Soccer Prospectus, Pt 1

By: Isaiah | November 20th, 2008

I just got my copy of College Basketball Prospectus, meaning that during the evenings I’m glued to both the TV and the page as I try to digest how well my Kansas Jayhawks are going to do this year. The news is somewhat grim from a KU perspective, but we’re going to rock (chalk) the house over the next few years as our freshmen develop into the polished killers they look like they can be.

Because of who I am and the nature of my two-sport obsession, looking at statistical puzzles and inferences in college basketball has led me down the path of “sabermetrics” and all that that entails for soccer. That is, I’ve becoming increasingly obsessed with figuring out how to apply the lessons being learned in other sports to The Beautiful Game. Now, I don’t want to turn soccer into baseball, which I find vexingly boring, but I do believe that baseball’s statisticians such as Bill James, among others, are leading the way into understanding the actual value of a player, beyond the hype and beyond flashiness displayed.

There are currently some companies working on developing such statistical analyses, such as England’s ACTIM, and individuals, such as Billy Beane, who are working on or have created formulas for determining player quality/efficiency, but none of that seems to be available to the general public (ACTIM, as I’ve commented before, suggests what it uses, but not necessarily how – its wiki page breaks it down a little, but not much). Before returning to how ACTIM goes about their business, though, I’d like to discuss the ways in which we currently read soccer statistics and ways in which we could grow that reading to encompass more ideas.

From here on out, please realize that I tried to organize this post, but some of it got out of control and rambled all on its own as I tried to work through particular stats that I think are important to explain before continuing with something else.

(the Legend of) Per Game Averages
Let’s start with the general idea of per game averages. Per game averages in soccer are misleading in the same way that RBIs are misleading in judging a baseball player’s abilities. RBIs require your teammates to put themselves on base before you are at bat or your double or single will amount to no RBIs for you.* The same is true in soccer on several levels, such as assists (because if Xavi gives, say, me a pass, I’m going to blow it and that would mean fewer assists for Xavi despite the fact that he has provided a pass any other striker in the world would put away), so an attempt must be made in any statistical measure to gain a wider perspective on a given player’s contributions to the game.

If, however, we are to give in and attempt to use a per game average for anything, I think it’s important to try and gain some level of perspective and put out a per-90 minutes average. I’ve given this example before in defending Thierry Henry, but here it is again, in longer form (and not concerning Thierry Henry – in fact, the following stats really are for fake people with fake stats, but I think if you follow along with me and act as if these are real players, it will help you to understand my conclusion): if at the end of a season Player A has 5 goals while Player B has 25 goals, who had the better season? Well, if Player A played 5 minutes per game and Player B played 85, I would say that Player B had the better season, but Player A was far more efficient in terms of goals scored per minute played (Player A scored at a rate of once every 38 minutes while Player B scored at a rate of once every 129 minutes).

Another way to look at this same stat is how many shots on goal they had. Let’s say that during their time on the field, Player A had 7 shots on goal, while Player B had 125 shots on goal. Thus, Player A had one shot on goal every 27 minutes, while Player B had one shot on goal every 26 minutes. Per shot on goal, Player A far outscored Player B, but Player B obviously got himself into a position to score more often.

Now let’s say that Player A had a total of 20 shots (remember, 7 on target) while Player B had 145 shots (125 on goal). When he took a shot, Player A put the ball on target 35% of the time. When Player B took a shot, he put the ball on target 86% of the time. So from this statistic, we see that, in fact, Player B does have pretty decent shooting boots after all, though we probably didn’t think so when we heard that he scored once every 129 minutes as opposed to Player A’s once every 38 minutes. Player B forced a giant number of saves out of his opponents, while Player B often put the ball “into Row Z” as they say. (For future reference, let’s call the number of shots on goal that didn’t result in goals as Saves Forced, or SF for short – please note that this excludes shots that hit the woodwork)

So now we’re beginning to get a far more complete picture of each player’s individual contributions throughout the season. However, we’re still missing obviously integral parts of the statistical landscape: everything other than shooting. Our Player A and Player B are both forwards (in case you hadn’t guessed), so let’s add a midfielder, Player C, and a defender, Player D, to our growing squad. We’re going to leave goalkeepers out of this until the very end, so let’s not consider them a part of these questions for now.

