3.9
2008STL36.42-1-4.4
2008CLE108.64-6-4.6
2008SEA108.64-6-4.6
2008KAN46.82-2-4.8
2008DET77.70-7-7.7
2007NWE129.21646.8
2007GNB881355
2007DAL98.31344.7
2007IND129.21313.8
2007CLE46.81063.2
2007JAX881133
2007TAM46.8952.2
2007NYG881022
2007TEN881022
2007PIT881022
2007WAS57.1941.9
2007SEA98.31011.7
2007SDG149.911-31.1
2007ARI57.1830.9
2007HOU67.4820.6
2007MIN67.4820.6
2007DET36.4740.6
2007PHI108.68-2-0.6
2007BUF77.770-0.7
2007CAR887-1-1
2007CIN887-1-1
2007DEN98.37-2-1.3
2007NOR108.67-3-1.6
2007OAK26.142-2.1
2007CHI139.67-6-2.6
2007SFO77.75-2-2.7
2007ATL77.74-3-3.7
2007KAN98.34-5-4.3
2007BAL139.65-8-4.6
2007NYJ108.64-6-4.6
2007STL883-5-5
2007MIA67.41-5-6.4
2006SDG98.31455.7
2006BAL67.41375.6
2006CHI118.91324.1
2006NOR36.41073.6
2006NWE108.61223.4
2006NYJ46.81063.2
2006PHI67.41042.6
2006IND149.912-22.1
2006GNB46.8841.2
2006TEN46.8841.2
2006DAL98.3900.7
2006STL67.4820.6
2006KAN108.69-10.4
2006SFO46.8730.2
2006BUF57.172-0.1
2006HOU26.164-0.1
2006DEN139.69-4-0.6
2006SEA139.69-4-0.6
2006CAR118.98-3-0.9
2006CIN118.98-3-0.9
2006NYG118.98-3-0.9
2006PIT118.98-3-0.9
2006ATL887-1-1
2006JAX129.28-4-1.2
2006ARI57.150-2.1
2006MIA98.36-3-2.3
2006MIN98.36-3-2.3
2006CLE67.44-2-3.4
2006WAS108.65-5-3.6
2006DET57.13-2-4.1
2006OAK46.82-2-4.8
2006TAM118.94-7-4.9
2005IND129.21424.8
2005SEA98.31344.7
2005DEN108.61334.4
2005CHI57.11163.9
2005TAM57.11163.9
2005JAX98.31233.7
2005NYG67.41153.6
2005CAR77.71143.3
2005CIN881133
2005WAS67.41042.6
2005KAN77.71032.3
2005MIA46.8952.2
2005DAL67.4931.6
2005MIN88911
2005PIT1510.211-40.8
2005NWE149.910-40.1
2005SDG129.29-3-0.2
2005CLE46.862-0.8
2005ATL118.98-3-0.9
2005STL886-2-2
2005SFO26.142-2.1
2005BAL98.36-3-2.3
2005ARI67.45-1-2.4
2005DET67.45-1-2.4
2005TEN57.14-1-3.1
2005OAK57.14-1-3.1
2005BUF98.35-4-3.3
2005PHI139.66-7-3.6
2005GNB108.64-6-4.6
2005NYJ108.64-6-4.6
2005NOR883-5-5
2005HOU77.72-5-5.7
2004PIT67.41597.6
2004SDG46.81285.2
2004NWE149.91404.1
2004ATL57.11163.9
2004PHI129.21313.8
2004IND129.21202.8
2004NYJ67.41042.6
2004JAX57.1941.9
2004BUF67.4931.6
2004DEN108.61001.4
2004GNB108.61001.4
2004BAL108.69-10.4
2004SEA108.69-10.4
2004CIN88800
2004NOR88800
2004HOU57.172-0.1
2004MIN98.38-1-0.3
2004ARI46.862-0.8
2004NYG46.862-0.8
2004DET57.161-1.1
2004WAS57.161-1.1
2004STL129.28-4-1.2
2004OAK46.851-1.8
2004CAR118.97-4-1.9
2004KAN139.67-6-2.6
2004DAL108.66-4-2.6
2004CHI77.75-2-2.7
2004TAM77.75-2-2.7
2004CLE57.14-1-3.1
2004TEN129.25-7-4.2
2004MIA108.64-6-4.6
2004SFO77.72-5-5.7
2003NWE98.31455.7
2003KAN881355
2003STL77.71254.3
2003IND108.61223.4
2003CAR77.71143.3
2003TEN118.91213.1
2003DAL57.11052.9
2003PHI129.21202.8
2003BAL77.71032.3
2003SEA77.71032.3
2003CIN26.1861.9
2003DEN98.31011.7
2003MIA98.31011.7
2003MIN67.4931.6
2003GNB129.210-20.8
2003CHI46.8730.2
2003NOR98.38-1-0.3
2003DET36.452-1.4
2003SFO108.67-3-1.6
2003HOU46.851-1.8
2003BUF886-2-2
2003TAM129.27-5-2.2
2003NYJ98.36-3-2.3
2003JAX67.45-1-2.4
2003WAS77.75-2-2.7
2003PIT10.58.86-4.5-2.8
2003ARI57.14-1-3.1
2003CLE98.35-4-3.3
2003ATL9.58.55-4.5-3.5
2003SDG884-4-4
2003NYG108.64-6-4.6
2003OAK118.94-7-4.9

The team that was most “disappointing” by this metric was the Tennessee Titans, who fell from 7 to 2 wins. Tennessee also led the way in coming up short by the basic method, while the Panthers (4.5 fewer wins in 2014, but only 1.7 fewer expected wins) help illustrate the difference between the two methods.

One more interesting note: The ’04 Steelers topped the list. You may recall that Pittsburgh team from such things as Ben Roethlisberger’s rookie season, AFC Championship Game losses in Pittsburgh, and Quarter-by-Quarter Team Win Probability Added. That last link is to a fun Neil Paine post that is worth a read. In 2004, Pittsburgh won 7 more games than an average team; Neil determined that 4.98 of those wins were due to the team’s 4th quarter performance, the most by any team from 1978 to 2012. That’s one reason the Steelers were able to far exceed expectations that year.

1. Just before the season, both Houston and Dallas had Vegas over/under odds of 7.5 wins, but the way the money lines were set up hinted that Vegas wanted to get more action on Dallas and the over. []
2. Since this has been studied to death. []