Hello and welcome to the double pivot the world's most agreeable soccer Alex podcast I am Michael Kaylee we are back and we are gonna be taking some mailbag questions this week We'll obviously be here to talk about the Champions League games when they happen maybe even the Europa League games I don't know could happen, but in the meantime it's time for the mail day We got these from the double pivot discord, which you can join and I'm joined by Mike Goodman who can tell you how Let's do it to be secure in the way as well There's please don't subscribe because happy as podcasters patreon.com slash double pivot is where you can subscribe to the podcast And you can remember the discord where there is lots of chat all the time about all sorts of Different things sometimes even in the channels that they are designated for we got these questions from the mailbag channel Which is the place where people are supposed to ask us questions, but is in fact It's generally just a place where somebody asks a question that a bunch of people sometimes one of us include it talks about the question That was asked so this comes from cucks kooks KKS asks Would you rather be a plus one xg team at 2.5 to 1.5 on average or 1.5 to 0.5 on average Is it different for league versus knockout competition? This is on one level a really easy question and then on another level It's a fairly difficult question when you start to get at the concepts that it is asking and what you are trying to weave into it And what we are trying to look at holistically when we think about soccer So I think maybe the place to start is like the easy version of the question the answer is 1.5 to 0.5 You would rather be the 1.5 to 0.5 team. That's the answer to the question. Yes Why I think that the easiest way to get at this is to take sort of a a walk through Analytics in other sports Because soccer is a more difficult sport to estimate points from goal difference Compared to projecting wins from run difference in baseball wins from point difference in basketball or American football because lots and lots of games do end in Ties and that changes the math significantly.
It makes it much much more complicated to do this But in all of those other sports people use some form of ratio of points goals runs Created to concede it and the most famous of these the place where starts obviously is baseball It is the Pythagorean theorem that was developed by Bill James back in the 70s and 80s He called the Pythagorean because it looks visually like the Pythagorean theorem for estimate size of right triangles It's a little bit messy that we still call it that because it's kind of not a great name for it to name it name a formula after another formula That it resembles that's confusing. But anyway, what it is is runs Squared divided by the sum of runs squared plus runs allowed squared and so what this does is it's a ratio But it's a ratio that slightly increases the Importance of having more runs or than the other team the larger the gap in your like you're just your ratio of runs scored to runs allowed As that gap gets larger the likelihood that you win games increases further and further That's why you square them that's what it does and then in the NFL the football outsiders use a very very similar number Which is they found to be about at one about point two point five But again a ratio that actually increases the gap as the gap gets larger in the NBA where points were is much much much much higher They have they use an exponent of between 14 and 16 depending whether you trust Darrell Murray or John Hollinger So again, that means points to the 14th power divided by the sum of points of the 14th power plus points can see allowed to the 14th power Well, it's become exceptionally large numbers The reason you do that again is to create a larger likelihood of winning from a relatively small difference So all of these sports you use a ratio and at the very limit case It's very very obvious why? If you think of a baseball team that just never allows any runs They win every single game eventually if they never allow any runs the same as true a basketball team Offsets a little get all the silly, but you can have this as certain because there is a zero point for points allowed and No maximum point for points scored There is always going to be it's going to be better To have to use a ratio that can account for that fact at the zero point and that this continues to be the case is the game goes on so all of those other sports you use ratios and this is It becomes the math becomes harder and the theory becomes harder and softer But that should always be your starting point is that you do want to think about how much better is our attack than our How much better are we as a ratio of creating to conceding that's going to be your basis? That is true that this is not exactly how you should like back of the napkin way do the math and soccer But that is peculiar to the soaring environment of soccer So then the next question to ask is so when we sort of understand this right that like you can score infinite points You can't concede negative goals like that's that's just the bottom line right the next place to go is okay That is the reason it is the limit of zero if the limit of zero didn't exist This is a weird thought experiment right like if we weren't so concerned with zero And this is like when you get towards basketball right because practically speaking you cannot concede zero points of basketball and you have to put in a much much much bigger exponent to start to see why it is that we that this matters Does it say something about how our skills are impacting the game right?
