Some value-based performance indicators

Yes, goals are the icing on the cake. Whether they are the epic outcome of the ultimate team interaction or the lucky result of an unexpected situation, we welcome goals effusively. Or hate them profusely, of course. If you see some hockey footage on the news, it will likely be goals, guaranteed. Arguably, top goal scorers are the most looked-after players, more prone to gain MVP awards, and better known by fans, with permission from goalkeepers, of course. In roller hockey, goalkeepers also are pretty relevant. And for the same reason as goal scorers, of course. The goal. So no wonder why we started our blog with goals, and we keep on analyzing a few goal-related questions in this blog. Here, we will look at the top goal scorers in terms of quantity (number of goals) and quality (value of goals). We will also look at the relationship between quantity and quality and bring up some implications. 

So, let's get down to the nuts and bolts. Have a look at the figure below. It shows the relationship between the number (x-axis) and the value (y-axis) of goals for every goal scorer in the 2022-2023 Parlem OK Liga. Well, by the time you read this blog, there will be more goals. Things may change a bit, but please realize that every dot on the graph is a goal scorer, and we're analyzing over 200 goals so far. Not bad at all to see what's going on. And I promise we'll return to this relationship at the end of the season, so you have the complete picture. But, the main point of this graphic will remain the same. The number of goals accumulates throughout the season. So does the value, since we use the Offensive Contribution to Victory (OCV, learn more about this indicator in this blog). 

We can see a strong positive relationship between the number of goals and their value (represented by the dotted line). For those more mathematically or statistically oriented, I have added the actual regression equation and the coefficient of determination. Also, notice that I have forced the intercept to zero, as no goal equals no value. In other words, the relationship shows that the more goals you score, the higher your OCV, which makes sense. On average, for every goal scored, you increase less than half your OCV. 

But I'd like to draw your attention to the variation in the graphic. The number of goals vs. OCV relationship would be a perfect fit if all dots (players) were precisely on the dotted line. The number of goals would then explain 100% of OCV, i.e., both metrics would provide the same information. But players deviate from the line, so the number of goals "only" explains over 80% of the OCV. I say "only" because it is, in fact, a lot! But anyway, have a look at the variation in the graph. For example, with four goals scored (highlighted in gold), the top player has contributed over a victory (OCV=3.41), while the bottom player has contributed less than a tie (OCV=0.83). You can also look at the graphic the other way around. We have three players with an OCV between 1.85 and 2.00 (highlighted in aqua). The player on the right needed 11 goals, while the player on the left required two to make about the same contribution. Despite the association between both metrics, counting the number of goals or quantifying their value tells you a different story. 

Marc Oller (@marcollergarcia on Twitter) will regularly publish the complete players' OCV lists for the Parlem OK Liga and the OK Liga Iberdrola competitions. You won't find the goal scorers list here either (it is publicly available on the Parlem OK Liga webpage). What you will find below is a graphic with the top ten OCV players five games into the competition. The figure shows graphically in blue bars the OCV value for each of the current Parlem OK Liga top ten OCV players (names and actual OCV values inside the light blue label on top of the bars). For reference, the light turquoise ring shows the average OCV in the competition (1.4 in the graphic below), highlighting the excellency of the OCV values of these players.

Alright. So, what? What are all these numbers telling us beyond ranking the players? Is there any additional reading we can make? Yep, no doubt about it. Several implications go far beyond the simple player ranking we just saw. Since the OCV relies on the Adjusted Goal Value, which uses the same coin used to rank teams in league standings (i.e., points), we can compare players and teams and use the comparison to learn about the player's performance. Just as an example, let's look at Marc Julià. When I ran this analysis, Marc Julià had an OCV of 6.16. Marc's team (Reus Deportiu Virginias, Reus for short) had played five games with four victories, one tie, and 13 points. Marc Julià alone has contributed 47.38% of Reus points. Cool. 

