What Expected Value and Radamel Falcao can teach us about good front office moves in MLS.

Recently there’s been a rumour doing the rounds that Falcao is a target for the Columbus Crew.

I really don’t like this rumour. It’s not that Falcao hasn’t been a great player previously but I think that front offices should be projecting forward and not making their decisions from previous performances alone.

He’s also very injury prone. In the past couple of seasons, he’s only achieved the following minutes per team (the graphic excludes this season, but he’s only seen 213 minutes of football at Chelsea so far)

Falcao minutes played by age. See more here: https://datawrapper.dwcdn.net/SKKEJ/1/

So although he’s likely to get a boost in his scoring rate in MLS due to it being a league of lower quality than Europe’s top 5 (although I think some teams are better than the lower level European sides) would it be a good move for the Crew?

Here’s where the use of Expected Value can help. I’m going to be using an example from health economics - so bare with me - but it will be useful for this analysis.

Expected Value is defined (by Google) as:

A predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence.

So in layman’s terms, it’s the probability of an event happening multiplied by that event. Taking an example from health economics - you may have a person who has just had surgery. That person has two possible outcomes - they’ll die or they’ll live:

Decision Tree displaying the probabilities and values post surgery

Each of these outcomes have a probability attached to them, and an end value. The value used in this case is years left to live. These are displayed at the end of the branches (0,15 and 0.5). The probabilities are the values in red that are on the branches (0.05, 0.95, 0.8 and 0.2).

These mean that if the person has surgery, there’s a 95% chance of them living, if they live there’s an 80% chance they survive and so on.

The Expected Value is then multiplying the probabilities by the values along the branches to see what the likely outcome is. The outcomes are as follows:

• Die: (0.05*0) = 0 years left
• Live: 0.95 * (0.8*15+0.2*0.5) = 11.495 years.

So overall the Expected Value of having surgery is 11.495 + 0 = 11.495 years.

If we were to compare this to - say - a course of drug treatments and not surgery, we could compare the Expected Value’s of both options and see which one is likely to maximise our output. For example if the drug treatment had an Expected Value of 15 - you’d choose that over the surgery.

You’re probably wondering why you’re still reading this, but I’m getting to the football bit now so read on!!

So back to the footballing problem - Falcao. If the Crew were to bring in Falcao for the start of next season we’re going to want to calculate his Expected Value. Evidently we’re not going to use years left to live in this context (although if I was Falcao personally, I’d like to see how much that dodgy knee is impacting my years left) but something to do with goals instead. Let’s take goals per game.

In this example I’m going to assume that the Crew have two strikers to choose from - Kei Kamara and Radamel Falcao. They can either have one or the other - but not both.

Falcao vs Kamara Expected Value Decision Tree

Starting at the yellow decision node the Crew can either pick Kamara or Falcao. The values used in this example are binary - whether the player scores a goal in the game (1) or not (0). The probabilities attached to them are the players goals per game (or per 90 - I’m assuming that each player will play the full game if chosen).

As you can see from the probabilities, Falcao has a far higher probabilty of scoring - 0.8 - but he is also far more likely to be unfit - due to his injury history. On the other hand, Kamara is likely to be fit around 80% of the time, but his probability of a goal is only 0.5 - or one every two games.

Bringing these two together, we can calculate the Expected Value:

• For Kamara: (0.2*0) + 0.8*(0.5*1 + 0.5 * 0) = 0.4
• For Falcao: (0.6*0) + 0.4*(0.8*1 + 0.2*0) = 0.32

So overall, despite his better finishing rate Falcao is the worst option when it comes to Expected Value. His injury history has a significant impact on his ability to add value to his team’s goals and therefore should not be pursued by the Crew - especially considering he’d likely be on a multi-million dollar deal.

For me, this wouldn’t be a good front office move for MLS. From a league office point of view you could change out goals scored with additional money made through merchandise/ticket sales with Falcao - but I doubt he’s still value for money.

So to conclude:

• Thank you for taking the time to read this piece - I hope you made it to the end! Feedback, shares and comments are all welcomed.
• Note that all of the data in this analysis is arbitrary and used only as an example of how Expected Value could be used. Given actual data, it would make an analysis like this far more useful for a team.
• I think this is only one area where Expected Value could be used in football - and even in this one case it marries together two very important features of a player in terms of goal contribution and fitness levels really well.
• If you didn’t get it by now - I really don’t like the Falcao move. He’s old, unfit and not worth the league or the Crew’s cash.
• If I was working within an MLS Front Office, I’d be looking to include some sort of Expected Value metric at a very basic level for appearances - to ensure that we are looking historically at player fitness levels and ensuring that we have enough cover across the season so that we have a good quality XI every week.

Once again, thank you for reading!

Dollars and Decisions.