We can’t conceivably use the same metrics with Players C and D as we did for Players A and B since neither C nor D will have many shots, saves forced, or goals, at least not compared to Players A and B (we’ll give Player C 2 and Player D 0). Let’s say that Player B is known for his passing ability, despite being a forward. Let’s say that during his 38 appearances (for a manly 85 minutes a game, remember – he missed only 190 minutes during the year) Player B had 6 assists**. That’s pretty rockin’ for a guy who also scored 25 goals and had 100 saves forced, but Player C had 18 assists during that same amount of time. Assuming that Player C also made 38 appearances for 85 minutes a game, that means he achieved an assist rate that is 3 times higher than Player B’s.

However, remembering that a Xavi-Isaiah partnership isn’t going to produce as many goals as a Xavi-Eto’o relationship, we have to consider that any midfielder who wants a lot of assists must rely on his teammates to turn his passes into goals. Assists are a good way to judge when a player was the second-to-last player to touch a ball before it was scored, but is not necessarily a good way to show that a player was anything other than lucky enough to poke a ball between a lunging defender’s legs. Consider this: Player B has 6 assists and has attempted 500 passes during his time on the field. Of those 500 passes, 100 of them found their mark. The other 400 were intercepted by opposing defenders or went out of bounds. Player C has 18 assists and has attempted 1,500 passes over the course of the season. (In case you think these are unreasonable numbers, that averages out to 39.5 passes per game for our midfielder – perhaps that’s a lot, but I think it’s about what Xavi averages, though I could be wrong) Of those 1,500 passes, 1,100 of them found their target. That means that despite Player C being intercepted just as many times as Player B (400 times), Player C has a pass completion percentage of 73%. Certainly that passer rating is better than Player B’s 20%. Stick to scoring goals, Mr. B. (Food for thought: assuming that Player C is responsible for all of the passes that Player B receives and turns into shots on goal, one can surmise that Player B has at least 100 assist opportunities in those 1,100 passes completed, but those “assist opportunities” are not recorded for posterity any more than dropped balls are considered in a QB’s completion percentage†)

Let’s say that Player D has a 60% pass completion rate (600 out of 1000). He is, of course, a defender, so perhaps we forgive him his distributive transgressions. Player C, though encroaches on his defensive territory, intercepting balls every now and then. Player C intercepted 35 balls during the season. Pretty good for a guy with 18 assists, but Player D, who played the same number of minutes as Players B and C (85 per game; man, this is a consistent team!) got 85 interceptions. Not only that, but Player D has also blocked 15 shots throughout the year while Players A and B have blocked 0 and Player B has blocked 3.

On the negative side, Player D has committed 45 fouls over the course of the season. Player C, though, has only committed 25, Player A has committed just 2, and Player B has committed 10. Let’s say A got 1 yellow card, B got 6 yellow cards, C got 8 yellow cards, and D got 9 yellow cards and a red card (that’s why he missed 180 of his 190 minutes). On the other side of that statistical group, Player A also drew just 2 fouls, while Player B drew 30, Player C drew 35, and Player D drew 15.

Back to the original point about per-game averages, if you boil all of these down into per-game averages, you end up with things like Player A gets 0.13 goals per game (5 goals in 38 matches), as well as 1 yellow card every 190 minutes of play. It’s better to extrapolate into 90 minute blocks (or even better, the number of minutes in an average game for that particular league – I suspect it’s something like 93 or 94 minutes in most leagues) because this removes some of the playing time questions about how well a player would perform given more playing time.

Quickly, assuming a 90-minute game (because it’s a round number), Player A’s goal scoring rate (5 in 190 minutes) translates to 2.37 goals per 90 minutes (an absurdly good rate, of course), meaning that in a 38-game season in which Player A played every moment, he would score roughly 90 goals, whereas Player B would score 26 or 27. Because we know that Player B has a better shooting percentage than Player A, perhaps those stats a bit skewed towards Player A by not incorporating all that we know. Keep that in mind going while reading the following sections because I’ll be returning to it.

Now that we have a glut of stats to consider; instead of continuing to pile them on (and there are certainly more), I’m going to shift gears a little bit. Let’s talk, for a moment (or two) about various types of statistics in other sports.

Replacement Players
I’ll begin with baseball’s Value over Replacement Player (VORP). To quote Wikipedia: VORP “is a statistic invented by Keith Woolner that demonstrates how much a hitter contributes offensively or how much a pitcher contributes to his team in comparison to a fictitious ‘replacement player,’ who is an average fielder at his position and a below average hitter.” This concept of a “replacement player” is an intriguing one, though I can’t claim to understand all of its ins and outs. I understand it based on this sentence (also from that same Wiki article), “to calculate VORP one must multiply the league’s average runs per out by the player’s total outs; this provides the number of runs an average player would have produced given that certain number of outs to work with. Now multiply that number (of runs) by .8, or whatever percentage of average the replacement level is designated to be; the result is the number of runs you could expect a “replacement player” to put up with that number of outs.”

