Login

juke · 04-19-2020, 12:29 PM

2000 words + graphs

Welcome to the first release of Corsi Corner (ty @"NeonLime" for the name idea), SHN’s spin-off series where we take a more in depth look into some of the numbers, trends, and other advanced stats in the league. This week’s piece comes from deep within the dungeon of the SHN’s statistics and graphing department, where Luke lets me out every few days for some sunlight and water, to take an investigative approach at trying to crack the formula behind FHM’s ‘game rating’ statistic. As a side note that will be disappointing to some of you, this piece only focuses on skaters, as there wasn’t too much of a mystery behind goalie’s game ratings, as they’re mostly a function of save percentage and goals against average.

Since we switched sim engines over to FHM, skaters in particular have experienced much more specificity in their builds, roles, and team tactics, opposed to the generic and mostly similar builds that we were seeing everyone use with Simon. Along with the more exciting player build and role options, we’ve also gained a much more expansive stats index, one that not only generates the normal player stats but also an array of advanced stats that are both more exciting to follow, and also give us more options to evaluate player and team talent.

One of the new stats on the index in FHM that we didn’t see with Simon are the ‘game ratings.’ These game ratings (GR) come in the categories of offensive GR, defensive GR, and overall GR, and in general there’s not a ton we know about these numbers and where they come from, other than it’s a somewhat arbitrary score given to players that determine how well they played within their role. We obviously know the higher the number the better the GR, and by looking at some of the top GR players in the league, we can see they all score a decent amount of points, though it’s important to note that some of the highest GR players don’t score as many points as some of the players rated below them. Looking at the graph below, we can see that the distribution of GR across the league is similar for forwards and defensemen and that the bulk of players are found in the 50 to 70 range, with both the mean and median GR being 62. We can also see that only 16% of players have a GR of 70 or above, so the players that find themselves above that threshold could be considered in the upper tier of game ratings.

The main question that I’m looking into for this piece is ‘what types of things are players doing on the ice that contribute to a better GR?’ Is it purely putting points on the board? How much do defensive stats such as blocked shots, hits, and takeaways contribute to GR? How heavily weighted are team stats like corsi for/against? Basically, trying to reverse engineer the GR formula. Trying to figure out some of these questions might help us decide exactly how important GR really is as a stat and where that number comes from, and how much stock we should be putting into seeing players with good vs. bad GRs. To start this process, the first thing we have to do is compile a list of player stats from the index, compare them with each player’s GR, and see which stats have the highest correlation with GR. The three graphs below show the stat vs. GR correlation for forwards, for offensive GR, defensive GR, and overall GR, and all of the stat values are normalized per 60 minutes of ice time for each skater.

Now, before we get into looking into the results, there’s a few things and flaws to address in the data. First and foremost, there are correlation stats (and are also in order from top left to bottom right by strength of the correlation), and as most introductory statistics class or a reddit comment thread argument will tell you, correlation does not equal causation. This means that even if a stat has a strong correlation to GR, it doesn’t necessarily mean that being good in that stat will automatically lead to a good GR. It just means that players who have higher GR ratings also have higher point scored, for example. The next thing to note is that like I said before, we know GR is dependent on player roles, and I don’t have that data, so we just have to look at this data as just skaters in general. With that aside, I don’t think it’s a surprise to see that points scored has the strongest correlation with GR for forwards. Goals and assists are also highly correlated, but redundant after including points. FHM apparently really likes when players take shots on goal, as it’s the 3rd best correlation with GR (2nd if you exclude assists being already counted for with points), however missing the net or having the shot blocked decreases the resulting GR, which we can see by corsi and fenwick ‘for’ being much lower in the list. Despite corsi and fenwick ‘for’ having much weaker correlations, corsi and fenwick ‘against’ are some of the strongest tied stats to GR, so perhaps FHM favors defensive minded forwards more for GR than purely offensive players. There’s a lot to look at and analyze here, but the last thing I’ll observe, which was a surprise to me, is that corsi and fenwick ‘percentages’ have absolutely no correlative power whatsoever, but their ‘relative percentage’ counterparts have some of the best correlations. I think this is a good feature that allows players on bad teams to not have their GR tanked, and they’re rewarded for holding down the fort when none of their other teammates can. The next set of three graphs represent the same data, displayed slightly differently. For offensive GR, defensive GR, and overall GR, it graphs the stats in order of their correlation coefficient, so basically in order of which stats go hand-in-hand with GR the most.

