Wednesday, June 16, 2010

The Value Of Assists

As hockey statistics continue to expand, new measures and multiplication factors are thought up every day. But for all the sophistication that is emerging regarding shots, saves and the like, we are still left as fans with the albatross of the NHL scoring leaders at the heart of everything.

As you well know, the NHL scoring leaders is a blunt tool to assess a player’s worth. A simple record of who touched the puck last, second to last and third to last as pucks flew by goaltenders into the net. It does little to instruct us on who created the goals, who made the play that unlocked the D or the goalie.

As you know, we at LIW took issue with this and undertook to examine each goal the Montreal Canadiens scored over an entire season. Instead of simply assigning equal points to the last three guys who touched the puck (as scoring leaders does), we decided to evaluate each goal on its own merits, assigning points to each of the players involved (not limiting the contributors at three, but sometimes stopping short as well). We called it goals created.

The product of this analysis was very interesting, and I promise to share it with you soon in an upcoming post. But today I wanted to talk about one of the by-products of the statistical compilation that we undertook: the average value of each component part (i.e., G, A1, A2, others). In particular, I wanted to address the value of the second assist.

What is the value of an assist?

I think we've all exclaimed at one point or another the silliness of assigning the same weight to some assists as a goalscorer gets for an unassisted goal. I think we can all remember thinking that perhaps goals and assists are not worth the same amount just because the stats page tells they do, and that some goals, some assists are better than others.

As I looked at the statistics we were gathering, I was curious to see what might have been written on this topic in the past. As it turns out, there is quite a bit.

The general consensus seems to be that a second assist is worth less than a goal and less than a first assist, but to what extent is (and will remain) unclear. James Mirtle chimed in on this a few years ago. And the new stats community has been in on the discussion. But it seems the area where this has seen the most light is among those who attempt to make the NHL statistics speak to player contribution through mathematical manipulation ¬ specifically Allan Ryder of Goals Created.

Allan writes an extensive thesis on how he thinks players contribute to the results (wins) on the ice. If you’re keen you can find some of his full work here. If you want to stick to assists today, then he wrote on those for the Globe and Mail a few years back too.

After reading all the fretting over the inadequacy of the NHL scoring methods, it came a quite a surprise that statistical experts have come to one of three conclusions on this:
  1. Analysts are limited by the information in the scoring reports, and only the NHL has the ability to increase the data
  2. Second assists are worth less, so we’ll remove them altogether for a G+A1 look
  3. Second assists are worth less, but we’re not sure how much, so we’ll assign a number based on individual intuition to create a correction factor

Obviously, point one is outdated and has been completely misproven by the work of Olivier in the Habs camp and many others like him around the league. Point two is an improvement, but discounting second assists altogether might be as wrong as counting them equally in the first place. The third approach is the step in the right direction, but it stops short of illuminating anything, as it is unclear how much data and research plays a part in the divining of those numbers.

In his lengthy 2004 report on player contribution, Allan Ryder wrote:
“I know of no research on the relative value of goals versus assists. So you will just have to live with my best guess.”
I don’t pretend to have taken the definitive step in settling this age old debate, but I think what we have done is at least an interesting starting point. By looking at all the goals individually and recording situation, players and contribution score we at least raise a flag to say that perhaps 0.5 a goal and 0.25 per assist is out of whack.

Goal distribution

Historical statistics for the NHL show that typically 5% of goals are unassisted, 20% of goals have one assist and the other 75% have the full two. This means there are 1.7 assists per goal scored.

This season, the Montreal Canadiens scored a total of 256 goals.

193 of the goals had 2 assists credited (75%)
45 of the goals had 1 assist credited (18%)
18 goals were unassisted (7%)

These numbers mean there were 1.68 assists per goal this year in Montreal.

That looks just about right, considering what we should expect. I agree the sample would be better with goals from all teams included, but at least the Habs aren’t some unassisted goalscoring anomaly to waste a season worth of data collection.

Value of goals

It seems that those who suggested a goalscorer should get about 50% of credit on all NHL goals might be vindicated. A season's worth of Habs goals puts goalscoring credit at about 54%, pretty close to half.

Interesting to note, however, is that not all goals are created equally. Shorthanded goals show a trend to being more goalscorer driven (not surprising), and PP goals have the goalscorer sharing much more credit with his teammates.

All in all, the goalscoring picture is about where we might have thought with a number out of the air. So far so good.

Value of assists

This is where things get interesting. With about 46% of credit left to dole out, an equitable soul might place the first and second assists at about 23% each. The most daring of stats guessers put the ratio at 3:2
(or 0.28 and 0.18, or thereabouts).

Total numbers showing 0.33 and 0.13 put these estimates way off.

Data for ES and PP all show the same - that a first assist is a major contribution to a goal, a second assist is a minor one.

What does this mean?

If this data is indicative of the way things happen elsewhere, then as suspected, the NHL scoring leaders do not do a very good job of representing player contribution.

While we already know that goals are better than assists, we can tease that information just by looking at the scoring breakdown. But if there is a massive difference between first and second assist then scoring summaries that don't split into two sets of helpers must be severely questioned.

This we mostly knew already. Hence the rise of the player contribution systems from both Allan Ryder and Tom Awad. There are implications for these systems too. Awad for example feeds all assists into his GVT at the same value, and may have a value for goals (0.43) that underestimates the triggerman.

The last, and probably most important thing, this data tells me is that generalizing values to situation (whether it be ES, PP or SH, or 1assists, 2 assists goals) creates error. If we as fans want to get to the bottom of player contribution, then we have have work to do.

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