If you can judge what the average player would be (say Joe Schmoe from the minors or, in soccer’s case, Fulano de Tal from the reserve team), then you can compare your players with that particular “average player” and determine if it’s worth keeping your player or replacing him with someone younger, cheaper, and, well, more average. Without having any idea how one would go about calculating what an average player is, it is hard to consider using this as a viable way to determine whether or not a player should be replaced. This is definitely a stat for the future that I think can help the game out. For instance, if Player D is no better than Player X (an exactly average defender) we would know that and we would get rid of Player D.

One important caveat is this quote from Keith Woolner, “Replacement level is a less concrete mathematical concept, but it is an important economic one. In particular, it more correctly values durability and playing time versus rates of production.” Basically, this means that if you can produce 10 goals over a 38-game period, you’re more valuable than the combination of a player who can produce 5 goals over a 10-game period (then gets injured) plus a player who can produce 5 goals over a 28-game period. [If I’m wrong about that, please point it out in an email to me; I admit to struggling a bit with VORP].

Efficiency
Then there’s the NBA Efficiency stat (EFF). I’ll admit that I’m not much of an NBA watcher (though ironically I’m watching the Mavs-Rockets / Bulls-Blazers doubleheader as I write this), so I don’t know how great EFF is at showing who the best players are, but I do think that the idea of weighting stats like this is a pretty good idea for soccer. Here’s how EFF is created:

[Points + Rebounds + Assists + Steals + Blocks] – [(Field Goals Att. - Field Goals Made) + (Free Throws Att. - Free Throws Made) + Turnovers)]

I believe that this stat is weighted towards the offense because if you score 4 points and you get 4 steals, you get 8 points even though your team may have scored 100 points and managed 8 steals. You have 4% of the total points, but you have 50% of the steals (let’s say for the sake of argument that all 4 of your steals led to 2-point field goals, so 8 points). There is some shift back when you incorporate FGA – FGM (let’s say you took 4 shots and scored 2 of them, that reduces your EFF by 2 points), but it doesn’t seem to value defense in the same way. Part of that is the unquantifiable nature of defense (if the guy you’re face-guarding doesn’t ever take a shot, you did your job really well, but you didn’t get any positive stats in your box score) and some of that is the unwillingness to find the proper stats to consider.

I like the concepts behind EFF (there are several others to consider, but they’re mostly hoops-specific so they’re fairly useless to us), especially when EFF is converted to Efficiency per-48minutes (EFF48M) and I’d like to try my hand at incorporating all of the stats discussed above into a single Soccer Efficiency stat. For ease of use, let’s call it Player Efficiency or PEff.

PEff = [Goals + Assists + Blocks + (Passes Intercepted/3) + (Tackles won/3) + Penalties won] – [(Shots – (Goals + Saves Forced)) + (Passes – Passes Completed) + (Fouls Committed – Fouls Won) + Yellow Cards + 2(Red Cards Earned) + Penalties Missed + Penalties Given Away]

Or, we can write it out as

PEff = [G + A + Blk + Int + TW + PW] – [(SH – (G + SF)) + (P – PC) + (FC – FW) + YC +2RC + PM + PG]

Let’s discuss this, shall we?

The first thing that jumps out at me as a potential flaw is the lack of consideration for how important goals are. However, because a select few players earn them, I think that making them worth 1 point each (as they are in reality) is acceptable. The same goes for assists since no one can get an assist and a goal at the same time, yet the assist is vital to the goal. It does, however, specifically remove secondary assists as a category, which may or may not be satisfactory. Remember that goal Keita scored against Huelva (it’s his only one in the blaugrana, shouldn’t be hard to remember)? Henry would get no real credit for that goal despite his beautiful cross, merely a completed pass. I did not add in crosses as its own category because a cross is merely a pass that’s in the attacking third and I did not want to put undo emphasis on things that happen closer to the opponents goal. If Thierry Henry’s pass to Eto’o wouldn’t have been completed, it would have shown up in the incomplete pass category, a mark against his efficiency, which is good enough for me.

I then tried to balance offense and defense with as many defensive categories as possible (blocks, interceptions, tackles won), but with a weight towards how many there typically are in a game. That is, you take the number of interceptions and tackles won and divide those numbers by 3. Otherwise an interception is worth the same as a goal, which doesn’t make much sense. You could conceivably put interceptions and tackles won into a single category of “steals” or “takeaways” if you wanted to, but I prefer to keep them separate if possible simply to note the difference at a glance (my guess is that a Yaya would have more Tackles Won while a Pique would have more Interceptions).

