March 11, 2016 by bsd987
[EDITOR’S NOTE: All averages and match results are taken from data contained on Darts Database. All other calculations are my own.]
So far in 2016, Michael van Gerwen is high-flying. Since the World Championships, van Gerwen has only lost four matches whilst winning five titles. He was only pushed to a deciding leg twice—by Phil Taylor at the Masters, and by John Henderson in a UK Open qualifier. He has been threatening to make 2015 look pedestrian.
Although average is in many ways a poor statistical measure—Wes Newton showed at Alexandra Palace that you can average ten points less than your opponent and still win fairly comfortably—when viewed over a longer period of time we can determine the form a player is currently playing at. Additionally, and it seems crazy that we are saying this, but the greater frequently with which a player can push 107.36, which is an average leg of 14 darts, and 115.62, which is an average leg of 13 darts, becomes significant in its own right because it requires more and more legs of no more than four visits. (more on that another time).
So far in 2016, van Gerwen has had an average average of 106.17 from 19 matches. The single-season record for highest average average is 104.91, set by Phil Taylor in 2009 (excluding the Grand Prix). This puts van Gerwen on an early pace to set a new mark.
There are numerous arguments why he cannot maintain that for a full year, but I’m going to try and dismiss a few of them here. One of them is that over a longer match, his average will go down, which means his average is currently inflated by higher averages. Another is that he physically won’t be able to keep up this level for an entire year. The numbers disprove the first and certainly question the second.
1. Won’t the longer matches later in the year hurt van Gerwen’s average average?
This first one is a myth I’ve heard a lot about. And it just isn’t true. First, van Gerwen is going to have over 100 matches for which we’ll have an average calculated in 2016. At most, ten of those will be ‘very long’ matches, coming exclusively at the Matchplay, the Grand Slam, and the World Championships (Grand Prix does not count in this analysis since it is double in). While if this theory were true those 10 matches would bring down his average, it’s not.
For the best players, the longer the match, the more likely a player is to hit his average average and the less likely he is to have a performance that is out of the ordinary in either direction. Van Gerwen isn’t going to put up a 123.40 in the World Championship final, but he’s also not going to average the 85.02 that he did against Kevin Painter on the Euro Tour last year in the World Championship final. Over best-of-13 sets, he might have one 123.40 set and one 85.02 set, but they counteract each other.
Over the 14 months since the 2015 PDC World Darts Championships, van Gerwen has had an average average of 103.62, with a standard deviation of 6.1862. This (oversimplified) means that a bit more than two-thirds of his averages should fall within the range of 97.43 to 109.81, and only about one-in-six averages should fall below 97.43 and about one-in-six about 109.81. If we take his average average of 103.62 as where he truly is right now, then that 123.40 is remarkably in the 4th standard deviation above the norm, the top one quarter of one percent of all scores he should be expected to have.
But let’s break up his matches based on number of legs in the match. When we do that, we notice that there is almost no difference between an average match of, say, eight legs, as there is in an average match of, say, 30 legs, other than that we don’t have enough 30-leg matches to make an analysis.
Notice from the regression line that there’s actually a slight (although far from significant) positive correlation: as matches get longer, van Gerwen’s average average actually goes slightly up.
But let us now look at three other players who are averaging over 99 over the past 14 months. Here is Phil Taylor’s chart:
And here is Gary Anderson’s chart:
And here is Dave Chisnall’s chart:
Both Anderson and Chisnall—in addition to van Gerwen—show that the number of legs played don’t make a difference, with only Taylor having a noticeable negative regression line. But even for Taylor, it’s only a very small decrease. It shows that for approximately every 20 legs, Taylor’s average will go down a point. So if Taylor is averaging 103 over 10 legs, we’d expect him to average 102 over 30 and 101 over 50. For everyone else, the difference is so negligible (and positive!) that it will have no affect on their averages.
Now, length of the match does have one noticeable effect for all players: the shorter the match, the more likely a player is to have a match outside one standard deviation from their average average. This means there’s more variety in shorter matches than in longer matches. As I’ve already noted, van Gerwen’s high water mark (123.40) and nadir (85.02) both came in relatively short matches. Let’s take a closer look at how shorter matches affect standard deviation but not average.
