Are the Stars Low-Key Really Good? An Overly-Long, Overly-Simple Look at Goal Differential, Shooting %, & the Variance & Implications of Each

I was playing around with some numbers and thought some of the results were neat enough to share. I guess this post will have a couple of purposes; one, to explore the correlation between a team's goal differential and that team's wins and losses, particularly how GD is a pretty reliable predictor of a team's point total. Second, to apply that principle to Dallas's poor luck this season on converting shots into goals, and to use simple arithmetic - nothing complicated or fancy, since that would be over my head! - to approximate how many points/wins Dallas would have if they'd gotten even average luck on their shot totals.

The tl;dr is that, while the Stars obviously aren't top-tier Cup contenders, they might be a bit better than a lot of us, at least myself, would've thought; there'll of course be plenty of caveats there, but for now, the best place to start is an interesting article I stumbled on, which started this whole chain of thought:

The takeaway from that article is the linear correlation between goal differential and points in the standings; if you have a team's GD, you can reliably estimate their points. You can see from the article's graph that the scatterplot points form a more-or-less straight line. There is some variance, and that's where the fancy-shmancy r-squared stuff comes in, but for the most part, it's just the plain ol' rise-over-run stuff from 8th grade algebra: if you know the relationship between X and Y, you can plug any X value into the graph/formula and get the its corresponding Y value. (Not trying to insult anyone by recapping how 8th grade math works, just pointing out that the math they're using is very simple, and even though the article uses five-dollar phrases like "linear regression", we're not really getting too far out in the weeds!)

The article's most interesting point is that we can expect a mediocre team that scores as many goals as they allow (i.e., a 0 GD) to finish the season with about 91 or 92 points. And every +3 or -3 in a team's goal differential will fairly reliably correspond to an increase or decrease of one point in the standings. E.g., a poor team that finishes -18 in GD should finish with 85 or 86 points, six points worse than the neutral 91/92-point team. A strong team that ends up at +35 in GD should finish with 101-104 points. There are always exceptions, but the correlation is pretty tight, as the article demonstrates.

It's late enough in the season, and the games played for each team close enough to 82, that we can use real teams as examples; consider, then, Tampa's appallingly-good 95 goal differential (!). That works out to an expected 31 or 32 points more than the GD-neutral team (95 divided by 3 is 31.667). That would give them 122-124 points - right in line with their actual current point total of 122.

"Hold on," you're probably saying. "That's all well and good that we can predict a team's points with just their goal differential, but you can just look up a team's points in the standings." That's true! But we can take that GD-neutral team's points percentage - 91 or 92 points of a possible 164 work out to a .55/.56 points percentage. That is, a mediocre, 0-GD team will get 55/56% of their available points.

That in mind, we can approximate a team's point totals much earlier in the season, when we don't have the 82-game sample size; if a team has only played 30 games, using the 3g=1pt rule only tells us how many points we can expect them to finish with if their GD doesn't change at all for the rest of the season (i.e., if their GD in the last 52 games is zero). Of course, this would be very unlikely unless the team is mediocre to begin with. If a team's GD through 30 games is, say, +18, and it's still +18 by season's end, we would expect 97 or 98 points from them. But with a +18 GD through 30 games, they're probably a strong squad and their GD will keep climbing over the last 52 games.

But we can summon that 0-GD team and their .55/.56 point% again; with their neutral GD through 30 games, you'd expect them to have 33 or 34 of the 60 available points. And that once again gives us a nice formula to estimate the +18 team's point total through 30 games. 18 goals above zero gives us about 6 points more than the GD-neutral team, or 39 or 40 points through 30 games.

Dallas has 84 points through their 76 games, with a GD of +6. The GD-0 team would have about 84 points at 76 games, so with the GD model we'd indeed expect Dallas to have about 86 points, give or take. Forecasting with GD is remarkably precise given how simple the model is.

"Look here, jackass, I have things to do besides read this aimless dissertation," you're probably saying. "It doesn't matter if you're 30 games into the season, or 76 or 82, you can still look up how many points they have. You don't need to estimate it with goal differential. Is there at least some point you're building toward?"

There is! I can't guarantee that this post still isn't a waste of your time, but have you ever wondered this year what the Stars' record would be if they weren't downright hexed offensively?

