## March 18, 2007

### First and Second assists

Most people would agree that a first assist is not the same as a second assist and many hockey statistics people have tried to explain how some assists are worth more than others (first worth more than seconds), with little actual analysis I might add. I’ve often wondered about the differences in them, but found it difficult to show one is worth more than the other. Founder of new hockey statistical analysis: Alan Ryder says: “It seems reasonable to conclude that, on balance, there is more value generated in a first assist than in a previous touch of the puck. The Forechecker says: “the general agreement is that 1st assists are generally ‘worth more’ than 2nd assists”.

About a year ago I did a regression on player’s salaries testing many variables, such as player contribution and many of the standard variables: goals, assists (first and second). In general hockey statistics people believe some assists are worth more than others (first worth more than seconds). However, the regression showed the second assists cost GM’s more. That is to say a GM was more likely to spend more on a guy with more second assists than a guy with more first assists. The difference was not statistically significant, but it was interesting none the less and suggested that people’s intuition, that second assists being worth first assists, may not be valid. What matters more than the ratio of first vs. second assists, but rather a players ability to get an assist on a goal (be involved), but even that can be flawed as some player’s roles don’t encourage assists (net presence)

Error Approximations

Even if we knew the absolute value of a first assist versus a second assist there would still be the perennial error lingering around that messes with the results. If you assume for the moment that a forward gets a first assist on 33% of goals and a second assist of 23% of and the player sees around 100 goals, then that player should have 56 assists plus or minus 10 (46, 66) and this would be perfectly within the random expectation. Now assuming they have 56 assists, the should get about 33 first assists and 23 second assists (33% and 23% of 100 respectively), with an error of 7, so anything from 26 to 40 first assists and 16 to 30 second assists, this implies the expected random variation in the ratio of 26/56 to 40/56 to or 46% to 71%, this can be seen here. For a player with half as many plusses as Crosby the expected ratio range is: 8.3/23 to 18.3/23 or 36% to 80%. In addition much of the ratio has to do with style and not necessarily increased value. Goal scorers don’t generally pass, but do create rebounds so their primary assist would be firsts (accidental firsts). The above shows there are a number of ways to get a “bad ratio” between first and second assists: either too few first assists or too many second assist. Too few first assists could be a bad thing or could be the result of random variations. Too many second assists could also be the result of random variations or it could be a good thing.

Expected Assists vs. Actual assists

Its interesting looking at how well different players did compared to the expected performance based on how many plusses the player gets in different situations (power play, penalty kill, even strength). I’m not sure how many people are familiar with the graphs below, but these are standard residual vs. fits graphs. They plot the expected value (number of assists you would expect given a certain number of plusses) against the errors (residual or difference from the actual number of assists). In these graphs the residuals are normalized so the typical range for 95% of the data is presented as the green area (-2, 2) and the rest of the residuals (|error|>2) is left as white.

In the first assist graph you will see a lot of play makers in the top half (residual > 2). I’m not sure what to make of all the names though, so I’ll let anyone else try and figure it out.

It’s the second assist graph that I find most intriguing. The most dominating players in this category include: Sakic, Thornton, Savard, Crosby, Brind’Amour, Weight and Elias, with Jagr and St. Louis close to making it as well. These players are all skilled play makers, should we say they're worse because of al these second assists? On the flip side: Smyth, Murray, Homstrom, Ovechkin and Kovalchuk. Interestingly, Selanne and Heatley fall close to this group. Other notables include: Parrish, Hejduk, Staal, etc. Both types of players are probably necessary on a given team (high second assist players and low second assist players), one may be able to argue that low second assist players may actually be contributing to more goals than their statistics might indicate (eg. Smyth’s point totals underestimate his value). It’s hard to argue that Crosby’s second assists over estimate his value, due to the fact he is part of a much larger number of goals than his plusses indicate. Personally, I would take a Sakic, Thornton or Crosby over an Ovechkin or a Kovalchuk. I’m not sure any of this shed more or less light onto assists though, but I think it highlights the variability and player styles in determining what types of assists a player gets.

Conclussion

What I’m trying to get across is that second assists and first assists are certainly different, but they don’t necessarily have different values. Certainly some second assists are the result of luck, but all players get some assists as part of luck, but often that pass was as important as the final pass.

#### 1 comment:

The Forechecker said...

Interesting stuff - my brain's kinda foggy at the moment (just got back from a beer league game, and am getting into the beer), but I'm thinking what we have here is a qualitative measure that might perhaps best be used to determine which players might work best together on the ice. For example, a puck hog that takes lots of shots (and high 1st-assist ratio) might well be paired with a banger who goes to the net for rebounds, whereas a soft-handed sniper might need a skilled passer who racks up more 2nd assists. Something to think about over the summer.