### A MODEL FOR OPTIMIZING INTRA-MATCH TACTICAL CHANGES

*Editor's Note: This the abridged version of this post. If you really want to get into the weeds on this then 1) you're a lovable nerd, and 2) you should click this link for Jared's detailed 5,000 word version of this post. *

By Jared Young (@jaredeyoung)

"Tottenham might as well have put the team bus in front of their goal," said **Jose Mourinho** in 2004 following a draw between his Chelsea club and the Spurs. Although he would later say the phrase was one typically used in Portugal, Mourinho was credited with coining the phrase 'parking the bus,' which described a team that was sitting the whole team behind the ball in an effort to block the goal. It's less frequent for team to play a full 90 minutes that way, but often teams with a lead will change tactics late in the game and park the bus in an effort to ensure victory. To do this they move their line of defensive pressure back toward the goal, committing more players to defense. The other team is allowed more possession of the ball but the bet is they'll have a lower chance of actually scoring the equalizer.

During this year’s FA Cup Final, Arsenal took a 1-0 lead over Aston Villa into halftime. They had thoroughly dominated the game and had taken eight shots to Aston Villa’s one. In that case, the obvious tactical choice was to change nothing at all. Arsenal logically kept up the pressure just as they did in the first half, added three more goals and finished with a shot advantage of sixteen to two.

The FA Cup Final shows us that it’s not always clear that a team should park the bus if they have a lead. Arsenal was in top form at that time, and were clearly the dominant side. They didn’t need to sit back defensively to ensure victory.

What are the factors that would indicate a team should change tactics, such as parking the bus? The goal of this post is walk through the building of a model that can be used to show teams when to park the bus and when to stay the course. The model should also be able to answer other tactical questions as well.

What changes in a game when a team moves their pressure line back toward their goal? From a results point of view there are four key changes to consider. The first is that the team down a goal will very likely increase the rate at which they shoot the ball. By lowering the pressure line, teams will concede possession and allow the opposition closer to the goal. This will result in more shots. The second change is that the team down a goal will finish a lower percentage of those shots. The point of committing more players to defense is to make it more difficult for the shooters to actually score - evidence of this trade-off to follow.

The third change is that the defensive team will shoot less often than they were previously. Conceding possession will mean they have the ball less and will have fewer chance to score. However, the fourth change is that the defensive team should be able to finish a higher percentage of their shots. This is the standard risk reward trade off of the counter attacking team. By sitting the defense deeper, they open up more space to cover when they get the ball. The best approach is to attack that space quickly, and when they do, they find fewer defenders to deal with and shoot at a higher percentage.

Below are charts that indicate that these four variables do move in relation to each other. The below chart shows that lowering the defensive pressure line does increase the rate at which opponents take shots. Passes allowed per defensive action is a metric that indicates how much pressure a team is putting on the ball. A higher number of passes per action indicates a low amount of pressure. A lower number of passes indicates a higher amount of pressure. This chart reveals that as defensive pressure is relaxed the opponent is able to take more shots.

The next chart shows that when one team takes more shots, the opposing team on average takes less shots. The blue points show the away shots on the vertical axis and the home team is on the horizontal axis. If a home team takes twenty shots the blue line indicates that the away team will take on average about 10 shots. If an away team takes 20 shots a home team would take on average about 13. This graph reveals that a team’s shot taking frequency is indirectly related the rate of their opponent’s shots.

The next chart shows that as frequency of shots increases the finishing rate decreases. This aligns with what is expected; lower defensive pressure allows more shots but at a lower rate of success. As one team increases their shot taking frequency their finishing rate decreases and their opponents shot frequency while decrease while their finishing rate increases.

As an additional note, we can extract from the regression equation that the optimal number of shots to maximize goals scored is about 18 (18.1, in fact, using that old Calc I). Below is the resulting curve. This chart highlights why sitting deep can work if the opponents shot frequency is high enough. Expected goals scored actually goes down after teams shoot more than 18.1 shots per 90.

Because the shot frequency relationship is different for home and away teams, the finishing rate should be looked at by home and away. Here is a chart of the MLS finishing rates by shots attempted split by home and away. There is about a 1.5% difference in finishing rates between home and away team, and this difference is even across all shot frequencies.

Changing the four variables by home and away teams - opponent shots, opponent finishing rate, team shots, team finishing rate - is the basis of this tactical model to determine the impact of changing the defensive pressure line. Before the model is built there needs to be some simplifying assumptions.

The four key assumptions:

1. **Shots occur in a uniform distribution**. Example: If a team is going to take three shots in a ten minute period this assumption means that those shots would happen randomly across the ten minutes, and there would be no bias to them happening earlier or later in the ten minute period.

2. **The teams in the model represent average teams**. There will be teams, as in the Arsenal versus Aston Villa example, where one team is clearly dominant over another. This model will initially only look at these curves as an average.

3. **Finishing Rate does not change as the game goes on**. The longer version of this article examines this assumption in more detail.

4. **The team setting the defensive pressure line is still looking to score**. This basically means that a team that is focusing on defense will still try to score on the counter and won’t just kick the ball back to the offense once they gain possession. This is important because it means that a coach’s objective is more than just stopping a goal, it is to increase the team’s chance of scoring the next goal. This will be the objective of the model.

The longer version of this post looks at how Finishing Rates and Shot Frequencies change for home and away side in the +1 game state (when one team leads by one goal). In this abridged version we skip to the model output for both away and home teams, and show scenarios with and without a particular game state.