I also take (P – PC) and divide by 100 because of their sheer quantity. Without this, even with a good passing rate (take Player C, below), you’d end up with a monstrously negative PEff. I then multiply the number of red cards by 2 because they are very important for understanding what a particular player did to his team. I’d like to find a way to include the number of minutes you left your team without a player because of those red cards, but I can’t think of a good way to incorporate them.

If PEff is to tell us the true value of players, it must be able to cover all facets of the game. Let’s go ahead and check out our team (well, our 4 players). I’ve filled in the blanks on any stats I haven’t mentioned earlier. The calculations are in the footnotes.‡

Player A’s PEff = -7.25
Player B’s PEff = 32
Player C’s PEff= 18.33
Player D’s PEff= 1

So Player B is an extremely effective player because he produces massive numbers of shots on goal (and goals) while Player A is extremely ineffective because of his horrible shooting rate and mediocre passing rate (50%). Note that Player B’s horrendous passing rate (20%) is overshadowed by his overwhelming shots on target rate (86%). Player C seems an efficient player because of his passing rate (87%) and his high number of assists (18).

Player D was penalized fairly heavily for his fouls committed (45). If he’d had an equal number of fouls received as committed, he would have been just as good as Player B thanks to his high numbers of blocks (15), interceptions (85), and tackles (50).

Because I’m not into the whole per-game thing, if you put the PEff into a per-90minutes mode, we could see some differences. Remember that Player A is given only 5 minutes each game in which to shine. So let’s weight this statistic into 2 categories: PEff and PEff90. The former is what we have already done and the latter is extrapolated based on trends set during time played.***

Player A is the only player worth considering here as he is the one who played such a small portion of the year that extrapolating will make a difference. Like we mentioned above, at his current rate, he’d have a fantastic year in front of goal (90 freaking goals – the best year ever!), but what is his effectiveness when putting all of his miscues into perspective in terms of opportunities?

If we pull each statistic into per-90-minutes, we would find that he would have a PEff of -130.5. A very wasteful player, indeed. For example, those 90 goals would have come from a whopping 360 shots, only 126 of which would have been on target. If Player B were given 360 shots, he would have put 250 of them on goal. This is, in my opinion, more efficient, in the end, because it provides you with more scoring opportunities.

It must be remember that the PEff stat is 1) a work in progress and 2) not a stand-alone stat. It should always be considered alongside the actual numbers, including the specific stats it incorporates. Saying Player X is wasteful without providing the details how that player is being judged wasteful is not a good way of going about the business of rating players.

If PEff is changed slightly to give more weight to goals (doubling their value), then our PEff ratings change:

Player A’s PEff = -2.25
Player B’s PEff = 57
Player C’s PEff= 23.33
Player D’s PEff= 1

Equally, if we just change the value of passes (meaning we make goals worth 1 point), by making our calculation (P – PC)/50, then all of the players lose several points on their totals.

Player A’s PEff = -7.5
Player B’s PEff = 28
Player C’s PEff= 17.33
Player D’s PEff= -3

I would like find a way to create benchmark (perhaps different for different positions) that would help to understand what is a good PEff and what is a bad PEff. As was pointed out in one of the links above pointed out, great players are a great rarity, good players are rare, average players are somewhat common, and bad players are absolutely everywhere you look (such as on the street corner, on buses, in my mirror), so being able to distinguish them is very important.

Goalkeepers
I promised I would return to goalies and so I will. There’s little to say about them because their stats are fairly well kept. Goals Allowed, Saves, Times Caught Picking Their Bums on Camera. I dislike the Zamora “coefficient” because it doesn’t mean anything. A terrible keeper with a brilliant defense in front of him can have a good goals allowed per game rate, but that does not a good goalie make. I propose the NHL method of determining goal keeper ability:

Save Percentage. If a shot comes your way and you stop it, good. If it goes in the net, bad. If your SV% is 95%, you’re probably pretty good. If it’s 76%, you’re probably pretty bad. However, it’s still instructive to see all of the stats laid out.

For instance:
Valdes has 8 goals allowed in 11 games. Woohoo!
Palop has 8 goals allowed in 11 games. As good as Victor!
Valdes has made 16 saves (a 66% save rate!)
Palop has made 32 saves (an 80% save rate…ooh, that’s better).