Does it say something about how various skills of a team or of players impacted the game or is it purely purely a mathematical Artifice because you can't score less than zero goals. Yeah, so to sort of rehearse why the zero point is important The thing what I want to emphasize is that in game in sports without ties if you never concede you have to have a win ratio of one so you've got to create something that goes to you know goes to the limit case and Point difference goal difference doesn't go to the limit case creating one run per game and conceding no runs for games The same difference is creating two runs per game and conceding one run per game But one of them is a limit where you win every single game and the other one isn't and so you need to have those ratios And as Mike was saying those ratios actually you have to expand the ratio more As you get further and further away from the limit case It remains the case that you need to expand these ratios more as you get further from the limit case now What is peculiar about soccer is that one because it is close to the limit? You would need to use a pretty small exponent as you do in baseball and football which are lower scoring and then soccer is even lower scoring than that so if you were to imagine a version of soccer without ties and It seems horrible obviously no one would like it. I guess you could make the goals incredibly large But if you imagine a version of soccer without ties You wouldn't have to use as a large an exponent as you do in baseball or football You'd be using a exponent for your ratio that is closer to one than it is to two or to fourteen And so you'd be getting closer and closer to looking just at goal difference You still wouldn't be but you'd be getting closer and closer to even if there were ties and then when you add in the fact that there are draws in soccer that then it means that the The effect of your goal difference on your points is muted because a lot of games will end with just one point for both teams And so you have a second dampener the first dampener is how low scoring the game is the second dampener is the existence of Draws and that gets us down to a point where we are seeing similar quality effects from goal difference and a simple goal ratio and so this is the key thing if You look at goal difference and goal ratio projecting points in soccer They are very similar.
It is not that goal difference projects points wildly better than goal ratio It is that at the standard level of scoring and soccer three-ish goals per game They're pretty similar and it's a little bit better to use goal difference was dad Altman who pointed this out to me I was first doing soccer analytics and I was using a single exponent goals ratio as the simplest way of doing I found that adding more exponents to it was bad He said look just use difference just use difference and I tested it But it's very close so what you're looking at is at the very limit case in soccer There is a very small value in using goal difference when you are looking at the relatively small range of Difference among soccer teams because again soccer means for the most part because the game is so stratified You don't have teams at one extreme end or the other the teams are the best at defending also the best attack And the teams are the worst of the defending are also the worst of the attack And so instead of having like huge differences in how much goal scoring there is in any individual teams games instead You get a pretty standard like one line goes up one line goes down Now let's take it one step removed. What if instead of talking about goals? We were talking about expected goals as you were saying There is an incredibly small difference here between difference in ratio, right? But because of that incredibly small difference you'd rather be 1.5 versus 0.5 then 2.5 versus 1.5, right?
That's where we start The question then becomes if you switch it to xg Would you rather be 1.5 xg versus 0.5 xg or 2.5 xg versus 1.5 xg is a team is there an Artifice of xg as it reflects the real world that might outweigh that right and so the question here is that While teams can concede very very small numbers of goals They're conceing somewhat more shots right and there's always and and those shots There's some random variation in whether those shots are scored in any given game And so you just sort of create more error bars more fuzziness around it There's also another question and that is is there a differentiator of skill versus xg or not? right if you are going from creating for yourself 1.5 xg to 2.5 xg and You are a team that is at the upper echelon of skill in soccer Presumably you were taking more shots while you do it presumably while you were also taking more shots You are in fact repeating in edge for your attackers against xg that is not reflected then in xg Do we think one that that is true and two if it is true it might be true enough? To make that approach better. Well, I have some questions about the premise of this question It's it is certainly the case from studies that I have done Some other people have worked on this as well You know better players are better at finishing teams with the best players that sign the best players who are good at kicking are good It's better at scoring.
This is why is one of the many reasons why people tend to use some kind of 70 30 ratio of xg to goals And there's different ways of doing this But like if you want to estimate how good a team is you do want to include real goal scoring in that because your estimate of how good a team is Should include some amount of how good is this team at finishing the shots that they take how good is this team at saving the shots that are Attempted against them and because again soccer is so economically stratified those two things go together in most cases teams that are better have better players better players are all are better at all of these things and so to me that is an argument for Using goals a little bit as part of your number and that would then decrease some of the fuzziness Around xg as a number because there is some greater as you are increasing xg You should be among the teams that have the best ability to increase xg increasing goal certainty a little bit more and vice versa so To sort of return to the original question And in our chat a nice deal went and just ran some simulations for us at xg And found that you would you get you should you get more points from being 1.5 to 0.5 And you get a slightly larger percentage boost In likelihood of winning a knockout game. So the other issue here is three points per win Which again, we don't have in baseball or basketball or american football and three points per win makes Drawing less valuable and drawing is obviously an effect of being lower sort So there is a punishment for having lower event lower scoring games because you only get one point for that You get three points for the win you get this bonus for having higher event higher scoring games Which doesn't exist in a knockout competition in a knockout competition. Oh win is worth two points Like exactly the same because you got the two leg it ties but more or less you could think about that way We end is is twice as good as as a draw and so there is some There is some lesser that there is some greater value to playing higher event games in the league than there is in a knockout And so being 1.5 to 0.5. You can actually do that You know, that is that is a very very hard thing to do How is two goals?
