Updated Game-by-game Expected Goals

By Drew Olsen (@drewjolsen)

Starting today, if you go to our xG by Game page (also listed at the bottom of this post), you'll notice that there are now two expected goals totals for each team. That's because we have multiple xG models, and they give different results. Crazy, we know. One is called the team expected goals model, and the other the player expected goals model. There are just two simple differences between these models, but they are significant. 

1. Penalty kicks are worth less in the team model. 
2. Sequential shots get their value diminished in the team model.

To elucidate the differences between these two different versions, it's easier to explain why we built them. The team model (abbreviated xGt) was built to measure a team's quality. It is meant to help clarify which team was able to create the better opportunities in the game, not just the luckiest ones. The player model (xGp) was built to measure the actual chances. It attempts to measure all shots at face value. 

Let me expand on the two distinctions listed above, starting with the different values for penalty kicks. As we know, there are lots of actions that lead to PKs. Sometimes it is a clear chance in the box that ends with the player getting fouled seconds before slotting the ball into the net. Johnny Russell receiving Andrew Tarbell's Mortal Kombat finishing move on Saturday was a great example of this (GIF to the right). 

But not all PKs are created equal. For every clearly denied opportunity there is also here is a random ricocheted cross that caroms off of an unwitting defender's hand. A good example of a PK that came from a chance that wasn't worth much is the one below. It's a clear penalty, but if David Horst hadn't have been dragged down the opportunity still wouldn't have been a very good one, and certainly nowhere as valuable as a penalty kick.

So while both infractions correctly resulted in a penalty, the circumstances were very different. Earning PKs is in large part (though certainly nowhere near entirely) due to some randomness, so the team xG model reduces their value. Don't get me wrong, they're still worth much more (0.248 xG) than the average shot, but because PKs usually come from chances that are much less valuable than a PK itself, the team model reduces their value significantly.

The player xG model is much simpler in concept. It doesn't try to mitigate luck or determine which team actually earned their opportunities; it just sums up all the actual opportunities that were had. So while the team model is designed to account for the fact that earning PKs involves some good fortune, the player model accounts only for the fact that that team earned a PK and one of its players shot it. Based off the fact that players make their PKs about 78% of the time, the player model awards their team 0.78 xG. It's based off of what actually happened, and is indifferent to the fact that some luck may have been involved.

The second difference between the models is that sequential shots get their value diminished in the team model. Matthias wrote about this last year, but here's gist: in our team model, no team can score more than 1.0 xG in the same sequence. The corner kick sequence from Seattle in the GIF to the right totaled more than 2.0 expected goals. Our exhaustive research has proven that only one real-life goal can be scored per sequence, so the team xG model only credits Seattle with 1.0 xG. But because the player model is the sum of all the shots, it still gives Seattle the full 2.1 xG that all the shots add up to.

So here's how we would recommend you use these two models: If you're looking to see which team created the better chances, then the xGt is more relevant. It's going to give you a better idea of how the game went and which team was more productive. If you want to know which team had the better chances, then xGp is more useful. It will tell you which team actually took the higher quality shots.

So next time a coach says "we deserved to win the game" when his team actually lost, go to our xG by Game tables. If his team had the higher xGt, he's trying to say that his side created better chances than the other team. If the xGp is higher, he's trying to say that his team had their shots, but they blew them. If his team lost all three of the actual goals, xGt, and xGp battles, then he's probably just a moron. But then again, "stats will lose to the human spirit every day" so what do we really know, anyway?

Date	Home	HG	HxGt	HxGp	Away	AG	AxGt	AxGp	xGDt	xGDp
2018-03-18	Kansas City	3	1.25	1.78	San Jose	2	1.50	1.61	-0.26	0.17
2018-03-18	FC Dallas	3	2.70	2.72	Seattle	0	1.00	1.02	1.70	1.70
2018-03-18	Salt Lake	1	0.51	1.04	New York	0	0.82	0.84	-0.32	0.20
2018-03-17	Montreal	1	1.32	1.33	Toronto	0	1.11	1.11	0.22	0.22
2018-03-17	DC United	2	1.41	1.43	Houston	2	1.69	1.69	-0.28	-0.27
2018-03-17	Minnesota United	2	1.93	2.23	Chicago	1	0.95	1.01	0.97	1.22
2018-03-17	Atlanta United	3	2.55	3.13	Vancouver	1	0.72	0.72	1.83	2.41
2018-03-17	New York City FC	2	0.85	0.85	Orlando City	0	0.79	0.79	0.07	0.07
2018-03-17	Philadelphia	0	0.63	0.63	Columbus	0	0.76	0.76	-0.13	-0.13
2018-03-11	New York	4	2.48	2.49	Portland	0	1.20	1.20	1.28	1.30
2018-03-11	Atlanta United	3	1.61	1.61	DC United	1	1.26	1.26	0.35	0.35
2018-03-11	New York City FC	2	1.61	1.67	L.A. Galaxy	1	1.47	1.47	0.14	0.20
2018-03-11	Orlando City	1	1.32	1.86	Minnesota United	2	1.15	1.15	0.18	0.72
2018-03-10	Columbus	3	1.90	2.98	Montreal	2	1.69	1.69	0.21	1.29
2018-03-10	New England	2	1.15	1.15	Colorado	1	1.52	2.13	-0.37	-0.99
2018-03-10	Salt Lake	1	1.72	2.33	Los Angeles FC	5	3.79	3.86	-2.06	-1.52
2018-03-10	Chicago	3	3.20	3.26	Kansas City	4	1.53	1.58	1.66	1.68
2018-03-10	Houston	1	2.07	2.07	Vancouver	2	0.68	1.24	1.39	0.83
2018-03-05	Kansas City	0	1.53	1.53	New York City FC	2	1.39	1.40	0.14	0.14
2018-03-05	L.A. Galaxy	2	2.72	2.96	Portland	1	1.49	1.49	1.23	1.47
2018-03-04	Philadelphia	2	3.46	3.49	New England	0	0.74	0.76	2.71	2.73
2018-03-04	Orlando City	1	1.27	1.27	DC United	1	1.63	2.33	-0.36	-1.06
2018-03-04	FC Dallas	0	1.31	1.35	Salt Lake	1	0.62	0.62	0.69	0.72
2018-03-04	San Jose	3	2.05	2.08	Minnesota United	2	1.10	1.11	0.95	0.97
2018-03-04	Seattle	0	2.35	2.52	Los Angeles FC	1	0.48	0.48	1.88	2.05
2018-03-04	Vancouver	2	1.25	1.25	Montreal	1	0.56	0.56	0.69	0.69
2018-03-03	Toronto	0	1.35	1.37	Columbus	2	1.31	1.31	0.04	0.06
2018-03-03	Houston	4	2.15	2.15	Atlanta United	0	1.20	1.74	0.95	0.42