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
1 point success rate
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.
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.
**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.