We can call this new metric built upon the OCV and the number of points the "OCV to points ratio (OCV2P)". Not very imaginative, but accurate enough to facilitate interpretation, I hope. I will present data as a ratio, not a percentage. So, Marc Julià's OCV2P is 0.47. Then, OCV2P values range between zero and… more than one! What? Am I saying that a player may have more points than his team? Yes, I'm sorry. It is what it is. Hard to understand? Well, it's, in fact, for the same reason we may not save money despite depositing our wages in the bank every month: there are expenses. We win and lose points in the games. Yes, players contribute to the victory. But it's not only your team's players. It's your opponent's too. You may provide a significant amount of points to the team, but somehow the team also loses some points. So OCV2Ps larger than one tell us that you have a contribution to victory larger than the team's capacity to win—a piece of exciting information that the OCV does not convey. Nor the number of goals. Nor any other statistic present in league tables and standings. Marc Gonzalez from the Reacam Làser CH Caldes (Caldes for short) has an OCV of 4.74, but after four games, Caldes has got four points (one victory, one tie, and two defeats). Caldes lost 0.74 of the points Marc contributed. Marc's OCV2P is 1.19. He contributed 19% more points than what the team got in four games. There may be multiple reasons behind those numbers. Marc may be an outstanding performer, well above the remaining team players. Or he may have been too fortunate in those four games. Or perhaps Caldes played against offensively more potent teams. Or it may stress a need to improve defensively to overcome a team's weakness. Or many other reasons, plus all the combinations you wish to add. The truth? It is what it is, folks. We observed something and quantified it. Now we can track it and use data to test for randomness and specific hypotheses to dig into the reasons behind what we observed. We can take apart what's real and what's not, discard what's irrelevant, and focus on what's best for our team. And do so efficiently. It's (part of) the beauty of science. The point here with this example is not to analyze anybody's performance but to show that the OCV2P can track and shed some light on the player's and team's performance. And, if interested, you can dig into the reasons objectively. 

Does the OCV2P measure the relative contribution of all players in a team? Well, let's face it. It's not the best option. It would be ideal that the sum of the relative contributions would equal the actual team performance. Even a single player may have OCV2P values over one. The OCV2P is an excellent metric to relate individual and team performance. But to compare all team players, we have a better indicator. We call it the players' Relative Offensive Contribution to Victory (ROCV), which is just the ratio of a player's OCV over his team's OCV. For every player in a team, ROCV is always between zero and one. The sum of all ROCVs in a team is one. So, ROCV includes no losses, a critical trait of this statistic. And if we multiply a player's ROCV by the total number of points, we will have the actual number of points the player has contributed to the team's points (RTP for short). Below you will find a table summarizing all these stats for the top OCV players mentioned earlier. 

So far, we have a way to evaluate player vs. team (OCV2P) and player vs. player (ROCV) performance. Can we assess team vs. team performance? You bet. Since team OCV and the total number of points in the league table standings are in the same units, we can divide the number of points over the team OCV to measure how efficient teams are. Unsurprisingly, we call this statistic Team's Offensive Efficiency (TOE). Some may think it's unnecessary since we already have the total number of points, goals for, goals against, and whatnot to compare teams. And you're right. We do have some stats, but none measure team efficiency. Have a look at the graphic below. We have the relationship between the number of points (y-axis) and the TOE (x-axis). Every dot is a team. Yes, both axes are related (the number of points is present in both axis), but we showed the graphic for you to see how some teams deviate from the pattern. For example, Calafell and Alcoi have the same number of points, but Calafell is the second most efficient team after Barça in the upper right-hand corner. That outstanding performance might get Calafell to the top of the table. (Okay, we now know that Calafell got the second position after game six – it takes me some time to analyze and write the blog…) Girona also has a larger-than-expected efficiency. After five games, Girona is the team with the lowest OCV of the Parlem OK Liga, but it's not in the last position. Vilafranca and Arenys de Munt, for example, have over three and four times larger OCVs than Girona but are less efficient. Whether or not Girona may also go up in the standings is uncertain. It will be hard to raise positions with such a low OCV.

Puf, okay, enough for today. We saw that goals' value helped us measure several performance indicators for teams and players alike. Having quantitative estimates of multiple concepts allow coaches and managers to have facts instead of opinions. We can use those metrics to track performance and make informed decisions. Often, some indicators may warn you that things don't go in the desired direction or, quite the opposite, that things could be even better than they are now. You may agree or disagree with whatever info they convey. They may or may not support your own opinions. But no doubt they'll be there for you to make the best out of them.