# What is the probability the Detroit Lions lose every game (again!)

I am from Detroit and I am a Lions fan; erstwhile, anyway. The Lions stink, stank, and have stunk since before I was born. They are lousy, appalling, and nausea-inducing. They are no damn good. Rotten, too. Few can remember when last they won a game. My dad always jokes that in their first game of each new season, a fan in the stadium holds up a sign reading, “Wait ’til next year!”.

Because of their rank dismalness, they are, paradoxically, the most-loved football team, and the reason is simple. What opposing coach’s heart is not filled with glee when he gazes upon the schedule and sees that he is pitted against the Lions? Several lucky clubs get to play them more than once! Bears fans can’t wait for the Lions to come to town. Ecstasy!

The Lion’s soaring stinkitude is also a blessing to statisticians like myself, because their ridiculous record makes for a perfect illustration of probability.

Last year, the Lions won no games. More thoroughly, they won 0 and lost 16. But this was reason to cheer, because this feat was a record! No NFL team had ever been so bad before. Now, you cannot do worse than losing all 16 games unless—and this is what interests us—a team compiles this same spectacular record a second year in a row. So our question is this: What is the chance the Lions lose all 16 games this year?

Textbooks statistical procedures won’t work for us, so we’ll use a technique called Bayesian predictive inference—you only have to know that the answer depends on what information we feed our calculations. What information is available? Tons. We know who the Lions will play and we can guage those team’s individual players and their capabilities, and the same with the opposing coaches’ attitudes, the kinds of stadiums, and on and on. It’s really too much information and we can’t incorporate it in our equations simply, so we’ll limit ourselves to just the Lion’s record and assume all other information is somehow wrapped up in that record. But do we only use last year’s record? Or do we use more years?

If we consider only the “record year”, the 0-16, then there is just over a 50% chance that the Lions will repeat defeat and win no games. There is a 90% chance that they will win 2 games or less. And do you want to talk about sheer improbability? Then, using last year’s data only, the Lions have only 1 chance in a billion of winning all 16 games.

We can picture the whole thing like this:

The red line in the left box shows the probability of winning 0 games, 1 games, 2 games, etc., all the way to 16. The probability of winning 6 or more games is near 0. It’s not—it’s never—exactly 0, though. This is easier to see by looking at the plot on the right, which expresses the odds against winning. The odds against winning no games is less than 1, for example, and the odds against winning all 16 is 1 in a billion.

But these numbers don’t feel right, do they? We should probably take into account more than just last year’s wins and losses and input several past seasons into our calculations. We don’t want to go back too far in time, because historical teams’ structures will be too different than the current team’s (different coaches, players, etc.). But we can add past seasons year by year until we feel comfortable we have balanced including enough data with excluding data on teams that don’t “look like” the current one.

We can picture doing it like this:

We have already seen the red line: it is the probability of winning from 0 to 16 games using only last year’s record. The other lines show what happens to this probability when we add in successive years of data. The first addition is the 2007 season, so that the total data is the 2007-2008 seasons. This combination is hidden in the figure by other combinations, so we’ll move to the first visible one. That is the data from the 2003-2008 seasons (pale green).

Already, we have a considerably different picture from that produced using just the 2008 data. The probability of winning 0 games using the 2003-2008 set has fallen to 0.7%, which is just under 1%; in other words, it’s not very likely that the Lions will repeat their pathetic year.

Adding in more years doesn’t change the picture much. The largest combination is the 2000-2008 set, where the chance of winning no games is 0.6%. The chance of winning 4 or 5 games is highest (about 20%), and the chance of winning all games is still low. This next picture shows the odds against winning games. Even including all the data from 2000, the odds against winning all 16 games is still 100 million to 1. The lowest odds is for 4 games, which makes sense, because this is the most probable number of games the Lions will win.

No matter which way you slice the data, the Lions do not appear to have even a reasonable chance of a winning season. And it doesn’t look like they’ll lose all their games, either. But it is likely they will continue emanating a sulphurous-like stench each time they take the field

———————————————–

Note: also see this hard-hitting news report.

Briggs

1. Mr. Briggs,

My name is David Fishbein, born & raised in Detroit too.

I loved the article and analysis. I also find it interesting that your last name is what Tiger stadium used to be called from 1935-1961, “Briggs” stadium. Now to the point.

Your’s is the funniest article backed up by statistical data I’ve ever read about the hapless Lions. Brilliant & funny – too bad it’s all true. Yesterday I wrote this letter to the Detroit Free Press Sports writer, Michael Rosenberg. I hope it will support and humor you as well. Thanks again for your time.

