Random Samples: Why Penalty Kicks Are A Necessary Evil In Soccer

July 19, 2011 - by Austin Link

After more than two hours of hard fought championship level soccer, the winner of the 2011 women’s World Cup was crowned by a controversial match ending mechanism: penalty kicks. Despite all of the skill, stamina, and strategy required to win at the World Cup level of play, eight simple swings of the leg decided one of the biggest sporting events of the year.

Many fans and experts alike considered it a tragic way to end a beautiful game.

The result begs the question: Is there really a convincing reason for FIFA to use penalty kicks to decide close matches – especially in games that determine a world champion?

Exploring An Alternative

While the golden goal experiment did not turn out as FIFA hoped, the option remains just to play additional overtime periods. This approach would move soccer more in line with baseball’s extra innings structure, where both teams get an equivalent yet finite opportunity to score. If the teams are still tied at the end of one extra period, they simply play another until a victor is determined, ad infinitum.

To examine the likely impact of such a rule change, we did some basic math, first looking at the average rate that goals were scored in the 2011 women’s World Cup. By making a few assumptions along the way, we can then forecast the expected number of overtime periods that would be played if penalty kick endings were abolished.

On the whole, teams in the tournament scored 1.26 goals per every 90 minutes played. At that rate, there’s roughly a 2/3 chance that a women’s World Cup team will go an entire 30-minute overtime period without scoring.

Goals Scored In One OT Period	Average Team’s Odds
0	65.7%
1	27.6%
2	5.8%
3	0.8%
4	0.1%

We can now use these odds to do a scenario analysis of the potential outcomes of a World Cup final that goes into unlimited extra periods. In other words, what is the chance that one team scores in the first overtime but the other team doesn’t? What is the chance that neither team scores in the first overtime but only one team scores in the second overtime? And so on.

A Slight Problem

In doing this analysis, we do need to take a few shortcuts to simplify the math. For our quick study, we assumed that goals are equally likely to be scored at any point in time during an overtime period, and that the two teams playing are approximately equal in scoring ability. (For a USA vs. Japan championship game that went to extra time, those feel like safe assumptions.)

What the math tells us is that there’s a 51.1% chance that two equally matched teams averaging 1.26 goals per 90 minutes will still be tied at the end of the first 30-minute overtime period. That translates to an expected 2.04 overtime periods needed to decide the match, or more than a full hour of additional playing time.

While there’s little doubt that playing for an additional hour would degrade the quality of play on the field, the table below illustrates how much worse things could realistically get. An expected value of 2.04 overtime periods means that there are decent odds the match would last much longer than that.

In fact, there would be about a 7% chance that it would take 5 or more overtime periods to determine a winner:

Overtimes Required	Likelihood
1	48.9%
2	25.0%
3	12.8%
4	6.5%
5	3.3%
6	1.7%
7	0.9%
8+	0.9%

It’s safe to say that a match structure in which it’s not unheard of for a 90-minute contest to be followed by more than 150 minutes of overtime play is undesirable on many fronts, unless watching two utterly exhausted teams (who are likely at far less than full numbers due players being sent off) walk up and down a soccer pitch is entertaining to you. By the time a fifth overtime rolls around, skill will have little to do with determining a winner.

The Verdict

What else can FIFA do then? Golden Goals result in play that is too defensive and make the match environment too large of a factor in the outcome, but allowing unlimited 30-minute overtime periods doesn’t seem feasible either.

Altering the length of continued extra play could make a slight difference. For example, playing 20-minute overtime periods instead of 30-minute periods would knock the expected overtime play duration down by 16%. Yet even a 16% reduction still leaves a high likelihood that overtime duration would outlast regular play. Imagine a baseball game that lasts 20 to 30 innings, and you get the point.

All of this analysis combines to leave only one option that ends a game in both a timely and relatively skillful manner: penalty kicks. Whether we like them or not as fans, game-ending penalty kicks are the least of the available evils for determining a winner in a close soccer match.