[Image: unknown.png]

Keep in mind that a high negative value still implies a strong correlation, just in the opposite direction, which is why we see large negative values for the shot/goal against stats as well as PIM. I use these graphs more later, but for now the thing I wanted to point out most is how on the defensive GR graph, the highest correlated stats still have relatively weak correlations to defensive GR, compared to the offensive and overall GR categories. I think that @sve7en explained this best when I was discussing this piece with the SHN crew: for offensive GR, there’s some pretty tangible stats to compare to, things like points, shots, etc. But a good defensive player might do a bunch of little things right that don’t end up on the scoresheet. Things like disrupting a passing lane, clearing the zone, controlling rebounds, forcing a turnover, will likely all contribute to a good GR, but not necessarily the scoresheet. Which is why trying to compare stats to defensive GR is slightly worthless. With the forwards and some minor data explanation out of the way, the next 6 graphs are just a pic dump of the same thing with defensemen.

There’s not entirely a whole lot of difference in observing the GR correlations in defensemen compared to forwards. Shots on goal and points are still the highest correlated stats with GR. I think it’s important to once again remind that correlation does not equal causation. In the case of defensemen, I doubt that scoring goals or taking shots is the only way to get a good GR, like I just mentioned earlier, but rather the defensemen who are good enough to be putting up a lot of points are probably also good enough to be doing well defensively too. Corsi and fenwick ‘against’ are once again highly correlated, as are their ‘relative percentage’ counterparts. Takeaways seem more important for a good GR in defensemen compared to forwards which is intuitive for their role, however I was surprised to see that shots blocked and hits had very minimal and no correlation respectively. The last graph in trying to crack the FHM game rating shown below, and is a good way to sum up the differences in GR for forwards vs. defensemen.

The correlation coefficient is plotted for each stat, colored coded by the two positions, and the line between the dots represents the difference in importance of the stat. Most of the biggest differences are in the already lowest correlated stats, where they went from no correlative power in one position, to barely any power in the other. The most interesting thing that jumps out to me is the huge difference PDO plays in defensemen’s GR compared to forwards. However, we know from the cor plots, that shooting percentage isn’t correlated with GR at all. This means that the part of PDO that’s correlated with GR for defensemen is from the goalie’s save percentage, and that low PDO in defensemen can drag their GR down. This is likely due to the fact that they’re letting up more high danger chances or rebounds, thus the goalie’s worse save percentage, and the defensemen’s worse GR. Now that we know which stats are highly correlated with GR, and we know the relative importance of each stat, I decided to try and come up with my own stat-based rating. The graph below shows this custom stat rating vs. their FHM game rating.

I created this rating using a player’s stat list and custom weighted multipliers based on the stat’s correlation coefficient from earlier and the player’s position. Meaning that things like points and shots on goal are still the most important factor of this new rating, while other stats like hits and corsi ‘percentage’ aren’t even included at all. Also important to note: the stat rating ranges from about -2 to 2, with 0 being a league average stat line. Negative scores indicate below league average, while positive indicate above league average. Additionally, ratings were calculated for forwards and defensemen independently, so defensemen didn’t get punished for not scoring as much as the forwards. As you can see, the new formula does a pretty good job at matching GR, and we have an r squared of 0.6. There’s obviously not too much use for this over FHM’s GR, other than we (or I) know exactly what stats the rating is based off of, and we know it’s purely a tangible stat rating, not game rating. This new rating basically quantifies a player’s season stat line as opposed to trying to track the little things they do right in each game. For anyone familiar with my past media, I’ve made this graph interactive and you can find it with the following link: https://plotly.com/~smalinowski7/39/#/ In this graph, you can hover over the data points and see more information, such as the player, their GR, and their new stat rating. Additionally, you can toggle teams on/off the graph by clicking their dot in the legend. To summarize players, I’ve also included a top 20 list for each position for the stat based rating. Since points are highly weighted, it’s no surprise that Wagstrom leads this category as well, Scoop is first among defensemen, and that the list is mostly made up of players from the best teams in the league. And finally, I put together a heatmap of all the teams and their players, color coded by the new stat rating, sorted by average rating. The overall order comes pretty close to matching the generic standings. Teams like Buffalo and NOL are lower on this list than standings, partly because goalies aren’t included and they’re both getting extremely strong goaltending as part of their success. It also speaks to the depth scoring that teams like NEW, HAM, and LAP are getting, since almost their entire roster is above league average in terms of stat line, and their lowest player is basically at league average.

[Image: unknown.png]

***Gwdjohnson*** · 04-19-2020, 10:11 PM

Wow this is really awesome. Wanted to do some research into how GR works, myself, to see how useful a metric it really is for determining how much a player is contributing to overall team success, but I'm lazy. Because GR strictly evaluates the players' performances relative to the roles they're playing, it seems like it's a good metric to tell how a player is doing in their given role, but doesn't really measure how well they mesh with their linemates/the team's style of play. So I think that GR doesn't automatically equal that a player is being used effectively, and could be a false positive that is potentially misleading.