A big part of the offseason is about projecting future performance, both for players and teams. The ZiPS projections for the Blue Jays came out earlier this month, Steamer forecasts are available on player pages at FanGraphs, and they have projected 2018 standings based on current depth charts. These are all great tools, but they are also just point projections. They do not consider the uncertainty around the projection, which is at least just as important.
Back in October, I wanted to get a handle on the Jays’ probability of contending, so I built my own probabilistic model. For each forecast starter, I projected five possibilities for playing time, and five levels of productivity. Combining those gave 25 different seasonal outcomes for each player, and then with a few more assumptions, I ran 100 simulations to create a distribution of team wins. It’s all overly simplistic, but it allows for introducing uncertainty and at least in my view, gets us most of the way there if not entirely.
Since there’s little else going on right now, I thought it would be fun to look at the distributions for individual players (since I only published team results then). For each, I’ve just taken the original 25 outcomes, with a bit of a smoothing factor to give the appearance of a more continuous distribution. They’re still somewhat choppy, so just smooth it a little mentally (I don’t want to adjust too far away from the original inputs).
Starting with Josh Donaldson, I think it look about right. The median is a little below 6 WAR, with a distribution that skews to the higher side and is generally flatter and wider, which is the case for highly productive players.
Likewise, I think things look about right for Troy Tulowitzki. After last year’s injuries and poor hitting, the median is about 1 WAR, implying significant possibilities of injuries and/or ineffectiveness. But the distribution is not symmetric and has a tail reflecting the low but non-zero chance of more of the old Tulo who stays mostly healthy. Overall it might be a tad conservative, and should be shifted a little.
Devon Travis too has a very particular distribution, with the peak of the distribution below 1 WAR, owing in large part to the possibility he misses a lot of time.
In hindsight I was probably a little too low on Kevin Pillar, with the distribution peaking in the 1-2 WAR range and a median just below 2 WAR, well below his career rates.
Steve Pearce has a similar curve to Devon Travis, which is appropriate given his history of productivity when healthy and trouble staying on the field.
I think Russell Martin looks about right, with a peak and median around 2 WAR, symmetrical, with a standard deviation of only about 1 WAR. That implies about a 95% chance of 0-4 WAR, which feels about right for his high and low end.
I think I might have been a little too conservative with Justin Smoak (over regressing), though the significant number of doubters might not think so. The dip in the middle is purely mechanical; realistically it should be more of a smooth curve.
The distribution for Kendrys Morales doesn’t reflect much hope, with the vast majority under 1 WAR and centred closer to zero. It extends past the -1 WAR cutoff, but I don’t see any chance of that, if he’s terrible in 2017 again he should be gone by midseason one way or another.
Tomorrow I’ll do the starting pitchers. In the meantime, let me know where you think of these - which look pretty good, which look off.