I sure have. Prior to the Winnipeg game, the Stars had the lowest shooting % in the league at 8.2%. It's now up to 8.3, ahead of only the Sabres and their dreadful 8.1%. Think of all the highlight-reel saves made against Dallas by mediocre goalies, all the games in which it's taken them 25, 30, 40 shots just to get a single goal - if that! - past some or other backup goalie. The year-to-year average shooting %, toward which all teams that score on an inordinately high or low number of shots eventually regress, is 9%.

A quick resource for those who aren't overly familiar with shooting %, the large degree of variance built into it, and its usefulness as a barometer for a team's offensive luck, or lack thereof:

The Stars have 2325 shots on goal this season (as of this writing, through the Jets game). Not particularly good, as it puts them 23rd in the league. Combined with their bad luck on those shots, they're third to last in goals scored, with just 193 on those 2325 shots. But how many goals would they have scored if they'd just gotten average luck on those shots? And how would it affect their point total? In short, how good is this team really?

It goes without saying that this will be an imperfect method, but I'll come back to those reservations shortly. The league average shooting % this season is 9.5. If the Stars had converted at that league-average rate, they would have 221 goals on their 2325 shots instead of 193. With their 187 goals allowed, if they converted their shots with merely league-average luck, the Stars would have a goal differential of +34.

Based on the 3g/1pt model, at 76gp, we would expect the Stars to have, currently, 94-96 points with six games remaining. That point percentage through 82 games would see them finish with 101-103 points.

True, we can't extrapolate a certain number of wins from those extra goals with any certainty - if most of the extra goals came in games that were already wins, it wouldn't affect their point total much, and if they were clustered so as to come in close losses, it would overstate the effect. We've made the modestly reasonable assumption that those goals would be clustered such that those two effects balanced each other out, and the pretty reliable 3g = 1pt rule would hold true.

Another caveat is that league average luck would see the Stars' goals against number rise slightly, since their .922 team Sv% is such an extreme number relative to league average. That's not to imply at all that Bishop, Khudobin & the team's defense haven't been excellent; they clearly have. But after all, a team's Sv% is just their opponents' Sh%, so it's equally prone to variance (though it does seem a bit more stable - I don't know if that's true mathematically, it's just intuition to be taken with a grain of salt.) So average luck in both goals for and against would see a large increase in the former and an unknown increase in the latter, but it would still likely be a net positive, and it seems a reasonable conclusion that the Stars are modestly better than their record indicates.

It bears repeating that the above scenario - 94-96 points, with a 100+ point season likely - assumes only that the Stars enjoyed average shooting luck up to this point. 95 points right now, warts and all, even including the long stretches of underperforming and generally weak possession numbers. An optimist might assume, given how demanding Montgomery's system is*, that it comes with a steep learning curve and the team is just now finding their rhythm in it. Might the team be better even than 100 points? And surely they'd have at least a couple more wins if not for lengthy injuries to core players - Klingberg missed 18 games, Radulov missed 12.

And if Zuccarello had stayed healthy too? Mightn't they be firmly in contention for the division title, if they could so easily have 95 points right now, even with those big injuries?

Of course, if we take it that far, we're essentially just daydreaming about a season in which nothing ever went wrong. We might as well daydream about the Stars scoring on 20% of their shots. But the main point here is how easily a 100-point season could be a near-lock, given just league-average shooting luck, even with all the team's warts. I'm still far from sold on Monty, but the team has played much better lately. Even if the wins haven't followed suit, I'm a good bit more encouraged than I was. Shooting percentages, especially ones as seemingly moribund as 8.3%, will always regress upward sooner or later.

Personally, I'm pretty excited to see the Stars play healthy and with Zucs back. I'm not ready to bet on a trip to the WCF or anything, but I'm a lot more excited about the playoffs than I was before I looked at all these numbers (and before that incredible win in Winnipeg, at that). I don't reckon anyone wants to draw us in the playoffs, and that's not something I would've thought earlier in the year.

*The Monty System: backcheck hard and collapse in the slot, a la Hitchcock - but then get all the way behind the low forecheckers and gain their zone with speed! To hell with the cake police, we're gonna have ours and eat it too!

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