The big news this weekend was obviously Lionel Messi’s injury, and the question is what Barcelona will do without him. Michael Caley issued his take at the Washington Post saying that Barcelona will largely be fine without him, and ultimately I agree. I ran Barcelona through my transfer simulator, and found that Messi gives Barcelona on average an approximately 5% greater chance of winning each game he plays in over his replacement (El Haddadi). Over 8 games that translates to a little less than a point.

That’s not a big difference, so Barcelona shouldn’t really worry too much. As great as he is, the rest of the team is strong enough (and the rest of La Liga is weak enough) that it shouldn’t make a huge difference. However, the average doesn’t tell the full story and if we’re going to call what we do “fancy stats” then we need to do better than just calculating the average and moving on.

To see the potential loss of points, I ran 100,000 simulations of an 8 game window for Barcelona with Messi, and then ran 100,000 simulations of an 8 game window for Barcelona without Messi. I added up the total number of points for each of the 200,000 windows, and compared each window with Messi to the corresponding one without Messi. Here’s what I found.

The first plot isn’t the easiest to read, so let me explain: the height of the line (measured by the y-axis) represents the proportion of simulations where Barcelona earns a specific number of points (represented on the x-axis). The dark blue, solid line represents Barcelona with Messi, the light blue, dashed line, represents Barcelona without Messi. Notice the higher light blue line at lower values on the x-axis: this shows Barcelona is significantly more likely to earn lower numbers of points without Messi. Then notice the higher dark blue line at higher values on the x-axis, showing Barcelona is more likely to earn higher numbers of points with Messi.

The next plot is a density plot showing the difference between the two scenarios: how often will Barcelona gain/lose certain point values when Messi plays compared to when Messi doesn’t play? The y-axis represents the frequency of each result in my simulations, and the x-axis represents the number of points Barcelona gained in each of the simulations.

The distribution looks relatively normally distributed (a rough “bell curve”) with a mean around 1, but the standard deviation is somewhere around 5. Barcelona is more likely to do well when Messi plays compared to when he doesn’t, but there is significant variation here. They could easily improve by 5 points, and there’s a 5% chance they improve by more than 11 (out of 24) points with Messi in the lineup compared to El Haddadi.

The final play I’m going to call the “luck” index. It shows the percentile of each possible point gain/loss based on Messi playing compared to El Haddadi. Basically depending on Barcelona’s luck, this is how many points they can expect to gain/lose.

Once again, this represents the difference in Messi vs. El Haddadi at every 10th percentile. So you can see if Barcelona gets really lucky (best 10% of all simulations) they will pick up 7 points with Messi. Even slightly above average luck (70th percentile, or 30% of the time) they gain 3 points with Messi playing over 8 games.

I largely agree with Michael Caley and Goalimpact’s analyses^{1} that Barcelona will be fine. But 8 games isn’t nearly enough for the law of large numbers to kick in, and in the short-term the probability distributions could hurt Barcelona substantially, especially with the razor-thin margins in La Liga.

- @Goalimpact on Twitter is a great resources, and his website is really interesting an creative for football stats fans ↩