For my money, Palop is statistically the better keeper, but Valdes has the better defensive unit in front of him. (For the record, Palop has 7 clean sheets and Valdes has 4). And for those of you who are down with Casillas being considered the best keeper on the planet (and I am), “San Iker” has allowed 17 goals and made 29 saves (meaning he has a 63% save rate). Not the best year for him at all. I don’t have access to all of the keepers in La Liga to go through them and say who is the best, so I’ll just leave it at that.

Wrap Up
As I said before, the PEff is a work in progress. I want to get your feedback on it as well as suggestions. This is the first of many posts, I imagine, especially since I didn’t really cover as much as I wanted to (and it’s just about 5,000 words long!); if all goes well, we’ll develop a good system by the end of the season.

As always, your feedback can be negative criticism – without some sort of negative response, I’ll get too big an ego and forge ahead without considering whether or not I could improve on PEff – though I definitely prefer constructive criticism to the casual “you’re an f-ing tool” remark. Mom, I’m looking at you.

Here’s a brief list of things I’m probably going to be looking at in the future; send me your suggestions about other things too, of course:

Stats by possession (how many goals per possession? This is a basketball stat that may or may not make sense with soccer)
Salary efficiency (how well does a team do, weighted by salary)

And with that, thanks for reading and have a good one. Oh, and by the way, because of how much time I’ve put into this one, I’m not planning on doing a Getafe preview, though I will put up a comments post before the game begins. Official prediction: 2-0. Goals by Eto’o and Bojan.

—-

FOOTNOTES:

*Take, for instance, Ichiro Suzuki, who had a record 262 hits during the 2004 season while netting 60 RBIs. During that same time, Miguel Tejada drove in 150 RBIs on 203 hits. Does that mean Miguel Tejada is just better at hitting or does it matter whether or not Tejada’s team was better during that year? Team on-base percentage (OBP) comes to matter more than an individual’s stats in this case, yet RBIs are routinely considered suggestive of a player’s abilities. They are not.

**Let’s assume that all assists are judged in a specific way and that there is no discrepancy between any player stats – that is, for our purposes here, they are collected in the same manner across the board. What is an assist in one place is an assist in another; the same is true for all other stats.

†For you NFL and MLB stat kids, if a walk (BB) is recorded as a non at-bat, then why isn’t a dropped ball considered a non-pass? There should be a statistical category in the NFL akin to the MLB’s Error for these situations. It doesn’t count against the pitcher if the first baseman pulls a Bill Buckner, so why should it count against a QB if his pass hits a target in the numbers, bounces off, and is intercepted? The same should probably be said for a midfielder whose pass arrives at the feet of a bumbling forward who shanks his shot out for a throw-in, but that’s too many judgment calls, I think.

‡PEff calculations:
PEff = [G + A + Blk + Int + TW + PW] – [(SH – (G + SF)) + (P – PC) + (FC – FW) + YC + 2RC + PM + PG]

Player A:
5G + 1A + 0Blk + (2INT/3) + (1TW/3) + 0PW = 7
(20SH – (2SF + 5)) + ((50P – 25PC)/100) + (2FC – 2FW) + 1YC + 0RC + 0PM + 0PGA =

13 + 0.25 + 1 = 14.25

PEff = 7 – 14.25 = -7.25

Player B:
25G + 6A + 0Blk + (10INT/3) + (5TW/3) + 6PW = 42
(145SH – (100SF + 25G)) + ((500P – 100PC)/100) + (10FC – 30FW) + 6YC + 0RC + 0PM + 0PGA = 10

PEff = 42 – 10 = 32

Player C:
2G + 18A + 3Blk + (35INT/3) + (20TW/3) + 1PW = 39.33
(45SH – (25SF + 2G)) + ((1500P – 1100PC)/100) + (25FC – 35FW) + 8YC + 0RC + 1PM + 0PGA = 21

PEff = 39.33 – 21 = 18.33

Player D:
0G + 2A + 15Blk + (85INT/3) + (50INT/3) + 0PW = 62
(15SH – (1SF + 0G)) + ((1000P – 600PC)/100) + (45FC – 15FW) + 9YC + 2(1RC) + 0PM + 2PGA = 61

PEff = 62 – 61 = 1

***I’d like to note here that I am not against per-game-statistics when we’re talking about full teams, though I do think that these stats, like individual stats, should be expressed as per-90-minutes or as per-average game length and they should consider Strength of Schedule (that is, who these numbers were achieved against – in soccer you could probably easily make a case for incorporating the average/median table position of previous opponents into these stats).