Chelsea when they won the champions league they were kind of that mikella artettas arsenal are kind of trying to be that right now 0.5 xg seems to be a real limit case and what anyone can do against serious competition And so You know just things go wrong things go wrong and soccer You just know what is ever perfect and it doesn't seem to be possible to be much better than that And so that really is seems to be our sort of practical limit case and at that practical limit case It really is true that it's better If you can do it and it's even better in a knockout competition than in a league competition where I think the questions get more interesting is recognizing that 0.5 xg allowed is As low as you can go in modern soccer and teams that do it for the most part the next season they still don't do it and so Are you at what point are you starting to make tactical sacrifices and cost yourself something chasing a statistical truth? Because I really want to emphasize that statistically this is just right. This is just true But where does it meet the road of actual soccer decision-making? Yeah, and I think that one of the places this becomes very very interesting is There is an idea in sports, although it's mostly mostly from basketball, but not exclusively from basketball That if you have a skill advantage if you are the better team you want to play a higher event gate more possessions, you know more actions more repetition of the thing because you have an edge so A good basketball team wants to play a game that has more possessions up and down in it against a bad basketball team because every possession They are effectuating their edge a bad basketball team Wants to play a lower possession game and you could see this.
This is why there's a shot clock now in basketball because you know when No surprise Ivy League teams figured this out in in college basketball and they've actually made an extremely Princeton a Princeton offense and extremely low possession style A low possession style where they would keep the ball and keep the ball and keep the ball and not allow lots of possessions back and forth This is Somewhat at odds with the fact that if you are the better team it is better for you Mathematically as a fact to be 1.5 vs. 0.5 vs. 2.5 to 1.5 because you score goals by having these events and What is going on with managers as they are navigating this is in fact a fairly fascinating question Right and I think that here Basketball being so peculiarly high event and high scoring really is a big difference Hockey is hockey is a little bit that way to be fair Even as a hockey in a lot of ways is a lower scoring version of basketball in that way Which really does complicate things and but that's because in hockey there are so many shots to relatively few goals And in hockey because there is so much more randomness in goals being scored There is the spectrum of you could do it expect the goals in hockey rate But the spectrum of value of shots is way compressed Yep, and one of the ways that expected goals ends up working in hockey as I understand it is by including player skill in shooting Yes, it's less that you want to get shots in good areas in hockey that's really really messy But you want to get your good shooters shooting Right, that is yeah, that's right And so I think this is where the 1.5 to 0.5 or it's 2.5 to 1.5 question Kind of misleads us from the real decisions being made There really aren't 2.5 to 1.5 teams they more or less don't exist The kind of team that would do that is an interesting theoretical question That is not relevant for Arsenal or Chelsea And that is not relevant for say the best teams that have Guardiola has put together If they tried to score more they would be adding more goals and more xg And they would be adding more opposition goals and xg, but it would not be an even ratio of the 2 If they attacked more because they're better They would be getting more xg that it's costing them exactly what that number is That's the operational question for soccer teams now think of it in reverse because When we talk about a lot when we talk about over conservatism is Teams making decisions to concede less xg That actually cost them More xg as a trait Right, and there are situations in which that makes sense when you have a lead for example But broadly speaking, I think that when we talk about Teams that are overly focused on control managers that are overly focused on You know, not conceding anything What we're talking about is They are making decisions to lower xg conceded And that I think what they think they are I mean they would never put it in these terms But if I were to think about the decisions they are making and put them in my terms I would say to you what they think they are doing directionally is going from 2.5 versus 1.5 to 1.5 versus 0.5 That's what they feel like they are doing That's what they want to be doing when in fact what they are doing is going from a team that is 2.5 1.5 to a team that is 1.5 0.5 these numbers are all exaggerated to make a point, but the idea here being that it's not that they are trying to move That they may think they are trying to move along a constant spectrum But what these decisions do in fact almost like Buying necessity is change your xg differential and consequently your goal differential theoretically, right And the place that we see this the most commonly is in knockout football This is the keep it tight away win at home theory If you can just defend and get a draw away Then you can win it at home and you can play your normal game at home If this is what went wrong for Liverpool against PSG and if you want to end And the problem is that There is again in there is a theoretically correct idea here I don't think exactly what managers are thinking. I think managers tend to think that zero goals conceded is possible And it's not and that's like one of the core Disagreements between the sort of tactically minded soccer people and the statistically minded soccer people who in another podcast we're gonna do Have a lot in common which is one of the things that makes it very hard to identify Where analytics has changed the game because so much of what analytics is saying is also what modern tactics say about soccer There's so many analogies and so many parallel evolutions there, but here there's I think there's a really big one I think that managers and people who work in football really believe that they can achieve perfection or something very close to it and The nerds are just like no.
