Today I'm happy to feature the first guest post on If We Assume, written by fellow astronomer
Peter Yoachim! He's discussing the
nowfamous debacle by the
replacement referees (see also
here) that occurred in last night's Seattle Seahawks game (Some are calling it the "worst call in NFL history"). Take it away Peter...

Getty Images 
After watching the refs botch Monday Night Football (Go Seahawks!?), I was wondering if
there's a way to quantify
just how bad the NFL replacement referees
are.
One thing that stood out in the game was how many calls went the
Seahawks' way on the final drivewhich reminded me of the discussion of
homefield advantage in
Scorcasting. They
concluded that referee bias is the primary driver in homefield
advantage across sports. They even note that in the NFL from 19851998,
the home team won 58.5% of the time, but after instant replay was
introduced, the home team only won 56% of the games (19992008).
If the replacement refs are much worse than the regulars, we might
expect the homefield advantage to grow. My logic being, if the refs
are botching more calls, those botched calls will tend to be in favor of
the home team, that gives them an advantage, so they should win more.
How have home teams fared so far? After 48 games this NFL season, the
home teams
have a record of 31 wins and 17 losses, for a whopping 64.6%
win rate! But is that
significantly more than 56%? 31 wins is actually
only 4 more wins than we would have expected with the regular refs. As
always happens when I try to calculate the statistical significance of
something, I got bogged down in an arcane
wikipedia page, when it
told me to look up some value from a table. Whenever a statistician
tells me to look something up in a table, I reply, "Fuck that, I
can Monte Carlo this in 5 lines of Python." So I did:
#play 10,000 seasons of football with 48 games each
hg = np.random.rand(10000,48)
#home team wins 56% of the time
hg[np.where(hg <= 0.56)]=1
#the rest are losses
hg[np.where(hg < 1)]=0
#total up the wins per season
ack = np.sum(hg, axis=1)
print 'probability of home team winning 31 or more games with 19992008
refs = %.2f'%(np.size(np.where(ack >= 31)) /10000.*100)+'%'
If you run that, you find out that we would expect 31 (or more) home team
wins only 15% of the time. To turn it around:
85% of the time the home
teams have fewer wins at this point in the season. We normally say
something is significant when we reach the 5% level, so we're not there
yet. If the home teams keep winning at a 65% rate (or higher) for
34 more weeks we should make it to significance! That's about the only
reason I've found to root for the replacement refs sticking
arounddamned,
scabs!