About player combinations

The question of player combinations has fascinated me for some time. The topic is predicated on the belief that a team is, more than anything else, the aggregation of its players. Coaches have an impact, but it is the players on the field. More than individual players, even, I have been looking for ways to understand the results of player combinations.

This post explains a few outputs that address this question, and gives some notes on their application.

Combination Tiles

Through the first 12 games of the season, a group of six players has emerged as this season’s stalwarts. While it is perilous to predict the future, even as far ahead as three days out (cough cough Sepp Blatter cough), observant fans of Crew SC have no doubt noticed that this hextet of players tends to be playing a great deal.

The six players in question form something of a spine for the team:

  • Goalkeeper Steve Clark
  • Defenders Emanuel Pogatetz and Michael Parkhurst
  • Holding midfielder Tony Tchani
  • Midfielders Federico Higuain and Ethan Finlay
  • Forward Kei Kamara

How do I come up with that list? What about Justin Meram – the final piece of the Crew’s attacking quartet?

Take a look at this:

combinations_1_150602This visualization – which can be seen as part of the season data page on this site – lists every player to have appeared for Columbus this season, in descending order of playing time. It also colors a field of hexagons according to how often two players have appeared together.

If you spend some time running your mouse over the visualization on the season page (the version above is just a screenshot), you’ll see tooltips that give more detail. Even a brief look at the image above, however, shows a pretty clear line between Federico Higuain and Mohammed Saeid. From Higuain and up, the cells are noticeably darker – indicating significantly more playing time among those pairs.

There is a second such demarcation emerging in this plot as well. Looking between Justin Meram and Hernan Grana, a pretty clear split is showing between darker gray with Meram and lighter gray with Grana. This isn’t quite as consistent a split as that between Higuain and Saeid, but it is there nonetheless. It will be interesting to see whether, as the team moves forward without Grana, that “below Meram” split gets more pronounced or whether playing time will be rotated among the players on the roster.

Performance Grid

This isn’t the only way to look at player combinations, however. There are two other visualizations to be found around this site:
This plot, which can be found on the Visualize Combinations page, goes a bit beyond just showing how often two players appear together. Here you can start to see how team performance changes as well.

Now, this can be a bit confusing – but let me try to explain a bit. The default view has two regions, split by a diagonal line that stretches from upper right to lower left. Each cell in the grid depicts a combination between two players, but with the entire roster listed on both horizontal and vertical axes, there are two locations on the grid for each pair of players (A + B, and B + A). To resolve this problem, and prevent a mirror image chart, the upper left region shows the performance when both players are on the field, while the lower right shows the performance while both players are off the field.

Cells are color-coded according to the Crew’s offensive output. Green shading indicates the team scores more often than average, while red shading indicates a less-than-average scoring. Cells with no (or dark) background indicate that the pair of players hasn’t appeared frequently enough together.

As an example, if you look at the cell combining Waylon Francis and Justin Meram, you see that the two left-sided players have been on the field together for 550 minutes. Hovering over that slot (again, on the actual page – not the screenshot above) displays a popup window stating that this is 51% of the season.



Additional information (seen above) indicates that the team has scored far more often than average with Francis and Meram on the field – roughly one goal every 40 minutes compared with a goal every 56 minutes on average. Of course, the defense is also more porous, conceding every 55 minutes instead of every 67 minutes – but overall this is still a net positive for the team.

A second method of inspecting this chart is to look for players whose combinations are consistently better or worse than the team average. Here let’s examine Meram and Kristinn Steindorsson. Meram’s combinations with other players (remember, the upper left of the plot) are almost all shaded green. Steindorsson – with whom Meram is competing for playing time – shows a much more consistent red hue.

There are many possible reasons for why the team may perform better or worse with Meram and/or Steindorsson – and those reasons may have little to do with the contributions (or lack thereof) from either player. This is still an area I’m investigating. But it does seem to be worth pursuing, considering the fanfare with which Steindorsson was added to the team last offseason.

Force Directed Graph

There is one more combination visualization that should be mentioned – and it is in some ways the least traditional:
combinations_2_150602This force-directed graph, which you can see live as part of the Season display, depicts players as dark blue dots, and games as light blue dots. Each line is the relationship between that player and the games in which he has played. Line thickness is determined by playing time – so an 89th-minute substitute would be the thinnest of lines, a player who goes the distance is shown by a very thick line.

Hovering over any dot will display a tooltip identifying that player or game. This isn’t the easiest of plots to investigate, so a bit of patience might be needed. For some years, and an inquisitive mind, however, some insight can be seen. Consistently-used players will gravitate toward the center of a ring, while a group of players who show in the same subset of games will distort the ring and flip to the outside. This can be particularly interesting in seasons like 1996, where the roster changes significantly from the first game to the last.

Closing Thoughts

Hopefully these displays are of some interest to you. I’ve been pondering this topic for some time, and I believe that – particularly in conjunction with each other – the above instruments will help observers identify trends to watch for during the course of a season. Future work in this area will focus on larger combinations, looking at groups of N players where N > 2. There has been some fascinating work in data analysis circles the last few years focusing on pattern mining, which I hope to apply to this site over the rest of this season.

Until then, please let me know if you have any feedback about any of these displays.


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