Why Elo is not plus/minus - trades

photo: CBS Sports

photo: CBS Sports

So far we’ve looked at player Elo-ratings based on goals for and against their team, while they are on the ice. This makes it like an improved measure of +/- that removes quality of competition bias and includes power-play and penalty-kill situations fairly. You might say “Plus/minus is biased by who you play with and who you play against. What makes you think your algorithm won’t be as well?” My answer is that the updating algorithm takes this into account implicitly. But don’t take my word for it – let me prove it to you!

First: how can we measure the bias in +/-?  By looking at what happens to players that get traded.

By comparing the increase or decrease in +/- when players get traded to good or bad teams, we can quantify the 'team' bias on plus/minus. As a dataset, we’ll look at players traded from bad teams over the last 6 seasons with at least 50 games experience either side of the trade. We define a bad team as one that did not make the playoffs (in the year the trade was made) and a good team as one that did make the playoffs. That makes 135 bad-to-good trades and 278 bad-to-bad trades (ahem, it looks like the bad teams are a tad dissatisfied with their rosters.) We show what happens to the +/- of the traded players before and after the trade.


In the plot, the x axis refers to games after the trade, meaning that x=0 corresponds to the time-of-trade. The red line is the +/- average (per 82 game season) for players traded from bad teams to other bad teams, whereas the blue line is for players traded from bad teams to good teams. The two take-home points from this plot are:

1) Before trade, the two lines are similar – showing that players being traded from bad teams average around -6 per season, with a downtick to around -20 right before the trade (presumably due to players getting traded after a string of poor games)

2) After trade, the lines diverge. The players traded to the bad teams recover from their downtick and are business as usual at around -5, whereas the players traded to the good teams increase to around +1 – a swing of 6 over an 82 game season! It would be too much of a coincidence that the players traded to the good teams were suddenly better, so this is a clear indication of the bias in +/-.

So does Elo suffer from this bias? No! Here is the Elo version of the above plot for the same group of traded players


The take home from this plot is that there is basically no difference whether players are traded to a good team or a bad team. This validates our assertion that Elo should not be biased by team performance. Also, the reproducibility of the pre-trade downtick and post-trade uptick provides for some interesting discussion, as it was observed in both trade datasets. My interpretation for the pre-trade downtick is that many players are simply traded while they are in a funk. The post-trade uptick could be explained by either the player being a better fit on the new team (e.g. utilizing more of his talents), or perhaps it could be mental – the invigoration of a ‘fresh start’, etc. Either way, there is some interesting stuff in this data!

Now for some fun anecdotes. As somewhat of a tragic Leafs fan, I’m sad at the loss of Daniel Winnik. He was the best player the Leafs had all season, lifting his game from a solid 1.55 rating at the start of the season to an elite 1.65 at the time of his trade to Pittsburgh. The Leafs decided to ‘sell high’ on the soon-to-be promoted free agent and got a fourth rounder and 2016 second rounder from the Pens - along with minor leaguer Zach Sill. Who can blame them if Winnik was expected to sign elsewhere next year, but is that all he was worth? A second round pick has about a 30% to play the number of games you can expect from half a season of Winnik, and he's more likely to re-sign than move elsewhere after the year. He’s certainly fitting in well with Crosby on the Pens top line (playing on the top line due to the injury to Perron). And while we’re on the subject of Pens trades this year – I love all their moves. With Perron, Winnik, Lovejoy and the up-and-coming defenceman Ian Cole (who had a great Elo rating on the St Louis third pairing, by the way), the Pens are gearing up!

Finally, I’ll comment to the trades of Marian Gaborik from an Elo perspective, to show off these cool career Elo plots. Looking at Gaborik's plot, we can see that he established himself as a premiere player at the Rangers (and probably before that in Minnesota, but I didn't go back that far with the data). And despite what many think – his form did not see a huge decrease while in Columbus (he was just injured a lot and couldn't take wrist shots). Then LA got a steal! His wrist healed and you see his rating shoot up from  1.6  to 1.67 now! If they held their ratings, a team filled with Gaboriks and Winniks should outscore average NHLers by 3.2 points per game and they both have very reasonable contracts! I'm so jealous of the Pens and Kings!

That's it for now. Next time I'll be showing examples of how we are using "Corsi-Elo". A shot-based version of Elo, which is unbiased to quality of team (and competition) effects and cleverly includes power-play situations. If you want to look at shot-possession, it's a big improvement over most advanced Corsi-measures. Bye for now!