Dave

The letter I sent out yesterday:

Dear Mr. Rosenberg,

My name is David Fishbein and I have been a Lions’ fan since I can remember (1962-3). I am 51. The Lions won their last championship in ’57!
I was born and raised in Detroit but have lived in Israel since ’83. This distance has not stopped me from rooting and following the Lions all my life.
We had season tickets for many years (1958-1975) when the Lions played at Tiger Stadium.
I never attended a game at the Pontiac Silverdome nor have I attended a game at Ford Field but I have followed the dismal team, year after year.

I have also written many emails to Detroit sports writers and have been rebuffed in the strongest possible terms by a Detroit News writer by the name of Mike O’ Hara but that is irrelevant now.

Back in the mid-60’s my late father, Dr. Herbert Fishbein, always lamented that the Lions were being held back from victory but what he termed the “Lions’ Front office”. I have come to realize that after 50 years, the Lions’ main problem has never really been player talent, coaches or fan support but continues to be the death-grip hold that William Clay Ford Sr. and Ford family have on the team.

I will not bore you with many details and analyses but the bottom line seems to be this and correct me if you think me wrong:

1) Even though symbolic, the Ford family must sell the team (which they are pertified to do) to another owner who will shake off the “Ford curse” and begin leading and managing them in a new direction…
2) There is no choice anymore but for sports officials and writers like yourself to call for either a fan boycott or team to be sold.

Does this sound too extreme? Then consider the following:

The team is the laughing stock of the NFL and holds some of the worst statistical records in the annals of the league.
How & what can justify a losing team, (barely profitable) to move to 2 expensive stadiums within the span of 30 years?
The Lions have tried to “rebrand” themselves with new uniforms and new look. Why? What about their core managment problems that lead them from losing season to losing season for the last 52!!! years?
Lions’ fans have been loyal through thick and thin (mostly thin) since the 1950’s. Why can’t you and other writers illuminate these issues?
Would it be too muntinous for Detroit sports writers to call for the team to be sold? Would it somehow be disloyal to the city of Detroit?
How much longer can a city’s spirit take a pounding?

It all seems so obvious from an objective point of view.

Thanks for your time and I hope you can give me some feedback on these issues.

Dave

2. Briggs says:

David,

Family rumor has it that we’re related to the old stadium namesake. I am also happy to report that there is no relation to the Lions.

3. Myron says:

Found this from a link on Climate Depot of all places. Funny but I must point out that it should be “lose” not “loss” in the title. Unless you retitle it, “What is the probability of a Detroit Lions loss in every game (again!)?”

4. Briggs says:

Myron, Damn! Thanks very much.

5. Doug M says:

I am not clear on how you got from here to there, and perhaps you can provide more information in a future article.

Is 2000 – 2003 data at all relevant? How much personel (player or front office) is on the team now that was also associated with the team then? In fincancial circle we use exponential weighting. The decision of how quickly to decay older data is always a subject of controversy.

If I were to approach this problem, using 2008 data only, I would say that Lions outscored their the Lions by a 2:1 margin. From that I would say that the chance that the Lions could have outscored their opponents is about 20%. With a 20% chance of victory, the chance that they could have lost 16 games is about 3%. Unlikely, but not imposible.

6. Doug M says:

Sorry, typing to fast.

1st sentence of Paragraph 3 — Lions opponents outscored the Lions by a 2:1 margin.

7. Mike Pauwels says:

Is it possible to weight the effect of earlier years on this year’s probability? It seems that 2007 performance would have a lot more relevance to this year’s performance than 2003, but that there could be some influence from 2003.

The analysis would be more interesting (but perhaps not to you) if applied to another team that had a less rare bad year.

8. JA says:

Over the very same years that the Lions were abysmal, global warming was purportedly taking place.
Coincidence? I think we all know the answer to that one!

9. DAV says:

If we’re going to pick on English, “lose” should be “will lose” (and presumably the time frame is “this season” or “remaining this season”.

“What is the probability the Detroit Lions lose every game” — zero if they’ve ever one one.

“What is the probability the Detroit Lions lose every game (again!)” — it’s impossible to repeat a never-ending streak so the answer is zero.

10. Myron says:

DAV
10 September 2009 at 12:41 pmIf weâ€™re going to pick on English

â€œWhat is the probability the Detroit Lions lose every gameâ€ â€” zero if theyâ€™ve ever one one.

one one or won one?

See what I’ve started?

11. Briggs says:

All,

There’s obviously lots more we could do with this data: exponentially down-weighting previous seasons is one, building a formal time series model is another, taking into account the other teams a third, and on and on. But is it really worth the effort?

12. SteveBrooklineMA says:

I’m baffled! Do you have a reference for how you are doing this?

13. DAV says:

Myron,

😀 What can I say?

14. Bernie says:

Are you saying that if I bet you \$0.01 on the Lions winning all 16 games and they did, you would pay me \$1,000,000?