**The model**

Combining these curves together with the away team up one goal the model can now be built to determine the impact of changing the tactic in question. Here's an example of how the model will work – an away team is up one in the 80th minute, and they reduce their pressure line so that the home team is now shooting at a rate of 25 shots per 90. The away team would now only be shooting at a rate of 8.5 shots per game. With just 10 minutes to go, the away team is forecasted to average under two shots while the home team is going to shoot nearly six. The home team will have a finishing rate of about 5% and the away team, now striking on the counter, will have a finishing rate of 14%. Is that a good move? The answer is, of course, it depends.

**Example one: Away team up one goal**

Here is the first model output chart to examine. The blue and orange points in these charts reveal the shots attempted in relation to each other. The gray line in this case represents the probability that the away team will score the next goal without being adjusted for game state.

Given the gray curve is U-shaped the best tactical move is going to be a function of where a team currently sits on the curve. Let’s take an example where the away team is up one goal and both teams are attempting shots at the exact same rate, at 10 shots per 90. This would be where the orange and blue lines intersect. The away team has a 50% chance of scoring the next goal according to the gray curve. The away coach wants to make a tactical change to increase those chances, and there are two options. The team can attempt to possess the ball more and create more shots. If they can increase their shots to 11 per 90 then they increase the likelihood of scoring the next goal to 60%. They could also choose to bunker in and reduce their possession. However, in order to improve their chances of scoring the next goal they would need to allow the home team to shoot the ball at more than 30 shots per 90 minutes, or once every three minutes. That means they would have to sit very deep to allow that to happen. The change would be extreme. It would be less of a change and possibly make more sense to attempt increase possession.

The team could attempt to push for more possession and if they see the game going in the wrong direction, they could then opt to sit deep. However, the model shows that in order for parking the bus to make sense, a team must fully commit. Going part of the way appears to be very dangerous as the odds of scoring the next goal can decrease to as low as 40%.

The yellow and blue curves are adjusted for game state where the away team is up one goal. The yellow curve, representing the probability of scoring the next goal at halftime, reveals that the away team's probably of scoring next are lower when up a goal. The blue curve gives an indication of how this probably will change as the game evolves. The benefits of playing possession oriented soccer diminish while the benefits of sitting deep stay flat.

**Example two: Home team up one goal**

Now the home team is up one goal in the 80th minute. The gray curve is higher for home teams than for away teams. The worst case scenario for the home team is that they have a 50% chance of scoring the next goal.

The other things to notice is there is far more upside for the home team to bunker down and secure the win due to the fact that the away team will be expected to get off fewer shots and finish less of them. The home team will always have at least a 50% chance of scoring the next goal, but they can give themselves up to a 90% chance by sitting deeper on defense.

Again, the yellow curve now represents the odds adjusted for game state at half time. The blue curve is that same probability in the 70th minute. In the case of the away team being up one, they end up shooting less frequently and finishing a lower percentage of those shots than the unadjusted model suggests, so in reality, they have a much lower likelihood of scoring the next goal. Notice the model actually shifts slightly in favor of possessing the ball. The yellow and gray lines converge just a bit as the away team takes more shots.

According to the dark blue line, as the game evolves the park the bus strategy gets less and less appealing. The probability is still in favor of sitting deep but the benefit of that strategy weakens as the game evolves.

**Going back to the Arsenal - Aston Villa FA Cup Final example**

Given Arsenal’s dominance in the game assume Arsenal had a home team advantage. At half time they have eight shots, or a rate of sixteen per 90 minutes. The away team should be shooting twelve shots per 90, but at halftime had only mustered one attempt. Given Arsenal’s shooting frequency rate of sixteen the model says they have a 60% chance of scoring the next goal. Given Aston Villa wasn’t even shooting at their expected shooting frequency, the odds were much much greater. In order to improve their chances of scoring the next goal Arsene Wenger would have had to employ an extremely bunkered defense to increase their odds. It clearly made little sense to make such a shift and this model highlights how that math plays out.

**Closing thoughts**

First of all, if you made it this far, I very much appreciate you taking the time to soak this in. There are a couple of key points I believe this model brings to light that I want to highlight.

1. **A team should push for either extreme possession or extreme concession**. Playing in the middle, in any game state, reduces a team’s chances of scoring the next goal. Coaches should commit to one pressure line tactic or the other and not remain in no man’s land. This seems at odds with how a number of MLS teams operate.

2. Which approach the coach chooses should be a **function of where on the curve the game is currently being played**. In the case of the Arsenal versus Aston Villa FA Cup Final, it made sense for Arsene Wenger to maintain their position of control. If an away or home team is up one and is losing the shots against battle, sitting deeper will be a more effective tactic to increase their odds of scoring the next goal.

3. Counter to current thinking, a home team with a goal advantage stands to improve their odds of winning more by parking the bus than an away team in the same situation, although this advantage diminishes as the game matures. Current thinking says the away team should bunker in to get the three points and the home team should try to control possession. This model contradicts that logic because the home team will be finishing a higher rate of shots at home and will produce more shots than expected, making a counter strategy more appealing.

4. The limits on the model can be stretched further to address the following questions:

a. Does the effectiveness of a low defensive line diminish over time? Are the odds of success consistent over 30 minutes or does the tactic have a limited shelf life?

b. How do the curves change when a good team is playing against a poor team?

c. Can data be collected by Opta or another provider to better understand the impact of defensive pressure lines on shots attempted? It would be great to isolate the times when teams sit more players behind the ball and observe the impacts on shot frequency and finishing.

And I’m sure there are many other questions and ways to push the model. Please let me know if you have any at @Jaredeyoung on twitter. Next time your team is up a goal and looking to finish off a game, how do they approach it?