No, you can't it's in your feet. What are you talking about? That's stupid and so the managers who are trying to effectuate this I think they're trying to go to zero But and that's where in theory you would think it would work But if it's not going to zero What you have to then ask is if you can get to zero great you did it good theoretically correct But if you cannot get to zero structurally as a fact about soccer Then the question you have to be asking is are these tactical changes costing me significantly more attacking value Then that they are gaining me defensive value And I think that in the vast majority of cases that is true That that you are making an asymmetric trade-off that you need to be in a very extreme situation for it to make sense The next question down the line here and it's one that came up in the discord is okay How does this interact with how we create and can see chances? How how do we turn the levers right because Ten shots of point one xg and one shot of one xg which is the thing that doesn't exist are not created equal And so are we impacting our chances of winning one way or another?
Based on how we are approaching connecting things. Yeah, and that is a Very complex question just statistically. Yes, so we have we have we have run sims in the world And the reality is is that All things being equal you would prefer to have more shots with your xg All things being super equal. There are a couple of reasons for that.
One reason is it reduces ties So if you have more xg than your opponent, um, you want the scenario in which there are less ties Um, the other reason for that and this is again a boundary issue Is that we're dealing with low numbers of shots for the high xg examples here And when you cap the number of shots you take you cap the number of goals you could score And so that brings you down artificially a little bit Below what the numbers would be if you had more shots at lower xg Yep, and so again, this is why theoretically in a knockout tournament There is some greater value to doing this because Playing without the ball playing conservatively playing on the counter is how you try is a simple way to try to get both fewer shots And greater xg per shot. And so if you're not playing for three points for a win, there's a little bit greater value in doing that But exactly as Mike is saying The theoretical stuff here is a little bit removed from the reality of it because when you are trying to add on more shots In practice What you are doing is adding on worse shots Right shots are choices. And if you want a team to shoot more you could tell them to shoot more They can just listen to the crowd that yells shoot and shoot and so to add on One two three five ten more shots at the same xg per shot That's not a thing a team can do unless they make a bunch of choices in how they attack which have defensive costs and Likewise a team that can create a bunch of high xg chances They have some choices that they could make to lead to more shots and lower xg per shot Which are different size and like this is where I think the whatever it goes to this question of like Would you rather have higher xg per shot or lower xg per shot? Again, there's a mathematical answer which is lower xg per shot But the fact that that's obviously crazy tells us that looking at this from purely statistical ends is going to mislead us When we think about the actual game of soccer and the choice of the coaches have to make The process of creating a shot is always Do I take this a relatively low xg shot now?
Or do I make passing decisions that have some risk associated with them that will leave to some chance of a higher xg shot Down the you know down the line, right? That's that's the question that is being asked. It is Absolutely possible To be making aggressive passing decisions that are too aggressive in the search for great shots It is and it is absolutely Possible to be making decisions in which you are just shooting too much in situations You should be taking risky passes. Um, I think for a very very long time in soccer The the math was on a fundamental level wrong people were not hunting good shots enough That's shifted a lot in the last decade and again.
This is a question that we were getting at before of Is it tactical? Is it analytics? They're informed by each other They both kind of say the same thing which was that you guys are shooting too much in low expectations chances We need to hunt better shots and like, you know Yeah, and so I think that is where we are going to take this in the next episode of this series I thought it was really important here to before we start talking about the ways the game has changed and ways that we might wish the game would change To lay out in a really as nerdy as we could as like gesturing with our hands on and describing Graphs in an audio medium way really right in my sweet spot as a podcaster Just our talk about the math here because I think it's it's important to understand the math in part in order to move yourself away From thinking in terms of the math when you were talking about the tactical choices that managers make because the tactical choices that managers make are dynamic in ways That undermine what the math of it tells us because the math that really does tell us you want fewer shots Sorry, you want lower numbers of goals sword lower xg and you want it from more shots Like the limit case if you actually tried to apply that would be just shooting from 30 yards all the time Diamante ball it would be Josie marigno against sam alleras. Yes, exactly And that is not in fact optimal Which tells us that when we think from limit cases as the math makes us We are missing important things about soccer.
There we go See like that was just a very nerdy podcast 40 minutes of nerdom to get us to say shut up nerds If you want to nerd out about soccer You need to understand what the math is telling you when it's telling you something And I think that like we will be arguing that we will be making the argument that the nerds are right about variance Yeah, the value of increasing variance and I think that because nerds believe in increasing variance for reasons that are Truly linked to the way the real game works It makes nerds also think that the underlying math says increase variance And it doesn't it really doesn't or it does on the shot side a little bit But for the most part it really does say keep it tight man lock it down defend That's the way to win And it is an understanding why I don't think that's really the case You can get to the interesting things that nerds have to say about the way that managers should approach the game somewhat differently All right, there we go. That's our nerd podcast. We will have more nerd podcasts in the future But probably we will be back later this week talking about the semifinals. We'll also do that cheers y'all