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.