## 26 January 2015

### Somebody has to lose a coin flip...

But nobody loses more of them than the Minnesota Vikings:
"The Minnesota Vikings haven't exactly been lucky on coin tosses, either. Since 1999 (when Pro Football Reference started keeping track), the Vikings have won fewer coin tosses than any team in the National Football League, having done so just 111 times in those 16 seasons (256 total regular season games)... The table shows the win-loss records of teams in games where they win the coin toss."

1. Statistically this also means that they may stay at the bottom of this table forever since every following coin toss has a 50/50 chance, which makes it UNLIKELY that they can ever catch up to a 36 toss lead, or even the ~15 wins to average.

1. I don't think you're right about that assumption, but I was an English major. I'll wait for some of the more mathematically-adept readers to chime in.

2. Total losses is irrelevant. About half the teams have a winning percentage below .500 - this is a more meaningful measure. Total losses ties into the measurement the number of games played. The Houstan Texans right above them on the list are at .398 winning percentage, and that is still not the lowest with Cleveland at .344 - which seems almost implausible mathematically. The coach needs to send a directive to only call Heads (or Tails) consistently so that the number can rise towards .500

3. Those listed winning percentages are for Win-Loss records in actual games where the team listed won the toss, and are entirely plausible since Cleveland and Houston have been mostly terrible over the last 15 years. Also, the reason Houston is so far down on the list is that they weren't even a franchise until 2002 so they have >48 less coin flips than every other team. If you look at % won/total tosses, Houston is almost at the top (6th place actually). I thought the % might change the order significantly, but it doesn't really for any teams other than Houston (same top 5, still MN at bottom, etc.).

Also, a toss is missing somewhere. There are 4071 wins, but there should be 4072 (16 teams times 16 games/season times 32 teams minus 48 games Houston didn't play 1999-2002 divided by 2 for the winners only). I thought the missing one might be the infamous Pittsburgh hea-tails call, but that was in 1998.

To answer the above question about likelihood of the Vikings getting back to average, if they are a bit lucky each year and win 10/16 coin tosses, they will do it in 8 years. Straight odds of that happening are about 1.53%. This represents their best chance if they have the same luck each year. If they are only a little lucky and win 9/16 tosses, they will do it in 16 years which only has a 1.09% chance of happening. Similarly, 11/16 takes 5 years at 1.33% and 12/16 takes 4 years at 0.69%. Of course some combination of this could occur. But it's the Vikings, so they will probably continue to have terrible luck (see, e.g., 1998 NFC Championship game).

Also "interesting" to note is that they play the Packers twice a year, and lost 21/36 tosses against their rivals. Of those, the Vikings are 8/16 when they play at Lambeau (meaning MN calls the toss), and the Vikings are 4/16 at home (meaning GB calls the toss). Against the rest of the league, GB is 67/120 (55.8%) at home and 60/120 (50%) on the road. GB just really tends to beat on MN I guess.