15. Briggs says:

Bernie,

Sure. But there’s the transaction fee we have to discuss…(and the non-linearity of utility!)…

SteveBrooklineMA,

Well, I have an example of this in my class notes-book. It’s a football example, too. Briefly: fit a binomial to the observed and then integrate out parameters to produce new observable predictive distribution. Click on the book link up top and you’ll find a link to the code that does this.

John M,

Now we—like many from Detroit, unfortunately—form a diaspora.

16. Bernie says:

Matt:
OK, you can halve the odds! I will give you \$0.02 and you give me \$1,000,000 if I win? The check is in the mail!!

As for diaspora – “Those with get up and go, get up and go.”

17. David Fishbein says:

OK, nitpick as much as you like guys but does my proposal of a fan strike or press writers call for the team be traded seem viable to anyone?

Thanks,

Dave

18. Speed says:

If you had performed this exercise in September of 2008, what would the probability of a winless 2008 have season been? Less than 1%? Yet they managed to pull it off.

More appropriate (unless you are a Detroit fan) would be the probability of ANY team going winless for the season. Or over a period of five or ten seasons.

19. Briggs says:

Speed,

Excellent question. When I return to my computer, I’ll calculate this. My quick, rough guess is a bound of no larger than a 17% chance that at least one team will lose all 16 games. But this uses the fact that the probability of winning 0 games is fixed at 0.006, a number which is too high for teams other than the Lions. If that probability were fixed at, say, 0.001 (probably more realistic), then the probability of at least one team losing all 16 is about 3%.

Now, if that were true, if the probability of at least one team losing all 16 was 3%, then the probability of this happening over the course of, say, 30 years is 60%. Over 50 years it is about 80%. You get the idea: the longer the time period, the greater the chance that at least one team blows it.

Bernie,

You forgot the (healthy) transaction fee.

Dave,

I’ve been boycotting them for years. Helps to be in NYC where the only game they show is on Thanksgiving.

20. Speed says:

Briggs: The point being that one team having a winless season sometime over the entire history of the NFL was not worth all the airtime devoted to it last year. Again, unless you were a Detroit fan.

More interesting is why this didn’t happen sooner. Perhaps it’s because winning and losing are not mechanistic clockwork type events. A losing team will make changes in strategy, buy and sell players, fire the coach, move to a new stadium and so forth in a constant effort to improve. Which of course changes the odds from week to week.

As they say, “Past performance does not indicate future results” and “On any given Sunday.”

21. Doug M says:

The Lions flirted with competence in the Barry Sanders era.

David,

I have been trying to figgure out how to fire the owner in San Francisco for several years. I surrendered my seats, but that doesn’t do much. Football gets 90% of its revenue from TV. TV revenue is shared across the league. There is little incentive to improve the “fan experience.”

Much of the fan base will support their team, rain, snow, or shine, regardless of the lack of tallent on the field. Building momentum on the fan boycott is an impossibility (okay, an extreme improbability on the level of the Lions linking consecutive defeated seasons.)

22. Bernie says:

Matt:
OK, how much is the transaction fee? I think we are having a Tversky moment.

23. Bob Hawkins says:

The polar opposites of the 2008 Detroit Lions would be the 1972 Miami Doplhins (14-0) and the 2007 New England Patriots (16-0). The 1973 Dolphins went 12-2, and the 2008 Patriots went 11-5. Those results seem to be in line with your analysis.

24. Bernie says:

Matt:
I owe you \$0.02!! There goes the excitement for the season! Is this some kind of record?

25. Briggs says:

Bernie,

26. David Fishbein says:

To Doug M:

OK, we’ve got 18 consecutive losses under our belts. What is the next NFL or sports record?
When does the dike break? So far I see that Detoit sports writers just keep tallying up the casualties with fine analyses. When is enough enough, jeez, I miss Mel Farr, Charlie Sanders and Lem Barney, even when they loss a playoff berth to Dallas in 1970(?) with an 5-0 score…

27. Briggs says:

I don’t know about you, Dave, but I’m taking a sort of perverse delight in their decomposition. Maybe they really need to hit bottom, and have another whole losing season, before anything changes.

28. David Fishbein says:

Briggs,

Yes, there is a sort of joy one takes in their misery like they kind of deserve it but are there not limit to the depths to which they can sink? I mean, ok, a losing team, losing seasons but this pattern going on ad naseum for 50 years? Isn’t that already outside of the boundares of any norm in nature? My beef is not with a lousy team with a lousy record, my problem stems from the fact that I don’t understand fan and sports writer passivity. There’s always hope but when hope dissipates there’s desparation, when desparation disappears then what are you left with? Anyone?

29. David Fishbein says:

OK, guys 19 consecutive losses, what is the probability of a win? Does anybody even care any more or are we wasting our time even figuring the numbers? Are the Lions worth that effort?