# Modern hockey is mathematics. Guide to basic hockey formulas

**Here’s how the basic statistical values are calculated.**

Yan Golubovsky, who worked from 2018 to 2020 as the general manager of Torpedo, in an interview with our site saidthat numbers for hockey are important, but they do not take into account the whole understanding of the game. One can agree with him. Hockey is still difficult to calculate, but with advanced statistics it at least became more real to do it. We decided to show you clearly how the main hockey indicators are calculated.**Base values**

**Goal and pass**… As a hockey player gets a scoring point, you probably all know, but perhaps we will clarify. If a player passes or scores the puck, he gets one point. Passing is a little more complicated, since two assistants are taken into account – the one who gave the last pass directly before the goal was scored (primer assist) and the one who gave the pass before that is secondary. The assistants may indicate one player, or perhaps none, if the hockey player scored without the help of partners.

**% Implementation, majority and minority**… The conversion rate for shots, as well as for the neutralization of the minority and the conversion of the majority come from the number of attempts and the direct goal.

For example, “Jokerit” in the playoffs-2020 threw 184 times on goal, 24 of them were successful. **% P =** (100 * Number of goals scored) / shots at the opponent’s goal. % P is the percentage of realization. We get that% P = (100 * 24) / 184 = 13.04%. Also, the KHL takes into account the implementation at home and away (all according to the same formula).

**Most** is done according to the same principle. “Jokerit” in this playoff played 22 times the majority, of these 22 times have thrown only 5 goals. **% B (realization of the majority)** = (100 * number of goals scored in the majority) / number of games in the majority. Hence,% B = (100 * 5) / 22 = 22.7%

**Minority neutralization percentage** calculated according to the formula -% M = 100% – the percentage of the majority realized by opponents. **Most realized by competitors **= (100 * missed washers in minority) / number of advantages received by the opponents. Jokerit have retired 26 times in the Gagarin Cup. For rudeness, the rival punished the Finns only 3 times. Most realized by rivals “Jokerit” = (100 * 3) / 26 = 11.5%. % M = 100% -11.53854615% (round up to 11.5%) = 88.4615385% – round up to 88.5%.

**% OB and KN**… For goalkeepers, the most important statistical factors are the percentage of reflected shots (% RP) and the safety factor (KN). **The percentage of reflected throws** calculated by the formula = (100 * number of reflected throws) / total number of throws.

SKA goalkeeper Magnus Hellberg saved 85 of 87 shots in the playoffs. Its% OB = (100 * 85) / 87 = 97.7011494% – round up to 97.7%.

**Reliability factor **is simply the number of goals conceded in 60 minutes of play. is he **calculated using the formula** = (60 * number of goals conceded) / for the total time on the court for all matches. Let’s analyze the example of the same Hellberg, who conceded two goals and played 173.27 minutes on the court.

KN = (60 * 2) / 173.27 = 0.69256074 – round up to 0.69.

Many analysts do not consider these indicators to be objective. And in the course is a comparison of the level of the goalkeeper on these two indicators in accordance with the entire league. For this, all shots on target, all shots reflected by the goalkeepers and all goals conceded in the championship are counted.

According to my calculations, in total for the 2019/2020 MHL regular season, 66276 shots were made on goal, goals conceded – 5985, reflected shots – 60291. Thus, the percentage of OB in the league = 90.96%, and KN = 2.8.

With this common denominator, analysts and coaches can compare whether their goalkeeper was above or below the League average.

If the goalkeeper has a percentage less than the average in the League, then this means that the club, first of all, has problems in defense. It is necessary to analyze how exactly the goalkeeper missed the puck, if it is constant one-on-one or throws from the slot without interference, then goals are the fault of the defencists. If the coaching staff has no complaints about the defense, then only then can the goalkeeper himself complain.

In general, calculating any indicator in 60 minutes is a universal scheme. With the help of this stage, you can see the average number of, for example, power techniques of hockey players and make a start, who and how behaves in the fight. The more time a team spends with the puck, the less strength it will have.

It should also be borne in mind that leaders (those who give results in terms of points scored) rarely go into a power struggle. At the youth level, as for me, the parameters (power moves and blocked shots in 60 minutes) can show who in the future is capable of becoming a good checker from an attack.

**“Plus-Minus”**… This indicator is made to clearly demonstrate how useful the player is in the team. Everything is very simple: if a hockey player was on the ice during a scored goal, he gets a “+”, if his team missed when he was also on the court, he gets a “-“.

There are, of course, exceptions to this rule. “Plus” is awarded only if the team scored in equal compositions or in the minority, and “Minus” – if the puck was also conceded in equal compositions or when the club played in the majority. If the goalkeeper is replaced by a sixth field player, then this does not go into the indicator of utility.

