# Zero

September 11, 2009

My fantasy football team, Does Not Compute, scored a respectable 74 points during week 1, thanks in large part to Thomas Jones who scored twice as many points as Yahoo! projected. Unfortunately my opponent, a long-time friend who has yet to rub salt in my eyes, scored 83 points, leaving Does Not Compute with the same record as my beloved Bears: 0-1.

The thing that irritates me about the loss is that Greg Olsen, the tight end on both my fantasy and real teams, had one reception for eight yards resulting in a grand total of ZERO fantasy points. Should I trade him away?

Naturally, I could not help but wonder whether this would be a common occurance for Olsen or whether this was a fluke of a performance as his quarterback Jay Cutler adjusts to a new offense. From Fig. 2 of my previous post, it was clear that all offensive positions frequently do not score any fantasy points. It just so happens that tight ends are the worst offenders (yuk yuk) and do not score any fantasy points 59% of the time.

Let me repeat that: 59% of the time, tight ends score zero points. Do you carry an umbrella if a weatherman says there is a 59% chance of rain? I do; 59% is a lot.

It is also misleading in this case. Most active NFL players are held in reserve and rarely play a single down. Those that do play can get injured and need to sit out several consecutive games. Both of these effects therefore introduce correlations in the frequency with which players score zero fantasy points, consequently biasing the 59% average in a non-trivial manner.

To better understand the
origins of the “zero effect”, I propose the following
simple Markov
model. In this model, a player either plays in a game or he
does not (in which case he can not score any fantasy points). We
then assume that a player plays in games during consecutive weeks
with probability *p* and with probability *q* a
player does not play in games during consecutive weeks. We can
then estimate these parameters *p* and *q* for each
player in the NFL to obtain a more detailed understanding of the
“zero effect” (Fig. 1).

Based on this description of players, three groups of players emerge: starters, who play in every game, are in the lower right-hand corner (*p*=1, *q*=0); bench warmers, who never play, are in the upper left-hand corner (*p*=0, *q*=1); and role players, who neither ride the bench nor start consistently. Interestingly, Olsen is a role player (*p*=0.83, *q*=0.29) and, because of his parameterization, we can see that there is almost a 30% chance that he will score zero points again next week.

While a 30% chance may be enough of a chance for some people to grab their umbrella, I think I will weather the storm and not trade away Olsen.