American sports fans aren't known for their love of tied games. Other than MLS, the NFL is the only league to currently allow games to end in a tie and we usually go an entire season without even one tied game. Fearing that Americans couldn't support a soccer league with games that frequently ended in a draw, MLS initially decided to end all tied games with a shootout in its inaugural season. Not the penalty shootouts you're use to seeing in the World Cup or UEFA mind you, but more like a NHL-style shootout where players charge at the keeper and try to get a shot off before the 5-second clock runs out. Because that would be more American. For those of you who didn't have the pleasure to see one of these in person, by the magic of Youtube, you still can.
Now this is clearly a sub-optimal way to decide a winner. MLS did at least try to dissuade games from ending this way by awarding 3 points for a win in regulation and only 1 point for a shootout victory. So were Americans more entertained by a NHL-style shootout? Did less games end in a tie? Should we have expected them to?
The answer to the first question is of course subjective but my guess is that the answer is a resounding "no". Otherwise, we'd still have the shootout. To answer if less game ended in a tie and whether or not we should expect them to, we can turn to the data and probability theory. Let's first see what we should expect to happen with a shootout.
Consider, as we did in the last post, a league where all teams are of equal strength and the likelihood of any team winning, losing, or tying a game is equal to 1/3. Now with shootouts, when a game in regulation is tied each team will have a 50% chance to win the shootout. So we have 4 possible outcomes for any given team, they can win, lose, win in a shootout, or lose in a shootout. The probabilities for the outcomes are PW=PL=1/3 and PSOW=PSOL=1/6. So we can model the outcomes of the games as draws from a multinomial distribution with four outcomes. Of course these probabilities are somewhat arbitrary. We could just as easily assume any numbers where PW=PL and PSOW=PSOL and still have an ideal competitive league. The probabilities chosen are simply for ease of illustration.
To be specific, the probability density function (pdf) of points is
Before any game, a team can expect
with a variance of
so that
If a game is tied in regulation, then each team has a 50% chance of winning or losing and the conditional expectation becomes
with a variance of
so that
The expected points earned in a shootout is much less than in regulation but does have a lower variance. So although the expected payoff in a shootout is lower, it is more certain. However, given the large difference in expected outcomes, a team would have to be severely risk averse to prefer to end a game in a shootout. Or, abstracting from both teams being of equal strength, one team would have to believe it had a very low chance of winning in regulation to prefer the shootout. There may be evidence that this is what the San Jose Clash were thinking in 1999 with their record 13 shootouts (more on that later).
So did this setup give teams incentive to try to win in regulation and avoid shootouts altogether? Let's look at what the distributions for expected points are for games are now without the shootout. We can repeat the process above for the situation where teams can win, lose, or tie with equal probability (1/3). Or we could just plug in a value of 1 game played (gp=1) in the calculation we did in the last post. Either way, we'll get
and of course if a game ends in a tie, each team gets a guaranteed 1 point with 0 variance. Now let's look at this all in a convenient table.
As we can see from the first 3 columns of data, the expected points earned when going from regulation to a shootout decreases by two-thirds (-0.667) and the outcome is much more certain. In the last 3 columns, we see that the decrease in expected points after regulation is half that of the shootout era (-0.333 vs. -0.666)! Furthermore, it's a guaranteed outcome of 1 point each. So having a tied game in regulation loses less points in expectation without the shootout. Saying it another way, teams have less incentive to avoid tied games when there is no shootout. So it seems the answer to the question of whether we should expect less ties in the shootout era is, yes. The payoff structure did suit the game well for avoiding games that were tied in regulation. But did it actually work?
You can recreate the graphs using this data and this R script.
While the graph above indicates that games were less likely in the initial years to end in a tie after 90 minutes, the switch doesn't seem to perfectly coincide with the end of the shootout era, which lasted from 1996 to 1999. So although the answer to our question of whether there was actually a higher chance of ending a game in regulation during the shootout era is "yes", we now have new questions that need to be answered. What is going on in 1999 that there were so many games going to shootout? And more importantly, why does the jump in games tied in regulation occur in 2003 and not immediately after the shootout era?
For a hint, below is the same graph with lines drawn around the period of time for which MLS essentially had a single table. I say "essentially" because there were actually multiple conferences during this time but entry into the playoffs was granted to the top 8 teams regardless of conference. This led to a somewhat odd situation where the entire Western Conference made the playoffs in 2002.
We'll dig into why divisions matter when it comes to whether or not games end in a tie next time. Until then, I'll leave you with pop culture's initial reaction to MLS a la The Simpsons.
| Regulation (SO) | Shootout | Difference (SO) | Regulation (Ties) | Tie | Difference (Ties) | |
|---|---|---|---|---|---|---|
| Expected Value | 1.167 | 0.50 | -0.667 | 1.333 | 1.000 | -0.333 |
| Variance | 1.806 | 0.250 | -1.556 | 1.556 | 0 | -1.556 |
As we can see from the first 3 columns of data, the expected points earned when going from regulation to a shootout decreases by two-thirds (-0.667) and the outcome is much more certain. In the last 3 columns, we see that the decrease in expected points after regulation is half that of the shootout era (-0.333 vs. -0.666)! Furthermore, it's a guaranteed outcome of 1 point each. So having a tied game in regulation loses less points in expectation without the shootout. Saying it another way, teams have less incentive to avoid tied games when there is no shootout. So it seems the answer to the question of whether we should expect less ties in the shootout era is, yes. The payoff structure did suit the game well for avoiding games that were tied in regulation. But did it actually work?
You can recreate the graphs using this data and this R script.
While the graph above indicates that games were less likely in the initial years to end in a tie after 90 minutes, the switch doesn't seem to perfectly coincide with the end of the shootout era, which lasted from 1996 to 1999. So although the answer to our question of whether there was actually a higher chance of ending a game in regulation during the shootout era is "yes", we now have new questions that need to be answered. What is going on in 1999 that there were so many games going to shootout? And more importantly, why does the jump in games tied in regulation occur in 2003 and not immediately after the shootout era?
For a hint, below is the same graph with lines drawn around the period of time for which MLS essentially had a single table. I say "essentially" because there were actually multiple conferences during this time but entry into the playoffs was granted to the top 8 teams regardless of conference. This led to a somewhat odd situation where the entire Western Conference made the playoffs in 2002.
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