How to estimate Time on Ice when it is missing
One the most useful stat people do not talk enough is Time on ice.
In itself, it tells more about how much a player is trusted by his coaches, for good and sometimes bad reasons depending if the coaches value more x or y qualities in a player.
But Time on ice becomes really useful as it allows analysts to look at a player performances relative to the minutes he played, usually calculating how many goals, assists, points, Win Shares, shots, and whatever stats said player recorded per 60 minutes.
It gets then easier to compare the impact of a player that played 25 minutes a night versus one that played 20, adding a lot of context to the analysis.
One of the worst case example is when a young player is playing in a pro league but with only some shifts here and there. Like Dmitri Simashev, picked by Arizona at #6 this past Draft, and who did not score a point in 18 KHL games this season.
But, according to the KHL, he only played 6:55 minutes on average per night. Which is kind of ridiculous.
We, ourselves, never include a player if he played less than 10 games in a league, but could very well set a minimum of minutes played as well in order to only keep relevant performances. If you have those minutes played.
eTOI
Researches on “estimated Time on ice”, aka eTOI, have been ongoing for over a decade and many great names, like Eric Tulsky, Ryan Stimson, Rhys Jessop, CJ Turturo have tried different ways all based on the same principle: a player’s eTOI must reflect how much action happened when he was on the ice.
In order to do that, the more events you have, the better. So if we know a player was on the ice for 50 goals for and against, when his team registered a total of 150 in the games he played, that player was on the ice for 33% of all goals witnessed by his team. Then the theory is that the player must have played 33% of the minutes available, hence 33% x 60 minutes = 20 minutes of eTOI.
You can do even better if you have corsi events, or mix the percentage of goals witnessed with the percentage of shots taken by the player, etc.
But what if you have none of those info? Which is the case for most of the leagues around the world.
Points production as a proxy
The only information we can use is points. But to build a model, we will have to use leagues with real TOI we can use as reference. Here we took the last five seasons of the NHL, KHL, SHL, NL, Czech and Liiga.
We also limited ourselves to players having played in the same team all season, and with at least 40 games played to avoid any low sample abnormalities.
We then ranked players on their points per game production inside their season, league, team and position (grouping all defensemen beyond the 7th spot and forwards beyond the 13th spot together). And then looked at the average TOI for each line-up spot, as well as the highest and lowest TOI recorded.
Number 1 defensemen on points in those leagues scored on average 0.57 points per game while playing 21.4 minutes a night. The highest TOI recorded was 28.1 minutes (Ladislav Smid in the Czech league in 2019-20).
We decided to look at the mean point between the average value and the highest value, in order to not limit players to the sole average value no matter their performance, mostly in the case of number 1 defensemen or forwards. For number 1 defenseman, the mean point between the 21.4 average and the 28.1 highest TOI is 24.8.
Same thing with the lowest value recorded, mostly with the players outside the top6 defensemen and top12 forwards in mind.
We reapplied those norms to our data sample, so every number 1 defensemen on points per game is attributed with a 21.4 eTOI on average, and a potential ceiling of 24.8.
If players had a better points per game performance than the average of their spot, we adjusted them per the following example:
This season in SKA St. Petersburg, defenseman Alex Grant scored 0.47 points per game, which was 4th among dmen of SKA, but 2.19 times higher than the average 0.21 points per game for #4 defensemen. Grant then saw his average eTOI for a #4 dman of 17.56 multiplied by 2.19, but with a ceiling of 20.49 for a #4 dman. Which puts him at 20.49.
Alex Grant really played 19 minutes this season.
We did the same adjustment but looking down for #7 dmen and #13 forwards, where their eTOI could go below the average eTOI but only to the point of the floor value for their spot.
Results
Over the 8,892 players in our database our eTOI predicted the real TOI with a r2 of 0.79.
Predicting 79% of the real TOI is not as good as the eTOI models using goals and shots that could go up to 0.96, but given the limitations of working with points, which is only an offensive perspective of the presence of a player on the ice, it is still a fairly decent approach.
Over the 8,892 players, the average difference between the eTOI and the real TOI is 1 minute.
63% of the players are within 2 minutes of their real TOI.
4% are beyond 5 minutes of the reality, by the looks of it, they were from very low scoring teams.
Usage
We feel pretty safe in using at least the average eTOI per line up spot moving forward, for leagues with no other possibilities. Feel free to use those values as well.