Soccer Stats 101: Projecting The Rest Of The Rapids Regular Season

Last week I created a formula called PCR, or Player Contribution Rating, in an attempt to quantify true player value. You guys gave me some awesome feedback and asked some great questions. This week, I want to try and answer some of those questions by providing some contextual information about PCR.

I understand "true value" may be a subjective term, but for PCR's intents and purposes I am attempting to assess how much a player positively contributes to his team. PCR is derived from many different traditional box score statistics such as goals, assists, passing percentages, tackles, interceptions, etc. Each contribution is weighted differently depending on the player's position. An average starter on an average MLS team should expect to record an end of season PCR of ~30, regardless of position.

As with most statistics, PCR benefits from large sample sizes, and I created it with the intention of quantifying player value over the course of an entire season. A player's PCR will fluctuate wildly during the beginning of a season, but as the season progresses it becomes more and more accurately indicative of a player's true value. For this reason, I have calculated PCR for four teams from the 2015 regular season. I am hopeful this will make it easier to differentiate between good, average, and below average PCRs.

Things to know:

-For these calculations, I used the thirteen players who logged the most minutes on these teams. I imagined these players as the ten most commonly played field players, and the three most common substitutes.

-The average MLS team in 2015 recorded 46.85 goals scored, and 46.85 goals against.

-The average MLS team in 2015 recorded 47.4 points on the season.

First up, the 2015 Supporters Shield winning New York Red Bulls. NYRB finished the 2015 season with a +19 goal differential, the highest in MLS. They scored 62 goals during the campaign, the highest total in the league.

The 2015 Red Bulls front line finds itself at the top of another table. Led by Bradley Wright-Phillips, who logged the third-highest PCR in the league last season, the Red Bulls offensive firepower is noted. The Red Bulls defense ranks about average in terms of PCR. The Red Bulls defense allowed 43 goals last year, slightly better than league average. The thirteen Red Bulls who logged the most minutes in 2015 combine for a Team PCR of 38.244. This translates to about 60.426 expected points, less than half a point off of their actual total, sixty.

Team PCR is calculated by finding the mean PCR of the team's thirteen players with the most recorded minutes. Simply add them up, and divide by thirteen.

Expected point totals are calculated by dividing the team's average PCR, in this case 38.244, by the theoretical average PCR, 30. Multiply that by the average point total of a team that year, in this case 47.4, and that will give you an expected point total based on team PCR. So for the 2015 Red Bulls it would be:

38.244/30=1.2748 1.2748*47.4=60.426 expected points

We can conclude a squad with a Team PCR of around 38 should expect to record about 60 points during the 2015 regular season. The NYRB offense kept the Team PCR well above average, which reflects the offense's contributions toward the Red Bulls regular season success last year. This is the high end of the spectrum. To investigate the opposite end of the spectrum, I calculated PCR for the 2015 Colorado Rapids thirteen most commonly used players.

Not quite the same as the 2015 Red Bulls, huh? The Rapids struggled in most facets of the game throughout the 2015 campaign, although the defense occasionally held its own. Despite their best efforts, the Rapids only had two players post average PCRs, Dillon Powers and Lucas Pittinari. Everyone else recorded a below average PCR, not surprising on one of the league's bottom feeders.

The 2015 Rapids recorded a team PCR of 21.943, good for an expected point total of 34.671. The Rapids slightly outperformed this projection, recording 37 points during the season. Considering the six of the Rapids nine victories last season were one goal wins, one goal could have been the difference there.

Now that we've investigated the two most extreme ends of the spectrum of success, I wanted to show you two teams that finished the season smack in the middle. The New England Revolution and Toronto FC recorded goal differentials of +1 and 0 in 2015, respectively. Both finished the season exceedingly average, but managed to get there in very different ways.

The 2015 New England Revolution were truly unspectacular last season, scoring 48 goals and allowing 47, almost exactly at the league average for both. Meanwhile, Sebastian Giovinco and Toronto FC scored a whopping 58 goals last season, good for second in the league. However, they also allowed 58 goals, good for the worst scoring defense in MLS. The Revolution finished with 50 points on the season, with Toronto FC right behind them at 49 points.

Obviously the most striking difference (pun certainly intended) is at the top of the tables. Giovinco was a transcendent MLS player last year. A 94.328 PCR is absolutely ridiculous, yet it isn't enough to carry Toronto FC to an above average Team PCR. While the New England Revolution didn't have any superstars of Giovinco's caliber, their depth makes up for the difference. Both teams finished a sliver above average in terms of Team PCR. Their respective Team PCRs projected Toronto FC to get 48.509 points and the Revolution to get 49.984, almost exactly the same as the totals they ended up actually recording.

Just for fun, with the Rapids now exactly halfway through the 2016 regular season, I quickly projected full season statistics for the team. For this exercise, I assumed the Rapids second half of the season would exactly mirror their first half of the season. There are two exceptions to this: I gave Jermaine Jones and Marco Pappa a 10% boost in minutes, while lowering Badji's playing time and accounting for the loss of Dillon Serna. :'(

Those projections were used to calculate these hypothetical end-of-season PCRs.

While these projections certainly won't hold perfectly to form, the thought of the Rapids finishing the season with a point total in the mid-fifties doesn't sound too ridiculous. I would expect some of the Rapids offensive players, namely Jones and Pappa, will outpace these projections as they begin to log more consistent minutes.

Additionally, if Sjoberg finishes with a PCR above 60, he'll be the first defender so far to crack that milestone. That makes sense, considering if the Rapids defense continues its first half of the season production, they would finish with 22 goals against. That would make them the best scoring defense in the past several seasons, and Sjoberg would be its leader and ironman. How do you guys feel about a 54 point projection? Do you agree or disagree with any of the individual PCRs?

If you made it this far, I appreciate you. I genuinely believe PCR can be a valuable statistic when looking to quantify player value, and I hope these contextual examples helped to illustrate its usefulness. PCR is derived completely from traditional box score statistics in order to quantify "player value," a traditionally subjective term. The fact that it checks out against so many different angles has me curious what else it can accomplish. I'm thankful for all of the feedback I received regarding last week's article. I encourage you to connect with me on Twitter or here on Burgundy Wave with any questions or comments or criticisms.