Tigers, Lions, and How Expectations and Understanding Randomness Impacts Fan Happiness

Posted on October 11, 2010 by


The Wages of Wins Journal is supposed to be one of the very top basketball blogs. But both The Wages of Wins and Stumbling on Wins devote the majority of their pages to something other than basketball.  And the majority of my published research is about something besides the NBA.

That being said… this forum is primarily about basketball. Except for today. 

The Detroit Tigers just finished a “disappointing” season (one can see the disappointment in Steve Kornacki’s season review at MLive.com).  In 2009, the Tigers won 86 times and finished tied with the Minnesota Twins after 162 games.  This past season, though, the Tigers only won 81 times and finished 13 games behind the Twins (although – and I know this might hurt fans of the Twins to hear this – both the Tigers and Twins won the same number of playoff games this year). 

These two results have left fans of the Tigers wondering what happened.  How did the Tigers regress?  For an answer we turn to my favorite baseball blog.  Lee Panas – author of Beyond Batting Average (an excellent book on sabermetrics) – has a blog called Tiger Tales.  Recently Lee offered a post  –The Tigers Lose Their Close Game Magic–comparing what the Tigers did in 2009 to what we saw this past season.  Here is some of what Lee had to say:

The 2009 Tigers barely outscored their opponents 745 to 743.  You would expect a team with such a small run differential to finish with 81 wins, but the Tigers managed to win 86 games.  The reason was because they had a record of 52-33 in games decided by just one or two runs.  At the time, I theorized that they won so many close games, in part, because of Fernando Rodney’s high save conversion rate (37 for 38), seven walk-off wins and some luck.

This year, the Tigers had remarkably similar runs scored and runs allowed totals to 2009.  They outscored their opponents 751 to 743, but won just 81 games.

…why did they win five fewer games this year when their run differential was six runs more than it was in 2009?  The reason was because they had less success in close games.  After finishing 19 games above .500 in games decided by one or two runs last year, they were 33-38 this year. It’s hard to blame their bullpen which was better than last’s year’s crew according to most statistics including ERA, FIP and WPA.  They also had their share of dramatic victories early in the season.  Some might attribute the difference in close game performance to poor managing or less desire to win, but I’m going guess that it was just a random thing

Lee’s analysis indicates that the Tigers in 2010 were about the same as they were in 2009. In fact, in terms of runs scored and runs surrendered, the 2010 team was a little bit better. But random elements (a note I put in bold) in the game led to slightly fewer wins.  And I think that should give the Tigers some encouragement going forward. 

This past season the Tigers suffered some fairly significant injuries.  Furthermore, the team gave a great deal of playing time to rookies (I think the Tigers in 2010 played more rookies than any Detroit team had played in more than 50 years).  Since rookies tend to get better, there is hope the Tigers will be better in 2011.  In sum, I think fans of the Tigers should be relatively pleased about how the 2010 season finished (given the injuries and youth of the team).  And fans should also be optimistic about the future.

Of course, I am also a Lions fan.  And as a Lions fan, I have become quite good at “unrealistic optimism” (something to remember in evaluating my comments on the Tigers). With the Lions victory yesterday, here is where the team stands after five games: 1 win, 4 losses, 126 points scored, 112 points surrendered.

If we focus on wins and losses – even with yesterday’s 44-6 victory over the Rams – Lions fans can’t be too happy.  But in terms of scoring, there is reason for optimism.

As we saw in the discussion of the Tigers, scoring can be translated into wins.  And if the Lions maintained this record with respect to points scored and points surrendered across an entire season, we would expect such a team to win 9.2 games.

This expectation is based on the following simple regression (estimated with team data from 2005 to 2009):

Winning percentage = 0.493 + 0.0017*Points Scored in a Season – 0.0017*Points Surrendered in a Season

Such a model explains 86% of winning percentage in the NFL.

One can also employ the Pythagorean approach.  This approach – adapted from the work of Bill James and applied by Pro Football Reference to the NFL – argues that a team’s expected record can be determined via the following formula:

Expected record =~ PF^2.37 / (PF^2.37 + PA^2.37)

I re-estimated the Pythagorean model with NFL data from 2005 to 2009 and I found the coefficient was 2.52 (as opposed to 2.37).  Either way, though, the model explains about 85% of outcomes and we should expect – if the Lions maintain their current scoring marks – to win about nine games (in other words, I am not convinced the Pythagorean approach – with either coefficient — is a vast improvement over a simple linear regression).

Of course, the Lions have already been “unlucky”.  Given their current mark, if they play as a 9-7 team the rest of the season the Lions will only finish with seven victories.  Still 7-9 is a huge step forward.  On November 4 of 2007, the Lions defeated the Denver Broncos 44-7.  This victory left the Lions with a 6-2 mark at the halfway point of the 2007 season.  From that point forward — up until yesterday — the Lions had only won three games in 44 contests (yes, the Lions had a mark of 3-41 across 35 months).  So if the Lions finish 7-9, fans of this team will hardly be disappointed.

And that leads us to an interesting observation.  How you feel about your team depends upon your recent experience, your expectations about the future, and your understanding of how “luck” impacts outcomes in sports.  Fans of the Tigers are disappointed because the team in 2009 came very close to the post-season, while this season the team – despite posting very similar results with respect to runs– was 13 games out of the playoffs.  If fans of the Tigers fully understood how randomness impacted outcomes, I think there would be less unhappiness.

Turning to the Lions, this team will probably not make the playoffs with a 7-9 record.  But if the Lions managed to win six more times this season, fans of this team would be extremely happy (at least, this fan would be very happy).

All of this suggests that if a team can manipulate expectations it can change the happiness of their fans. So maybe this is why the Lions lost 41 out of 44 games.  It was all done to make us happy with a 7- 9 team.  And if that was their objective, I have to say it probably worked.

– DJ