**Part of advanced statistics**

**Xg. Xg **– a kind of parameter that takes into account the probability of a goal. Based on the formulas (algorithm), the computer determines the probability of a goal, taking into account the distance, obstacle to the goalkeeper, the player’s position, and so on. Of these introductory notes, each shot at goal is awarded a score from 0 to 1.

Let’s take as an example a conditional shot from our blue line, where the probability of a goal being scored will be approximately 1%. The computer awards 0.01 for this roll. If a hockey player shoots at goal without interference from the slot, then the probability of a puck is 30% – the computer gives 0.3 points (approx. – all numbers are taken conditionally). That is, in the course of the match, clubs gain a certain number of points. Using this indicator, you can see which team had the advantage.

However, this indicator has its drawbacks. Firstly, it does not take into account the moments if the player missed the puck – that is, for a dangerous moment there are only shots on target (or towards the goal). Secondly, in order to predict matches with maximum accuracy and minimum spread – Xg needs more than 30,000 games. The sample for a season in hockey is extremely small, as the club has 62 regular season matches and several in the playoffs (maximum 28). In addition, everything may also depend on the change of coach, tactics, and so on.

**POD and percentage of shots on target from both sides**… This figure is considered better than Xg. The logic is very simple – the more a team makes shots at the opponent’s goal, the more chances it has to win the match. PDO acts as a kind of coefficient of luck. Ideally, the PDO should be 100%, if it exceeds this value, then the team is considered lucky. If not, then vice versa.

PDO is calculated corny = **BV% (percentage of shots realized by the team) + OB% (percentage of shots reflected by the team)**… For example, “Boston” implemented 10.1% of their shots. The percentage of reflected throws for “Bears” is 92.45%. This gives us a POD of 102.55%.

**The percentage of the number of shots on target from both sides (BVZ%) **is defined as follows: ((BVZ / (BVZ + BVP) * 100. BVZ – the number of throws made by the team. BVP – shots on goal inflicted by the enemy. “Boston” scored 3036 shots, and on their goal – 2940. From this it turns out that BVZ% = ((3036 / (3036 + 2940)) * 100 = 50.8% It is also worth noting that usually these two indicators are calculated for certain game periods of time, for example, every five matches, to analyze the situation.

**Corsi and Fenwick**… In some ways, these indicators are similar to “plus / minus”, however, take into account the shots on target of the player and the opponent when the hockey player was on the ice. During the calculation, all rolls are taken.

Corsi clearly shows how players own the puck and what a team is like when a particular player is not on the court. This indicator is taken in the game with equal compositions – 5 by 5, 4 by 4 and 3 by 3. On the NHL website there are indicators only when playing 5 by 5, so we will build on this. There are several types of Corsi:

**1. Corsi-For **– throws inflicted by the team or throws of a specific player (excluding teammates, and so on). Let’s take the data on the example of Artemy Panarin. Its Corsi-For is 1066

**2. Corsi-Against **– throws inflicted by the opponent on the goal of the club when a particular hockey player was on the court. Panarin has it equal to 1050

**3. CF% **– a kind of Corsi, which is Corsi-For from the sum of Corsi-For and Corsi-Against as a percentage. That is, CF% = (Corsi For / (Corsi For + Corsi Against)) * 100. Panarin’s values are 1066 (Corsi – For) and 1050 (Corsi – Against). That is, its CF% = (1066/1066 + 1050) * 100 = 50.3%

**4. CF60 and CA60** – the same first two indicators, only for 60 minutes of playing time. CF60 and CA60 are calculated using the formula: **CF60 = (CorFor * 60) / total playing time. CA60 = (CorAga * 60) / total playing time**…** **Since we immediately said above that we are considering a 5v5 game, the total playing time of Artemy in equal compositions is 1162.43 minutes. There is an error in this parameter, since our shots are counted when the clubs play 5 on 5, and the time on the ice is when Artemy played in equal compositions. For an illustrative example – CF60 = (60 * 1066) / 1162.43 = 55.02. CA60 = (60 * 1050) / 1162.43 = 54.19

**5. Corsi On **– Corsi difference between CF60 and CA60. It follows that COn = CF60-CA60. From Panarin we get a difference of +0.83. This is the difference between the shots at the Rangers’ goal and those of the Blueshirts themselves in 60 minutes when Panarin is on the court.

**6. Corsi Off **– everything is the same as CorsiOn, only reflects the value of the shots when the given player is not on the court. In simpler words – all hockey players are counted without taking into account Artemy using the same formula that was above.

**7. Relative Corsi **– the difference between Corsi On and Corsi Off. This measure objectively measures puck possession by taking into account the difference in Corsi when a player is on the court and he is not.

**Fenwick **– the same as the Corsi, except for blocked shots.

Fortunately, these are not all aspects. There are also a bunch of parameters, such as Xp, XGa, as well as some of the most significant structures of progressive statistics – QoC, OZS and QoT.