Now that the college season is over, football fans can concentrate on what really matters: Tebow-mania!  Timmy Terrific has led the Denver Broncos to the AFC Divisional Round of the NFL playoffs.  The Broncos, who started the season 1-4, turned their season around by winning 7 of their last 11 games, many in dramatic fashion, with Mr. Tebow at the helm — good enough to squeak into the playoffs at 8-8 and even earn a home playoff game.  In that game, played Sunday, January 8th, they drew the heavily favored defending AFC champs the Pittsburgh Steelers, who took an early 6-0 lead.  Denver battled back with a big second quarter, but the Steelers made their own charge and ultimately the game went to overtime.  This was the first time a playoff game had gone to overtime since the inception of new NFL overtime rules.  Previously, overtime was sudden death, with the first team to score, either a touchdown or field goal (or safety), winning the game.  Under the new rules, only a touchdown on the first possession will end the game immediately; a field goal allows the other team a chance to possess the ball.  Needless to say, Denver won the coin toss (Pittsburgh called tails) and needed only one play to score a touchdown.  The play was an 80 yard pass over the middle that went the distance.One reason this occurred was because the Steelers had been bringing a lot of defenders close to the line of scrimmage, as they did not believe Tebow could beat them with his passing ability.  It was widely believed among the “experts” that Tebow, who is one of the greatest college football players of all time, and his style of play would not translate to success in the NFL.  Many people still believe this.

I hadn’t really thought much about Tebow one way or the other until one of his stats caught my eye.  In Denver’s week 10 win over the Kansas City Chiefs, Tebow’s passer rating was 102.6 based on 2 completions in 8 attempts, good for 69 yards, 1 touchdown, and no interceptions.  For some context, 102.6 was good enough for 7th best rating among starting quarterbacks that week.  This seemed odd to me since 2 for 8, 69 yards, and 1 touchdown seems like a terrible game.

So this got me wondering: What exactly is passer rating?  This website describes the formula in detail along with some of its history, but the basics are as follows.

1. Compute completions divided by passing attempts, subtract 0.3, and multiply by 5.
2. Compute yards divided by passing attempts, subtract 3, and multiple by 0.25
3. Compute touchdowns divided by passing attempts and multiply by 20.
4. Compute interceptions divided by passing attempts, multiply this by 25, and subtract this from 2.375

If any of the results of the four parts is less than 0 or greater than 2.375, that component is rounded up or down to the respective bound.  Now, add the four, possibly rounded, components together, multiply by 100, and divide by 6.  This yields a maximum score of 158.3.  (I swear I didn’t just make all of that up; the NFL actually uses this.)

Now since I like football and I love R, I decided to do some graphical exploring with passer rating.  Since the only topic anyone wants to talk about in the NFL right now is Tim Tebow, I figured I had to look at him.  And who better to compare him to than his opponent next week, three time Super Bowl champion Patriots quarterback Tom Brady.  Using the data from their regular season games (Tebow started 11 games and came in at half time in week 5; Brady started all 16), I created these graphs for Tom Brady and Tim Tebow.  Each individual graph shows how quarterback rating would vary based on number of completions and total passing yards for a fixed number of passing attempts, touchdowns, and interceptions. The green dot in each plot represents where each quarterback actually fell that week in their game.

What stands out to me in looking at these graphs is Brady’s consistency.  The green Brady dot seems to be always in the right, upper half of the graph.  Week in and week out he puts up around 300 yards (with the occasional 517 yard game thrown in) and a completion percentage in the mid to high 60s.  In fact, Brady had a completion percentage of over 50% in every single game this season.

Tebow, on the other hand, is, to put it politely, all over the place.  In week 13, Tebow put up a nearly perfect passer rating of 149.3, which is almost 14 points higher than Brady’s best passer rating of the season.  On the other hand, Tebow had a lower passer rating than Brady’s worst passer rating, 75.4, in 5 out of the 12 games Tebow started.  So you could say that almost half of the time this season, Tebow was worse than Brady’s worst.

This all adds up to the fact that the Broncos should lose to the Patriots.  Based on the stats, Brady is too good and Tebow is too inconsistent to amount to a Denver victory.  Of course, while you may find all of this interesting, in the end none of these numbers or pretty pictures mean anything at all to Tim Tebow, who, as they say, only cares about one stat and that’s winning.