Over the past 14 months, which includes everything since (but not including) the 2015 PDC World Darts Championship, van Gerwen has averaged 103.62 from 135, with a standard deviation of 6.1862. In his 90 matches over that time of no more than 12 legs, van Gerwen’s average is 103.54, but the standard deviation rockets to 6.8556, an increase of 11 percent despite cutting out only the longest one-third of his matches. If we limit ourselves to the 31 matches that were over in no more than 8 legs, his average is 103.04, but the standard deviation is a remarkable 7.5887. The points are becoming much more scattered on the graph: An average of 96 suddenly should be expected about once every six matches when overall it should happen substantially less often. But just the same, a score over 110 is not abnormal now.
Conversely, when we limit ourselves to only the long matches, the standard deviation shrinks. In those 45 matches that were longer than 12 legs, van Gerwen has averaged 103.76, with a standard deviation of only 4.6312. If we limit that even further just to the really long matches—those of 18 or more legs—the average actually balloons to 104.22, but the standard deviation shrinks to under 4 (3.8114).
As matches get longer, the ridiculously good and ridiculously bad legs counteract each other and we’re left with a more true indication of where a player is. We are more likely to see in one 20-leg match a player’s true ability than we are over, say 10 legs. If we have 90 matches where a player has played 10 legs, they’ll average out to where he was over a 20 leg match, sure, but we need more data to extrapolate. In short, it’s no accident that Gary Anderson averages just under 100 overall and had three matches in the World Championships that he averaged just under 100: over the longer format, we get more predictability.
2. Can van Gerwen keep this up?
But that brings us to the next issue: Can van Gerwen keep this up over a year? Or, more significantly, is he actually improving, or have the past few weeks in the Premier League just been three abnormally good performances accidentally thrown in back-to-back-to-back (excluding, of course, the UK Open, which was in the interim)?
Let’s break down the data in a couple different ways. First, here’s a chart comparing the last 14 months, the last 5 months, and the last 2 months:
We’ve already talked about the 14-month numbers and briefly mentioned the 2-month numbers, but let’s take a deeper look at the 5-month numbers. Since van Gerwen lost the Grand Prix final, he has recorded an average average of 105.47 over 44 matches, which is nearly two full points greater than his 14-month average. Simultaneously, the standard deviation has decreased to 5.49823 despite dealing with a smaller sample size. When you have a smaller sample size, your standard deviation is likely to increase because outliers—like that 123.40—will have more of an effect. Granted, there are a greater percentage of long matches in that 5-month set, which breeds more consistency, but overall, over the past five months, van Gerwen has gotten better and he’s gotten more consistent. That’s doubly frightening if you’re anyone else in the world.
But let’s look at the last group. Since losing to Raymond van Barneveld at Alexandra Palace, van Gerwen is averaging 106.17, with a standard deviation of 7.32902. However, this sample is almost exclusively short matches—where standard deviations are greater—and only includes 19 matches. If we eliminate the top average (123.40) and the bottom average (95.99), our average shrinks slightly to 105.76, but the standard deviation becomes 5.93449. Suddenly, our numbers for the past two months aren’t all that different than our numbers for the past five months.
Michael van Gerwen has already been playing at this ridiculous level since early October, and he’s kept it up for five months.
But let’s go one step further and say that van Gerwen is still improving by looking at averages outside one standard deviation from the mean.
In the past 14 months, a little more than two-thirds of van Gerwen’s averages should fall within the range of 97.43 to 109.81—one standard deviation either way. And, in fact, they do. Of the 135 matches for which we have averages, 20 are above 109.81 and 18 are below 97.43, fairly close to what should be expected.
But the outliers are slanted toward van Gerwen improving. Six of those 20 high scores have come in 2016; only two of those 18 low scores have come in 2016. And if we look at the last five months, we can add in two more high outliers, bringing us to eight out of 20 high scores occurring since early October. We’re still only at two of 18 low scores in five months.
In the past five months, van Gerwen has lifted his ceiling and his floor, and it seems it’s continuing into 2016.
If these were real outlier scores, we’d expect to see at least a comparable number at the other end of the spectrum: we don’t. They just don’t exist.
Which brings us to the conclusion that it’s not just that van Gerwen is throwing better than he ever has but that he is in fact better than he ever has been (or, for that matter, than anyone has ever been). And if van Gerwen is in fact better, then there’s no reason to think he can’t keep this up over a full year.
I mean, if we use October as the starting point, which in many ways it was, he’s already almost halfway there.