Sports Basics Overlooked: The 2 point conversion

Often overlooked in sports are common trends that have been around for years...shooting free throws overhand, taking jump shots from anywhere on the court if you have a good shot, picking a corner and height for penalty kicks, why nba teams dribble to half court instead of rolling the ball, and what I will look at briefly today: the option to kick an extra point in college football or attempt 2 point conversions.

For simplicity, we will just look at the first half of games and success rates.  This is because the second half of the game brings in much more complexities that change the math due to the situational and point differences with less time on the clock.  An obvious one would be after tying the game with 10 seconds left, and being able to go for 2 or kick the extra point.  That is an extreme example, but drives the point home the easiest as to why I won't discuss it, and will leave it to a Yale stat major to look at in the future.

Almost always, a coach routinely just sends his kicking unit out after scoring a touchdown, but WHY?   I'm under the impression that sports will nearly always stick to the norm in situations until someone clearly shows that the original mold is flawed.  This has become evident after my years abroad and seeing how almost the whole World tries to fit in to this conventional way of thinking that you need to go to high school, college, then work for a steady company.  That is another topic for another day though.

This is where basic math comes in to play, the answer to why should be looked at with simple algebra.

an extra point counts as 1 point

and a 2 point conversion counts for 2 points

Now, earlier in the game when other factors are less significant, the only math needed to do is whether the 2 point conversion will yield more points than an extra point**.  This is very basic

average yield = success rate * points for success

avg yield (extra point) = success rate(ex pt) * 1

avg yield (2 point conv) = success rate (pt) * 2

If avg yield (2 point conv) > avg yield (extra point), then coaches all over should be rethinking their normal game plans for these situations.


Let's take a look at college football with statistics from 2008-2011 which is a good indicator of the present times and gives us a 4 year sample.1


2 point success rate
2008: 37.0%
2009: 40.6%
2010: 40.0%
2011: 43.5%

1 point success rate
2008: 96.4%
2009: 95.8%
2010: 96.4%
2011: 96.2%


You would need to actually take average weighted averages here, but again, for simplicity I will merely take the average of each of these (it's close enough for my blog).

2 point success rate  = (.37+.406+.40+.435) / 4 = 0.40275 = ~40.3%

1 point success rate = (0.964+0.958+0.964+0.962) / 4 = 0.962 = 96.2%

Subbing these numbers in to our basics equations will give us the yields on average over the past 4 years.


avg yield (1pt - extra point) = .962*1 = 0.962 points per attempt

avg yield (2pt conversion) = .403*2 = 0.806 points per attempt


Damnit! 0.962 points > 0.806 points, so we should always go for the extra point in college football when other factors are less signicant....or SHOULD WE?

While it is clear that the extra point does maximize points on average, we often are not dealing with the average.



These often come in to play in games earlier in the college football season when we see powerhouses playing weaker schools.  In general, their offenses and offensive lines are much more prolific than the average weight means taken above.  Couple this with the fact that the defenses they face in the early weeks are generally much weaker on defense along with much weaker defensive lines.  These variables will significantly push the success rate of the 2 point conversion higher for the powerhouse teams here.

Unfortnuately, it is extremely difficult to classify these games, let alone find any meaningful sample to classify these.  The main thing we can do is to find the breakeven success rate needed for coaches to know where it is neutral between kicking the extra point or going for the 2 point conversion.

x*2 = 0.962 will be our breakeven point, solving for x gives us 48.1% as the breakeven point for coaches.  Thus, earlier in games, when the other variables are much less significant, a coach could basically flip a coin on the sideline for fun in deciding when to go for 2 or kick the extra point.

This result shows that the coach should be 7.8% (0.481-0.403 = 0.078) more confident in his team's chance of success in the 2 point conversion than the norm in the situation or greater to realize it yields more points.  While this will be hard to classify, it is almost certainly true for teams with great offensive lines such as Michigan State and Alabama when they are playing very inferior teams early in the season.  Thus, the coaches should highly consider going for 2 points here instead of the extra points.  Just some food for thought.  For more late game scenarios and some models, refer to this site.

http://www.advancedfootballanalytics.com/index.php/home/research/20-game-strategy/74-two-point-conversion-calculator

-Presh





**please note that I ignored the odds of a team returning a point conversion for a score and games in which are likely to be really low scoring and more intensive math has to be done.  My apologies, but these are rare occurrences and not worth my time.

1) http://aztecmesa.proboards.com/thread/24784

FAST AND CONSISTENT WINS THE RACE

The saying "slow and steady wins the race" always seems to be in the back of my mind.  However, I don't really abide or believe in it, I see it as a classic saying to try and keep those falling behind to stay motivated to not give up.  I believe more in my own thinking of "fast and consistent wins the race".  Through out my poker career, I was fortunate to get great at one game and just took off running with it.  I pushed the studying, I pushed the hours, I pushed all that I could with it.  Below is a graph of my lifetime results in this game, I have left out the monetary values on the y-axis as I don't think it's relevant for people to see how much I've earned.





Big bets represent units that we use to track our winnings, and the stakes I've played over my career range from $1/$2 to $500/$1,000 where the figures 2 and 1,000 here would equal 1 big bet for these games.
Anyhow, after a great career, I've began to venture in to other forms of poker to increase my overall earn and future.   Below is my graph for this game, the y-axis here corresponds to big blinds, 100 blinds is equivalent to a standard buy-in, so I am up 60 buy ins so far in this game at stakes ranging from buy ins of $200-$1,000.





I have carried over too large of an ego to this game though, and just assumed my poker prowess would take me on a nice ride to the top.  This is extremely far from the truth, the fact is I just have not put in the hours or thought about the game deep enough to deserve to be a big winner yet.  This is clear from my disappointing graph thus far.

I have been slow and steady instead of fast and consistent, and it's led to an extremely frustrating start to my career in this game.  I've stepped back this past week and cut my ego out of it, I will be studying more and analyzing my game much harder.  In addition, I'll be utilizing my best poker friends as resources to accelerate the learning curve.  I was not proactive over the last year in learning and it is very apparent from the above graph.  That is a mere roadblock in my career.  It is very common for people to study and put in countless hours to get good at a field, and then let complacency sit in when you think you've reached the pinnacle.  I lost some of the drive and desire.  It has been humbling thus far learning this game, but I have the drive again and the next graph I post of this game will be much more impressive.  

The morale of this post is to basically tell those who ease you in to believing that slow and steady wins the race are merely behind the curves themselves and trying to keep you there with them, or that their drive is not too strong to achieve greatness in their field.  Push the limits, push the boundaries, climb up the exponential ladder to success.  Feel free to leave any comments below and I'll respond to them.

-P12