Introducing ICER Calculations for Comparing Players .
In a recent blog I introduced the usage of Expected Value (EV) to calculate whether it is worthwhile Columbus Crew gambling on the signing of Radamel Falcao in the near future. The theory used in that was taken from the subject of health economics. A field that I will use another tool from in this blog - the ICER.
ICER stands for Incremental Cost Effectiveness Ratio, and essentially allows a health economist to compare the viability of two procedures comparing a financial metric (usually cost) and a quality metric (usually QALY - or Quality Adjusted Life Years).
For this example I am going to use the ICER to compare strikers for two teams - the Philadelphia Union and Columbus Crew. The reason for doing so is that, at the time of writing, both sides only have one striker on their roster - a number which really needs boosting before the season kicks off:
The pool of strikers that I am going to use for this analysis are those who were in the recent pool of players for the Re-Entry Draft and played at least five 90's for their club last year. I ended up with the following strikers:
Now admittedly it’s not the longest list in the world or the most exciting - but all of these guys have been in MLS for a few years and “know the league”. They also are on varying wages and have different levels of productivity too in terms of shots taken - as you can see.
They are also likely available too - and would be very low cost to scout too considering the availbility of video of their MLS games and the fact that most of them reside in the US still.
Now before I show you the ICERs for these teams, a little more about how to read them.
First of all the axis are not absolute values, but the difference from the comparator. The comparator - the player that we will be comparing with in our analysis - will be at the origin (0,0) on the graph. This makes it easier for us to compare him to other options to us.
For example, if player A (our comparator) has a salary of $20,000 and player B (our option) has a salary of $30,000 then on the chart player B would be placed at +$10,000 on the y axis - as he costs $10,000 more than our comparator.
Secondly there is a line on the chart called Rc, which is the “Ceiling Ratio”. The Ceiling Ratio is the upmost amount you are willing to pay for a given amount of something.
Say the Ceiling Ratio relates to the cost of goals for a player. The Ceiling Ratio is the maximum wages you are willing to pay for one more goal - essentially the marginal cost.
If the Ceiling Ratio is set at $20,000 - as a GM I’m willing to pay $20,000 per goal a player provides for the team. For that reason, I’d be willing to buy a 10 goal player for $200,000, or a 5 goal player for $100,000.
Equally, as the diagram below shows, there are areas that are acceptable that are not on the Ceiling Ratio line. I’ve outlined what each point from the example below means.
- Point A - Never acceptable because the player would be of a higher cost and produces a lower output.
- Point B - Not acceptable because although the cost is less, the difference in goals (going back to our example) is less than the ceiling ratio requires.
- Point C - Not acceptable because although the player scores more goals, he is above our Ceiling Ratio as he costs too much.
- Point D - Always acceptable because the player scores more goals and costs less than our comparator - and therefore is easily below our Ceiling Ratio.
- Point E - Acceptable because the player costs less but scores fewer goals than our comparator, but is well below our Ceiling Ratio.
- Point F - Acceptable because the player scores more goals than our comparator, but despite costing more is still below our Ceiling Ratio.
For the examples below, I’m using Jack McInerney for Columbus Crew as the comparator (as he’s the only striker apart from Kamara who has got substantial minutes last season) and Conor Casey for Philadelphia Union, as he’s played a large minutes over the last couple of seasons. Note both of these guys just left their respective teams, hence the reason for looking for a replacement.
Instead of goals I’m using shots per90 for each player - something that I debated with Harrison Crow of American Soccer Analysis on Twitter the other day.
First up is Jack McInerney:
From this it’s obvious that Jason Johnson is easily a great replacement for McInerney - he’s a lot cheaper and takes more shots. Note that all the players come just under the Ceiling Ratio line apart from Robbie Findley, meaning that they would be acceptable replacements at their 2015 wages apart from Findley - who’s cost per shot is too high.
The reason for all of the players bar one being accepted is likely down to McInerney’s large wage last season of $334,000 - and with him taking just 2.2 shots per90. For a player on this high wage, you should probably expect more.
Here’s Conor Casey’s ICER plot:
Casey’s plot is a lot more different for the Union. Once again Jason Johnson is a noticeable player - but only Bright Dike and Danny Mwanga sneak under the Ceiling Ratio line. The rest of the players either cost too much or in Jairo Arrieta’s case, don’t take as many shots per90 considering the similar wage bill.
I like the use of an ICER as it’s a strong visual to show what players are cost-effective and what players are not. It is also really easy to change the ceiling ratio depending on the number of shots/wages of the player. With a greater sample of players it’s really easy to separate the good from the bad.
This type of analysis is by no means perfect though. There is the problem of just comparing players using shots - although a potential solution would be to create multiple charts while varying the x-axis to key-passes, crosses, through balls etc. With shots alone there is a large level of team effects in my opinion (i.e. the teams have an effect on the number of shots a player takes, boost or drop their tally vs. average).
Finally it’s worth noting that there are many other variables to think about around a transfer - but I believe if you start off in the right place by looking at the stats, you can look at all the other areas of a players game after. For example Conor Casey was a very physical player and that is something that counting shots cannot tell you - so it’s something that the video of the player can reaffirm.
Now, I need to go and look at some video of Jason Johnson to see if he is the real deal….
Dollars and Decisions.
